Once I get all these equations worked out, figure out how to use all these symbols, especially in Maxwells (4) Equations for Electro-Magnetism and “Induction”, then I THINK I can finish my “Grand Unifying Theory of Everything” “How We Exist, The Genesis of Relativity”, and show exactly how everything in existence works “fundamentally”, including predicting all properties of all elements and ions and isotopes and chemicals and alloys, figuring out force field technology like impulse and warp drive from “Star Trek”, how to literally cure all disease, and create basically anything we can imagine, including a lot of things we might not have been able to imagine before figuring all this out!!! I’m getting really close now too!
________________________________________________________________
Here are the “Fundamental Principles” of “How We Exist” and “The Genesis of Relativity” itself:
The “Standard Model” of Physics currently (as of 6.25.2022), as devised by physicists so far, concludes there are “force carrying particles” like W and Z “Bosons” and there are “Fermions”, that “Photons” of “Light” can be considered like “particles” of “matter”, and that “Electrons” and “Protons” and “Neutrons” are made of more sub-atomic particles, and concludes there are four “Fundamental Forces” in Nature:
1) Electro-Magnetism;
2) Gravity;
3) Strong (Atomic Nuclear Binding) force; and…
4) Weak (Radioactive Atomic Decay) force;
I believe these are similarly as incorrect as the four “Fundamental Forces” suggested by “Flat Earth”:
1) Magnetism (Leaves out Electrical Forces which are separate from Magnetism itself);
2) Density (Measured as Volume Divided by Mass/Gravitational Pull);
3) Pressure; and
4) Light (which is not a “force” but an effect of Electro-Magnetism);
WHAT I AM SAYING IS, THE “FUNDAMENTAL FORCE” OF “HOW WE EXIST” ARE:
1) Causality, Cause and Effect, Causality, for every Action there is a Reaction of Equal Force and Opposite Direction; aka “Law Conservation of Energy”;
2) Motion and Pressure, each of which cause the other and cannot exist without the other (according to previous “fundamental principle(s)). We call this “Electrical Pressure” or “Voltage”, and motion thereof “Current” or “Amperage”, and the one multiplied by the other gives the total “Energy” measured in “Watts” (One “Volt” of Pressure x One “Amp” of current past one point for one second), or “Joules” (same amount of pressure and current without time measurement, an instant measurement);
3) Harmonic Resonance, vs. Dissonance, which is how pressure and motion form stable structures and the ILLUSION of “Solid Matter”. So the “Strong Force” which causes “Electrons” and “Protons” and “Neutrons” in “Atomic Nuclei” to form together and Atoms to share Electrons to form “Molecules” (aka “Chemicals” and “Chemistry”), is really a product of “Resonance”, and the “Weak Force” which causes “Radioactive Decay” and “Radiation” from “Nuclear Fission” is actually “dissonance”, which is what also causes “Thermal Energy” or “Heat” which is vibrations outside this “Harmonically Resonant” structure of Pressure and Motion which God Created called “The Periodic Table of Elements”, thanks to the “Constant” “Speed of Light” and “Plancks Constant” and four “Electron Orbital Configurations” and the internal structure of the “Electron” and “Proton” and “Neutron”, which function according to these “Laws of Physics” herein;
4) SPIN, of that Pressure in Motion, causes “Lines of Magnetic Force” which have a “Magnitude” (Like “Voltage” or Pressure, a Scalar Field with only Magnitude) and Direction (Transverse Force or Vector Field), like “North” and “South” “Magnetic Poles”, in a “Magnetic Dipole” formed by the spinning of pressure in motion;
So, “Gravity” is an EFFECT of the fact resonant attractive forces increase over time whereas repelling dissonant forces decrease over time, so the attractive forces are stronger than repulsive forces overall, making “Gravity” an inevitable end result or effect of the resonance which keeps pressure and motion in self-sustaining forms of stable “solid matter”;
And “Weak” and “Strong” “Nuclear Atomic Forces” are also EFFECTS of this “Dissonance” for the “Weak Force” which causes atoms to break apart (“Fusion”), and “Resonance” which causes the “Strong Force” that binds Atomic Nuclei Together;
The same goes for all the “Chemical Properties” in “The Periodic Table of Elements”, they are all an effect of these “fundamental forces”, and the geometry or relative angles of the “particles” in and shared between “Atoms”, causing the properties of all “Atoms” and “Ions” (more or less Electrons than Protons), and “Isotopes” (more or less Neutrons than norm atoms with that # of protons), and Molecules (Atoms bound together by sharing electrons when they have fewer than protons. Btw “Acid” means more electrons than protons causing atoms to not bond into “molecules” like “alkaline” atoms are more bound to do);
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AND SOME BASIC EQUATIONS WE NEED TO COMPREHEND THE FUNDAMENTAL PRINCIPLES AND FORCES OF “HOW WE EXIST”:
Trigonometry basics:
SohCahToa (Ratio of Angles to Side lengths in Right Triangles)
PixR^2 (Area of Circle)
Pi x Diameter (Circumference of a Circle)
a^2+b^2=c^2 (area of square on hypotenuse equals area of squares on other 2 sides of right triangle combined)
…what am I missing?… this is a work in progress…
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Here are some Wikipedia pages on the most basic “Laws of Nature” I/We need to comprehend in order to fully comprehend “How We Exist” and “The Genesis of Relativity” itself (Including Origin and Nature of “God” or “Consciousness” btw, which must necessarily exist long before “matter” possibly can by this model or theory):
https://en.wikipedia.org/wiki/Standard_Model
https://en.wikipedia.org/wiki/Newton’s_laws_of_motion
https://en.wikipedia.org/wiki/Maxwell’s_equations
https://en.wikipedia.org/wiki/Einstein_field_equations
https://en.wikipedia.org/wiki/Ohm’s_law
https://en.wikipedia.org/wiki/Faraday’s_law_of_induction
https://en.wikipedia.org/wiki/Trigonometry
https://en.wikipedia.org/wiki/Pythagorean_theorem
https://www.ixl.com/math/calculus
10 min Into to Calculus: https://www.youtube.com/watch?v=WjJ-kpgps1c
https://en.wikipedia.org/wiki/Integral
https://en.wikipedia.org/wiki/Gradient
https://en.wikipedia.org/wiki/Divergence
https://en.wikipedia.org/wiki/Scalar_(mathematics)
https://en.wikipedia.org/wiki/Scalar_field
https://en.wikipedia.org/wiki/Transverse_waves
https://en.wikipedia.org/wiki/Tensor
https://en.wikipedia.org/wiki/Tensor_field
https://en.wikipedia.org/wiki/Stress%E2%80%93energy_tensor
https://en.wikipedia.org/wiki/Differential_(mathematics)
https://en.wikipedia.org/wiki/Differentiable_manifold
https://en.wikipedia.org/wiki/Curl_(mathematics)
https://en.wikipedia.org/wiki/Del
https://en.wikipedia.org/wiki/Delta-v
https://en.wikipedia.org/wiki/Lorentz_force
https://en.wikipedia.org/wiki/Planck_constant
https://en.wikipedia.org/wiki/Planck_relation
https://en.wikipedia.org/wiki/Planck%E2%80%93Einstein_relation
https://en.wikipedia.org/wiki/Principal_quantum_number
https://en.wikipedia.org/wiki/Magnetic_quantum_number
https://en.wikipedia.org/wiki/Azimuthal_quantum_number
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And I will need to make a table which explains all the funny symbols…
https://www.rapidtables.com/math/symbols/Calculus_Symbols.html
https://mathvault.ca/hub/higher-math/math-symbols/calculus-analysis-symbols/
Del, Gradient:
Del Dot, Divergence:
Del Cross, Curl:
B=Magnetic Field (Units= …) ; H=Magnetic Field (Units= Henry…);
V=Volts, Electrical Pressure;
E=Electrical Field;
J=Joules of Energy, in Volts x Ampere x1 Second to equal 1 Watt;
freeornottobe 
HOW ABOUT THIS IDEA… I have been thinking for a while to make a new version of the Declaration of Independence which declares these “self-evidence” “fundamental principles” of “the common law” for the benefit of all Humans on Earth…I COULD USE SUGGESTIONS TO IMPROVE THIS…
We the People, of the Human Race, find certain truths to be self-evident, including the fact that Governments are created by We the People in order to secure the Blessings of Liberty to ourselves and our Posterity, and to establish Justice whenever these fundamental principles of the common law of Human-Kind and any individual Human right is violated;
Here is the transcript for the Declaration of Independence and US Constitution, and maybe some more links to “sources of authority” for the “fundamental principles” used herein…
https://www.archives.gov/founding-docs/declaration-transcript
https://www.archives.gov/founding-docs/constitution
http://www.usconstitution.net/const.html
“treason to the constitution”
https://supreme.justia.com/cases/federal/us/19/264/
“sovereignty devolved on the people”
https://supreme.justia.com/cases/federal/us/2/419/
“undoubted right to resist an unlawful arrest”
https://supreme.justia.com/cases/federal/us/332/581/
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THIS PAGE MAKES A LOT MORE SENSE THAN THAT WIKIPEDIA PAGE, as this uses more common letters instead of odd greek symbols…
https://farside.ph.utexas.edu/teaching/316/lectures/node116.html
…TOO BAD IT WONT PASTE THE EQUATIONS RIGHT BUT ON THE PAGE THE IMAGES ARE CLEAR, and this one was much easier to understand than the wikipedia page using Greek Symbols (like Omega for a “Volume” and “Sigma” for a “Surface”, where this uses just S and S’ and C instead)…
” Maxwell’s Equations
In the latter half of the nineteenth century, the Scottish physicist James Clerk Maxwell demonstrated that all previously established experimental facts regarding electric and magnetic fields could be summed up in just four equations. Nowadays, these equations are generally known as Maxwell’s equations.
The first equation is simply Gauss’ law (see Sect. 4). This equation describes how electric charges generate electric fields. Gauss’ law states that:
The electric flux through any closed surface is equal to the total charge enclosed by the surface, divided by $\epsilon_0$.
This can be written mathematically as
… (305)
where $S$ is a closed surface enclosing the charge $Q$. The above expression can also be written
…(306)
where $V$ is a volume bounded by the surface $S$, and $\rho$ is the charge density: i.e., the electric charge per unit volume.
The second equation is the magnetic equivalent of Gauss’ law (see Sect. 8.10). This equation describes how the non-existence of magnetic monopoles causes magnetic field-lines to form closed loops. Gauss’ law for magnetic fields states that:
The magnetic flux through any closed surface is equal to zero.
This can be written mathematically as
… (307)
where $S$ is a closed surface.
The third equation is Faraday’s law (see Sect. 9.3). This equation describes how changing magnetic fields generate electric fields. Faraday’s law states that:
The line integral of the electric field around any closed loop is equal to minus the time rate of change of the magnetic flux through the loop.
This can be written mathematically as
… (308)
where $S’$ is a surface attached to the loop $C$.
The fourth, and final, equation is Ampère’s circuital law (see Sect. 8.7). This equation describes how electric currents generates magnetic fields. Ampère’s circuital law states that:
The line integral of the magnetic field around any closed loop is equal to $\mu_0$ times the algebraic sum of the currents which pass through the loop.
This can be written mathematically as
… (309)
where $I$ is the net current flowing through loop $C$. This equation can also be written
…(310)
where $S’$ is a surface attached to the loop $C$, and ${\bf j}$ is the current density: i.e., the electrical current per unit area.
When Maxwell first wrote Eqs. (306), (307), (308), and (310) he was basically trying to summarize everything which was known at the time about electric and magnetic fields in mathematical form. However, the more Maxwell looked at his equations, the more convinced he became that they were incomplete. Eventually, he proposed adding a new term, called the displacement current, to the right-hand side of his fourth equation. In fact, Maxwell was able to show that (306), (307), (308), and (310) are mathematically inconsistent unless the displacement current term is added to Eq. (310). Unfortunately, Maxwell’s demonstration of this fact requires some advanced mathematical techniques which lie well beyond the scope of this course. In the following, we shall give a highly simplified version of his derivation of the missing term.
…”
https://farside.ph.utexas.edu/teaching/316/lectures/node116.html
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This I need too, a calculator for curvature of Earth, shows the equation for calculating the curvature of a circle according to distance from your point on the circumference, which is a basic calculation needed for calculating interactions between spherical fields (electrical, gravitational, magnetic, etc.)…USING THIS EQUATION:
a = √[(r + h)² – r²]
https://www.omnicalculator.com/physics/earth-curvature#curvature-of-earth-per-mile
…
“Curvature of Earth per mile
How large is the curvature of Earth, then? As we don’t notice it in our everyday lives, it has to be relatively small. Most sources consider 8 inches per mile as the most accurate estimate. That means that for every mile between you and an object, the curvature will obstruct 8 inches of the object’s height.
How far can I see before the Earth curves?
The first thing you can find with our Earth curvature calculator is the exact distance between you and the horizon. You only need to know two values: your eyesight level (in other words, the distance between your eyes and mean sea level – assuming you are looking out to sea) and the radius of the Earth. Input these numbers into the following equation:
a = √[(r + h)² – r²]
where:
a — Distance to the horizon;
h — Eyesight level above mean sea level; and
r — Earth’s radius, equal to 3959 miles or 6371 km.
This equation can be derived using the Pythagorean theorem. You can try to derive it yourself – it is not that hard!
Calculating the obstructed height of an object…”
https://www.omnicalculator.com/physics/earth-curvature#curvature-of-earth-per-mile
https://uploads-cdn.omnicalculator.com/images/earth-curvature.svg?width=425&enlarge=0&format=webp
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Back to Learning how to use Maxwells Equations for Electromagnetism, lets find several sources explaining what the symbols mean, so we can get a better understanding (So far the cursive lower case l and the curl symbols like a lower case a I dont see a good explanation of yet… lets see if this displays these symbols right:
ℓ … ∂D/∂t)…
…THIS LOOKS LIKE A GOOD ONE WITH A LONG EXPLANATION AND SHOWS THE “RIGHT HAND RULE” WITH AN IMAGE WHICH HELPS TO COMPREHEND “ELECTROMAGNETIC INDUCTION” A LOT SIMPLER (All this math is over-complicated really, as we try to figure out better ways to calculate these actually fairly simple concepts of ‘Energy’ and ‘Forces’ between ‘Matter’)…
https://www.cantorsparadise.com/maxwells-equations-7484212839b1
…THIS ONE LOOKS LIKE A GOOD EXPLANATION PAGE ALSO…
https://www.fiberoptics4sale.com/blogs/electromagnetic-optics/a-plain-explanation-of-maxwells-equations
….Some of these pages dont use the lowercase cursive l which I think just means length, which I see in the Wikipedia page…
https://spie.org/publications/fg08_p07-08_maxwells_equation?SSO=1
…This wiki page does not use the lower case cursive l…
https://simple.wikipedia.org/wiki/Maxwell%27s_equations
…This page uses simpler symbols which I can copy and paste (ds for both Faradays Law of Induction and Amperes circuital law instead of lower case cursive l)…
https://physics.info/maxwell/
…This is the one I started on which does in Faraday’s Law of Induction (3rd Eq) and Amperes circuital law (4th), it uses dl (lower case cursive l) just before the first equal sign and after multiplying by the E or B field respectively)…
https://en.wikipedia.org/wiki/Maxwell's_equations
…This one explains pretty simply these equations, I think quoting how Maxwell originally phrased them which helps, and using dS and dr instead of that cursive lower case l, so I think it means difference in length along a Surface (dS’) or a radius (dr) of a loop of wire…
https://farside.ph.utexas.edu/teaching/316/lectures/node116.html
https://www.iop.org/explore-physics/physics-stepping-stones/maxwells-equations#gref
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/maxsup.html
Let There Be Light: Maxwell’s Equation EXPLAINED for BEGINNERS
…OK SO NOW I NEED TO FINISH LEARNING HOW TO USE THAT CURL SYMBOL (∂D/∂t) AND THIS PART (from the Wiki Page I started on):
“Σ is any surface with closed boundary curve ∂Σ”
…And I need to practice with how to calculate the B and H and D Magnetic Fields and Use the Integral Function too…this video really simplified that one for me…
…And some pages I plan to learn from on different ways to use the “integral operator” in 1 or 2 or 3 dimensions…
https://en.wikipedia.org/wiki/Leibniz_integral_rule#General_form:_Differentiation_under_the_integral_sign
https://en.wikipedia.org/wiki/Line_integral (1D)
https://en.wikipedia.org/wiki/Surface_integral (2D)
https://en.wikipedia.org/wiki/Volume_integral (3D)
This Wiki Page use that “Partial Derivative” function and that curly operator above I dont fully get yet…
https://en.wikipedia.org/wiki/Partial_derivative
And to practice with calculating the Magnetic Field (Note the Gravitational and Electrical and basic Heat and Pressure Fields are generally 1D or “Scalar” whereas “Magnetic Lines of Force” are an effect of SPINNING Electrical Pressure giving them a “transverse” or “tangent” property “perpendicular” to the direction of “Gradient” of greatest “Differential” of Pressure…
https://en.wikipedia.org/wiki/Magnetic_field
https://en.wikipedia.org/wiki/Magnetic_flux
https://en.wikipedia.org/wiki/Magnetostatics
https://en.wikipedia.org/wiki/Magnetic_dipole
https://en.wikipedia.org/wiki/Magnetizing_field
https://en.wikipedia.org/wiki/Magnetic_permeability
https://en.wikipedia.org/wiki/Magnetic_quantum_number
And for the funny symbol for Permeability of Free space…
https://en.wiktionary.org/wiki/permeability
https://en.wikipedia.org/wiki/Magnetic_permeability
https://en.wikipedia.org/wiki/Permeability_(electromagnetism)
…a note from that wiki page on Maxwells Eqs…
“In materials with relative permittivity, εr, and relative permeability, μr, the phase velocity of light becomes
vp = 1/μ0 μr ε0 εr
which is usually[note 5] less than c. ”
And for the Symbol for Permittivity of Free Space…
https://en.wikipedia.org/wiki/Permittivity_of_free_space
https://en.wikipedia.org/wiki/Vacuum_permittivity
https://en.wikipedia.org/wiki/Permittivity
And I should not forget this symbol I need to learn how to use also:
“Ω is any volume with closed boundary surface ∂Ω, and”
…Here is a link on “boundary” and what that means…
https://en.wikipedia.org/wiki/Boundary_(topology)
SO FAR SO GOOD. I THINK THIS COVERS EVERYTHING I NEED TO LEARN IN ORDER TO COMPLETE THIS “GRAND UNIFYING THEORY OF EVERYTHING”!
When I am done, I plan to be calculating just relative pressure and motion in 3 or more perpendicular “dimensions”, and showing how all “electrical” and “magnetic” and “gravitational” and “strong” and “weak” and “chemical” and all other “forces” in “existence” in “reality” are ALL “fundamentally” JUST Pressure and Motion and Harmonic Resonance in specific Geometric Patterns we call the Four “Electron Orbital Configurations” (S=2,P=6,D=10,F=18 max “electrons” in each “shell” in each “atom”), and the “Proton” and “Neutron”, and “Plancks Constant”, are the basic structures which God created, after two or more pairs of equal and opposite forces of pressure in motion came together from “The Void” or random pressure and motion (where no “Time” or “Space” can be measured) to create a self-sustaining “chain-reaction” (called “The Flower of Life” in ancient “sacred geometry” btw) which necessarily must have become “Conscious” long before it became complex enough to create stable “Solid Matter” and “The Periodic Table of Elements” (as a product of creating those “fundamental principles” of “How We Exist, The Genesis of Relativity” as described above)!!!
THIS IS MY REAL LIFE’S WORK, WHICH HAS BEEN PUT ON HOLD FOR ALMOST 13 YEARS BECAUSE OF CORRUPT “GOVERNMENT” TAKING EVERYTHING I HAD BACK IN DEC. 2010, BUT NOW THAT I HAVE SUCCEEDED AT MAKING THEM STOP THAT, NOW I AM TRYING TO REBUILD A NEW LIFE AND EARN A LIVING WITH THIS KNOWLEDGE AND RESUME BUILDING MY WEBPAGES AND INVENTIONS. So anyone wanting to donate can do so here:
https://www.paypal.com/donate/?cmd=_s-xclick&hosted_button_id=ZNHZJPHYFBDUG
And anyone wanting to hire me can contact me via facebook or gmail (username: harleyborgais). I charge $25/hr for Paralegal work, and I am working next on one clients parents rights case (kid taken by CPS unlawfully. Family courts have no such authority, only criminal courts can via “due process” for “criminal prosecutions”), and trying to improve http://www.NRDL.org homepage so its more useful (and more people will hire me because of it), and these pages too…
http://www.NRDL.org/notice_template/
http://www.NRDL.org/sources/
http://www.NRDL.org/lawdocs/
http://www.GovernPublicServants.com
http://www.HowWeExist.com
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WOW THE THINGS RACING THROUGH MY HEAD RIGHT NOW…As I am learning finally how to use these fancy symbols in “Maxwell’s Equations” for Electricity and Magnetism and “Induction” or “transformation” of one “force” into another (the performance of “work” done by “transforming” “potential energy” into “kinetic energy”), AND putting together these “fundamental principles” of “How We Exist” and “The Genesis of Relativity” as well as “the common law” and “the supreme Law of the Land” under the US Constitution… as well as “fundamental principles” of the Human Mind and WHY we “Destroy the Earth” as I think God is trying to explain to us via “Revelations”, through three branches of government and 7 major international industries which We the People give and allow too much “authority” and ALLOW even demand that those in “Authority” abuse that power and “Destroy the Earth”!
So as a result, due to Seven “fundamental” “Animal Survival Instincts” called “Seven Deadly Sins” (though I think change gluttony to fear or cowardice and pride to arrogance or hubris to be more accurate), aka “The Beast” inside all of us WE “Destroy the Earth!
BUT WE CAN OVER COME THIS USING THESE “Seven Holy Virtues” (But change the opposite of gluttony to opposite of fear or cowardice, to bravery or courage, and instead of hubris or arrogance, modesty or humility)!
SO…As I am going over these four “Maxwells Equations” for “electromagnetic induction”, and three of “Newtons Laws of Motion”, and other basic “Laws of Conservation of Energy”, CHECK OUT WHAT I AM FIGURING NOW…
I can “Quantifiable” PROVE what is and is not “Lawful” now according to these “fundamental principles” of “law” I have put together and the “Precedents” our US Supreme and State Courts have set so far since establishing this Constitutional Republic!
So that means we can show in fact, MATHEMATICALLY, what does and does not fulfill the “Purpose of government” and “the supreme Law of the Land” according to these “fundamental principles” of “Law” I am putting together!
And, when I finish this work on http://www.HowWeExist.com, I believe I will be able to finally create one “Grand Unifying Theory of Everything” which explains the “fundamental principles” of “Energy” and “Matter” and Human Psychology and even “Constitutional Law”, Logic and Reason, Fact from Fiction…
…I believe I will be able to explain exactly what is “Electricity” and “Magnetism” and “Gravity” and “Strong” and “Weak” “Nuclear Atomic Forces” and “thermal energy” and what is “Time” and “Space”, and the “Fundamental Principles” of “How We Exist” and “The Genesis of Relativity” itself!
This should included predicting ANY “Alloy” or “Chemical Properties” of any “Molecule” or “Element” in “The Periodic Table of Elements”, any “ion” or “isotope” (meaning more or less electrons than protons in nucleus for ion, and more or less neutrons for isotopes btw), and this should mean being able to PREDICT the properties of chemicals and materials never even imagined, and create things never even thought of before!
This means I believe I can develop actual functional “impulse drive” and “warp drive” and “force field” and “replicator” technologies like in “Star Trek”, and possibly a LOT more than that too! (I have been thinking about these things since 1999 and now that I am finally learning the math, my mind is RACING!!!! Even despite the fact I just discovered my father just died today. That just drives me more I think!).
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I NEED TO RESUME THIS STUDY HERE…
“The Maxwell-Faraday equation
Suppose that we want a charged particle, initially at rest, to move in a closed loop. This means that we must make the electric field nonconservative, so we must give it a nonzero curl. We turn to dimensional analysis to guide our intuition. Since E has units of N/C, ∇⨯E has units of N/C⋅m. We know that B has units of Teslas, and 1T = N⋅s/C⋅m. Therefore ∇⨯E has units of T/s. Since ∇⨯E is a vector field, this means that we must expose a charged particle to a vector field with units of T/s if we want it to move in a closed loop.
Since the quantity -∂B/∂t is a vector field with units of T/s, it’s possible that this is the quantity that we’re looking for, and Maxwell determined that it is indeed the case that ∇⨯E=-∂B/∂t by interpreting Faraday’s experimental data. …”
https://www.cantorsparadise.com/maxwells-equations-7484212839b1
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But this page was better for showing me the equations with actual text I can copy and paste instead of images like most of the others (for these fancy symbols)…
https://physics.info/maxwell/
Lets see what that looks like when I paste it here and post this on wordpress with all these fancy symbols (I have to fix a lot of formatting is what!)…
1. Gauss’s law
There are two types of charge, positive and negative, just as there are two types of real numbers, positive and negative.
Electric field lines diverge from positive charge and converge on negative charge
2. No one’s law
There are no magnetic monopoles.
Magnetic field lines neither converge nor diverge (have no beginning or end).
3. Faraday’s law
Electric field lines don’t curl…
except when the magnetic field changes.
4. Ampère’s law
Magnetic field lines curl around electric current…
and also curl when the electric field changes.
integral notation
Gauss’s law
∯ E · dA = Q/ε0
No one’s law
∯ B · dA = 0
Faraday’s law
∮E · ds = − ∂ΦB/∂t
Ampère’s law
∮B · ds = μ0ε0 x (∂ΦE/∂t) + μ0I
differential notation
Gauss’s law
∇ · E = ρ/ε0
No one’s law
∇ · B = 0
Faraday’s law
∇ × E = − ∂B/∂t
Ampère’s law
∇ × B = μ0ε0 x(∂E/∂t) + μ0J
tensor notation
Gauss’s law and Ampere’s law together…
∂α x F^αβ = μ0 x J^β
No one’s law and Faraday’s law together…
∂α x Fβγ + ∂β x Fγα + ∂γ x Fαβ = 0
…”
https://physics.info/maxwell/
_______________________________________________________
SO I HAD TO EDIT THAT A BUNCH, SO I AM NOT 100% CERTAIN IF I DID IT COMPLETELY CORRECTLY.
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HERE ARE SOME OF THE ANSWERS I NEEDED…
∂ = a partial derivative…
“The character ∂ (Unicode: U+2202) is a stylized cursive d mainly used as a mathematical symbol, usually to denote a partial derivative such as ∂ z / ∂ x (read as “the partial derivative of z with respect to x”).[1][2] It is also used for the boundary operator in a chain complex, and the conjugate of the Dolbeault operator on smooth differential forms over a complex manifold. It should be distinguished from other similar-looking symbols such as lowercase Greek letter delta (𝛿) or the lowercase Latin letter eth (ð). ”
https://en.wikipedia.org/wiki/%E2%88%82
https://en.wiktionary.org/wiki/%E2%88%82
https://en.wikipedia.org/wiki/Partial_derivative
https://en.wikipedia.org/wiki/Partial_differential_equation
https://math.stackexchange.com/questions/1620533/%E2%88%82a-cup-b-is-a-subset-of-%E2%88%82a-cup-%E2%88%82b
https://www.khanacademy.org/math/multivariable-calculus/multivariable-derivatives/partial-derivative-and-gradient-articles/a/introduction-to-partial-derivatives
https://forum.wordreference.com/threads/%E2%88%82y-%E2%88%82x-pronunciation.3561549/
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THIS REALLY HELPS ALSO… THE “FARAD” OR UNIT OF ELECTRICAL “CAPACITANCE”, COMPARED TO MANY OTHER UNITS OF MEASUREMENT…
https://en.wikipedia.org/wiki/Farad#Equalities
“Expressed in combinations of SI units, the farad is:
F = s^4⋅A^2/m^2⋅kg = s^2⋅C^2/m^2⋅kg = C/V = A⋅s/V = W⋅s/V^2 = J/V^2 = N⋅m/V^2 = C^2/J = C^2/N⋅m = s/Ω = 1/Ω⋅Hz = S/Hz = s^2/H …
where F = farad, C = coulomb, V = volt, W = watt, J = joule, N = newton, S = siemens, H = henry.”
…NOTE HOW IT TOOK OUT MANY SYMBOLS SO I HAD TO CORRECT THESE EQUATIONS ABOVE!!! Here is a link to that image directly…
https://wikimedia.org/api/rest_v1/media/math/render/svg/b5af21cec70d0ad73bf937d0090eff90aa90ce8a
https://en.wikipedia.org/wiki/Coulomb
“The coulomb (symbol: C) is the SI derived unit of electric charge.[2] Historically, it was defined as the charge delivered by an electric current of one ampere in one second, with the ampere being defined as the current needed to generate a magnetic force of 0.2 micronewtons per metre between 2 parallel wires 1 metre apart.[3] Under the 2019 redefinition of the SI base units, which took effect on 20 May 2019, the elementary charge was assigned the exact value of 1.602176634×10^−19 C, making the coulomb exactly 1/(1.602176634×10^−19) = 10^19/1.602176634 elementary charges. The same number of electrons has the same magnitude but opposite sign of charge, that is, a charge of −1 C. This makes the coulomb one of the few SI units to depend on the value of only one of the SI defining constants. Despite this, the coulomb is, somewhat incongruously, still classified as a derived unit, and the ampere is still classified as an SI base unit.” -NOTE I ADDED THE ^ SYMBOLS TO SHOW “TO THE POWER OF” WHEN IT CHANGED THE TEXT FORMAT WHEN I COPIED AND PASTED FROM THE WIKI PAGE-
https://en.wikipedia.org/wiki/Elementary_charge
“The elementary charge, usually denoted by e or sometimes qe is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 e.[2] This elementary charge is a fundamental physical constant. To avoid confusion over its sign, e is sometimes called the elementary positive charge. ”
https://en.wikipedia.org/wiki/Volt
“The volt is the derived unit for electric potential, electric potential difference (voltage), and electromotive force… One volt is defined as the electric potential between two points of a conducting wire when an electric current of one ampere dissipates one watt of power between those points.[2] Equivalently, it is the potential difference between two points that will impart one joule of energy per coulomb of charge that passes through it. It can be expressed in terms of SI base units (m, kg, s, and A)…”
https://en.wikipedia.org/wiki/Watt
“The watt (symbol: W) is a unit of power or radiant flux. In the International System of Units (SI), it is defined as a derived unit of (in SI base units)[1][2] 1 kg⋅m2⋅s−3 or, equivalently,[3] 1 joule per second. It is used to quantify the rate of energy transfer.”
https://en.wikipedia.org/wiki/Joule
“The joule (/ˈdʒaʊl/ JOWL, also /ˈdʒuːl/ JOOL;[1][2][3][disputed – discuss] symbol: J) is a derived unit of energy in the International System of Units.[4] It is equal to the amount of work done when a force of 1 newton displaces a mass through a distance of 1 metre in the direction of the force applied. It is also the energy dissipated as heat when an electric current of one ampere passes through a resistance of one ohm for one second.”
https://en.wikipedia.org/wiki/Newton_(unit)
“The newton (symbol: N) is the International System of Units (SI) derived unit of force. It is defined as 1 kg⋅m/s2, the force which gives a mass of 1 kilogram an acceleration of 1 metre per second per second.”
https://en.wikipedia.org/wiki/Siemens_(unit)
“The siemens (symbol: S) is the derived unit of electric conductance, electric susceptance, and electric admittance in the International System of Units (SI). Conductance, susceptance, and admittance are the reciprocals of resistance, reactance, and impedance respectively; hence one siemens is redundantly equal to the reciprocal of one ohm (Ω−1) and is also referred to as the mho.”
https://en.wikipedia.org/wiki/Henry_(unit)
“The henry (symbol: H) is the SI derived unit of electrical inductance.[1] If a current of 1 ampere flowing through a coil produces flux linkage of 1 weber turn, that coil has a self inductance of 1 henry. …The inductance of an electric circuit is one henry when an electric current that is changing at one ampere per second results in an electromotive force of one volt across the inductor…”
https://en.wikipedia.org/wiki/Weber_(unit)
“In physics, the weber (/ˈveɪb-, ˈwɛb.ər/ VAY-, WEH-bər;[1][2] symbol: Wb) is the SI derived unit of magnetic flux whose units are volt-second. A flux density of one Wb/m2 (one weber per square metre) is one tesla. ”
https://en.wikipedia.org/wiki/Ampere
“The ampere (/ˈæmpɛər/, US: /ˈæmpɪər/;[1][2][3] symbol: A),[4] often shortened to amp,[5] is the SI base unit of electric current…defined by setting the magnitude of the elementary charge to 1.602176634×10−19 C (coulomb),[6][9] which means an ampere is an electrical current equivalent to 1019 elementary charges passing every 1.602176634 seconds. Prior to the redefinition the ampere was defined as the current that would need to be passed through 2 parallel wires 1 metre apart to produce a magnetic force of 2×10−7 newtons per metre. …”
https://en.wikipedia.org/wiki/Metre
“The metre is currently defined as the length of the path travelled by light in a vacuum in 1/299 792 458 of a second. The metre was originally defined in 1793 as one ten-millionth of the distance from the equator to the North Pole along a great circle, so the Earth’s circumference is approximately 40000 km.”
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RELATING TYPES OF WAVES OF ENERGY, “TRANSVERSE” “ELECTRO-MAGNETIC WAVES” WHICH FLUCTUATE PERPENDICULAR TO THE “DIRECTION OF PROPAGATION”, OR “LONGITUDINAL” WAVES LIKE SOUND WAVES WHICH HAVE PRESSURE FLUCTUATIONS IN THE SAME “DIRECTION OF PROPAGATION”…
https://en.wikipedia.org/wiki/Transverse_wave
https://en.wikipedia.org/wiki/Longitudinal_wave
I was misunderstanding what “Scalar” meant because I was thinking it meant the same as “longitudinal” having only a value in one dimension not two or more like “Transverse” waves…
“The term scalar is also sometimes used informally to mean a vector, matrix, tensor, or other, usually, “compound” value that is actually reduced to a single component. Thus, for example, the product of a 1 × n matrix and an n × 1 matrix, which is formally a 1 × 1 matrix, is often said to be a scalar. …”
https://en.wikipedia.org/wiki/Scalar_(mathematics)
https://en.wikipedia.org/wiki/Matrix_(mathematics)
https://en.wikipedia.org/wiki/Tensor
Well this seems a bit more like what I was thinking though, a “Scalar Field” is a map of temperature or pressure, a 1D value…
“In mathematics and physics, a scalar field or scalar-valued function associates a scalar value to every point in a space – possibly physical space. The scalar may either be a (dimensionless) mathematical number or a physical quantity. In a physical context, scalar fields are required to be independent of the choice of reference frame, meaning that any two observers using the same units will agree on the value of the scalar field at the same absolute point in space (or spacetime) regardless of their respective points of origin. …”
https://en.wikipedia.org/wiki/Scalar_field
https://en.wikipedia.org/wiki/Scalar_field_theory
Some more basic math terms I/We need to be familiar with to comprehend these “fundamental principles” of “How We Exist”…
https://en.wikipedia.org/wiki/Vector_(mathematics_and_physics)
https://en.wikipedia.org/wiki/Euclidean_vector
https://en.wikipedia.org/wiki/Vector_field
https://en.wikipedia.org/wiki/Vector_space
https://en.wikipedia.org/wiki/Vector_calculus
________________________________________________
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I have to add these (and edit all this later)….
https://en.wikipedia.org/wiki/Magnetic_field#The_B-field
See “Scalar” herein (Referred to this page by “scalar magnitude” in the above page:
https://en.wikipedia.org/wiki/Norm_(mathematics)
“The oersted (symbol Oe) is the coherent derived unit of the auxiliary magnetic field H in the centimetre–gram–second system of units (CGS).[1] It is equivalent to 1 dyne per maxwell. ”
https://en.wikipedia.org/wiki/Oersted
https://en.wikipedia.org/wiki/Dyne
https://en.wikipedia.org/wiki/Maxwell_(unit)
https://en.wikipedia.org/wiki/Gauss_(unit) “The gauss, symbol G (sometimes Gs), is a unit of measurement of magnetic induction, also known as magnetic flux density. ”
https://en.wikipedia.org/wiki/Tesla_(unit) “The tesla (symbol: T) is a derived unit of the magnetic B-field strength (also, magnetic flux density) in the International System of Units. ”
https://en.wikipedia.org/wiki/Magnetic_field
https://en.wikipedia.org/wiki/Magnetic_field#The_B-field
https://en.wikipedia.org/wiki/Magnetic_field#The_H-field
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RELATING TYPES OF WAVES OF ENERGY, “TRANSVERSE” “ELECTRO-MAGNETIC WAVES” WHICH FLUCTUATE PERPENDICULAR TO THE “DIRECTION OF PROPAGATION”, OR “LONGITUDINAL” WAVES LIKE SOUND WAVES WHICH HAVE PRESSURE FLUCTUATIONS IN THE SAME “DIRECTION OF PROPAGATION”…
https://en.wikipedia.org/wiki/Transverse_wave
https://en.wikipedia.org/wiki/Longitudinal_wave
I was misunderstanding what “Scalar” meant because I was thinking it meant the same as “longitudinal” having only a value in one dimension not two or more like “Transverse” waves…
“The term scalar is also sometimes used informally to mean a vector, matrix, tensor, or other, usually, “compound” value that is actually reduced to a single component. Thus, for example, the product of a 1 × n matrix and an n × 1 matrix, which is formally a 1 × 1 matrix, is often said to be a scalar. …”
https://en.wikipedia.org/wiki/Scalar_(mathematics)
https://en.wikipedia.org/wiki/Matrix_(mathematics)
https://en.wikipedia.org/wiki/Tensor
Well this seems a bit more like what I was thinking though, a “Scalar Field” is a map of temperature or pressure, a 1D value…
“In mathematics and physics, a scalar field or scalar-valued function associates a scalar value to every point in a space – possibly physical space. The scalar may either be a (dimensionless) mathematical number or a physical quantity. In a physical context, scalar fields are required to be independent of the choice of reference frame, meaning that any two observers using the same units will agree on the value of the scalar field at the same absolute point in space (or spacetime) regardless of their respective points of origin. …”
https://en.wikipedia.org/wiki/Scalar_field
https://en.wikipedia.org/wiki/Scalar_field_theory
Some more basic math terms I/We need to be familiar with to comprehend these “fundamental principles” of “How We Exist”…
https://en.wikipedia.org/wiki/Vector_(mathematics_and_physics)
https://en.wikipedia.org/wiki/Euclidean_vector
https://en.wikipedia.org/wiki/Vector_field
https://en.wikipedia.org/wiki/Vector_space
https://en.wikipedia.org/wiki/Vector_calculus
________________________________________________
https://physics.info/symbols/
For the “Integral Equations” for “Maxwells Equations”, the “Sigma” or large E symbol representing a “surface”, and the “Omega” symbol for “volume”…
” Ω is any volume with closed boundary surface ∂Ω, and
Σ is any surface with closed boundary curve ∂Σ, …”
https://en.wikipedia.org/wiki/Maxwell's_equations
https://en.wikipedia.org/wiki/Volume_element
https://en.wikipedia.org/wiki/Volume_integral
“In mathematics (particularly multivariable calculus), a volume integral (∭) refers to an integral over a 3-dimensional domain; that is, it is a special case of multiple integrals. Volume integrals are especially important in physics for many applications, for example, to calculate flux densities. ”
https://en.wikipedia.org/wiki/Charge_density
“In electromagnetism, charge density is the amount of electric charge per unit length, surface area, or volume. Volume charge density (symbolized by the Greek letter ρ) is the quantity of charge per unit volume, measured in the SI system in coulombs per cubic meter (C⋅m−3), at any point in a volume.[1][2][3] Surface charge density (σ) is the quantity of charge per unit area, measured in coulombs per square meter (C⋅m−2), at any point on a surface charge distribution on a two dimensional surface. Linear charge density (λ) is the quantity of charge per unit length, measured in coulombs per meter (C⋅m−1), at any point on a line charge distribution. Charge density can be either positive or negative, since electric charge can be either positive or negative. ”
https://en.wikipedia.org/wiki/Homology_(mathematics)
“In mathematics, homology[1] is a general way of associating a sequence of algebraic objects, such as abelian groups or modules, with other mathematical objects such as topological spaces.”
https://en.wikipedia.org/wiki/Volume
“Volume is a scalar quantity expressing the amount of three-dimensional space enclosed by a closed surface.”
https://www.electronics-notes.com/articles/basic_concepts/letters-symbols/greek-alphabet-characters-list.php
https://en.wikipedia.org/wiki/Greek_letters_used_in_mathematics,_science,_and_engineering#%CE%A3%CF%83%CF%82_(sigma)
https://en.wikipedia.org/wiki/Sigma
“Sigma (/ˈsɪɡmə/;[1] uppercase Σ, lowercase σ, lowercase in word-final position ς; Greek: σίγμα) is the eighteenth letter of the Greek alphabet. In the system of Greek numerals, it has a value of 200. In general mathematics, uppercase Σ is used as an operator for summation. When used at the end of a letter-case word (one that does not use all caps), the final form (ς) is used. In Ὀδυσσεύς (Odysseus), for example, the two lowercase sigmas (σ) in the center of the name are distinct from the word-final sigma (ς) at the end. The Latin letter S derives from sigma while the Cyrillic letter Es derives from a lunate form of this letter. ”
https://en.wikipedia.org/wiki/Omega
“Omega (/ˈoʊmɪɡə, oʊˈmiːɡə, oʊˈmɛɡə, oʊˈmeɪɡə/;[1][2] capital: Ω, lowercase: ω; Ancient Greek ὦ, later ὦ μέγα, Modern Greek ωμέγα) is the 24th and last letter in the Greek alphabet. In the Greek numeric system/isopsephy (gematria), it has a value of 800. The word literally means “great O” (ō mega, mega meaning “great”), as opposed to omicron, which means “little O” (o mikron, micron meaning “little”).[3] ”
https://physicscatalyst.com/article/omega-symbol-physics/
https://en.wikipedia.org/wiki/Greek_letters_used_in_mathematics,_science,_and_engineering#%CE%A9%CF%89_(omega)
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I AM PRETTY SURE I CAN EXPLAIN WHY WE HAVE SOME OF THESE “QUANTUM MECHANICS”, “QUANTUM NUMBERS”, AND FOUR “ELECTRON ORBITAL CONFIGURATIONS”, DUE TO THESE FOUR “FUNDAMENTAL PRINCIPLES” OF “ELECTROMAGNETISM” CALLED “MAXWELL’S EQUATIONS”…
https://en.wikipedia.org/wiki/Maxwell's_equations
https://en.wikipedia.org/wiki/Spin_(physics)
https://en.wikipedia.org/wiki/Spin_quantum_number
https://en.wikipedia.org/wiki/Principal_quantum_number
https://en.wikipedia.org/wiki/Azimuthal_quantum_number
https://en.wikipedia.org/wiki/Magnetic_quantum_number
https://en.wikipedia.org/wiki/Planck_constant
https://en.wikipedia.org/wiki/Planck_relation
https://en.wikipedia.org/wiki/Planck%E2%80%93Einstein_relation
These basic physics are WHY we have the “Periodic Table of Elements” with the Four “Electron Orbital Configurations” S,P,D, and F, which hold 2,6,10, and 18 Electrons (Max) each (In “Orbital Shells” around “Atomic Nuclei” due to the “Plancks Constant” and all of this due to “Harmonic Resonance” and basic “Trigonometry”) like this…
https://ptable.com/#Properties
When I finish learning how to USE these equations and fancy symbols hopefully soon, I believe I will be able to figure out pretty much literally ANYTHING, including all the “Science Fiction Technologies” in “Star Trek” and a lot more too!
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NOW I NEED TO LEARN HOW TO GRAPH CIRCLES AND TRIANGLES AND SQUARES, in 2 Dimensions (x & y), so that I can learn how to put those together in 3Ds, so I can better understand these things like the “Gradient” (Using the upside down triangle for “Partial Differential”), “Dot Product” (A symmetrical Gradient on two opposite sides of one dimension or axis), and “Cross Product” or “Curl” (A symmetrical gradient on two perpendicular dimensions or axis)…. Like how it shows the Electrical field CAN be asymmetrical with the first of Maxwells Laws called Gauss’s Law (according to the electric charge divided by the ability of electric charge to conduct in free space), but a Magnetic field is NEVER Asymmetrical along the North and South Poles in Gauss’s Law for Magnetism…
https://saylordotorg.github.io/text_intermediate-algebra/s11-03-ellipses.html
https://www.dummies.com/article/academics-the-arts/math/calculus/how-to-graph-a-circle-190930/
https://www.dummies.com/article/academics-the-arts/math/calculus/how-to-graph-an-ellipse-190940/
https://www.khanacademy.org/math/geometry/xff63fac4:hs-geo-conic-sections/alg2-graphs-of-circles-intro/v/graphing-circles-from-features
And some of those terms I was just learning for this are here:
https://en.wikipedia.org/wiki/Partial_derivative
https://en.wikipedia.org/wiki/Directional_derivative
https://en.wikipedia.org/wiki/Differentiable_function
https://en.wikipedia.org/wiki/Del
https://en.wikipedia.org/wiki/Gradient
https://en.wikipedia.org/wiki/Dot_product
https://en.wikipedia.org/wiki/Cross_product
And this website explains Maxwells equations pretty well so far:
https://farside.ph.utexas.edu/teaching/316/lectures/node116.html
..this one too I think…
https://www.cantorsparadise.com/maxwells-equations-7484212839b1
Better than that wikipage did I think:
https://en.wikipedia.org/wiki/Maxwell's_equations
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Here really quick for that graphing figure 8…
y^(4)=3(y^(2)- x^(2)) https://www.mathway.com/Graph
Note how you can add a 2 or .2 before each variable and change the 3, and see how they change the size (dimensions) of the figure 8… That is basically what I have to work with in order to show the relationship between different “electron orbital configurations” S,P,D,F, and to use the four maxwells equations, and include some parts about resonance (convergence in graphs and equations) vs dissonance (divergence), and how these geometric shapes cause the illusion of physical matter and gravity and strong and weak forces, due to electrical pressure and magnetic lines of force produced when that pressure spins, and how all of “How We Exist” is due to these “fundamental principles”!
So in this case we can change these variables to represent the structures that make up electron orbitals and protons and neutrons, and molecules…
https://ptable.com/#Properties
And I believe we can show the Universe IS a functioning “Brain” basically, based on the “Large Scale Structure of the Universe” as we have been putting it together, which DOES seem to be similar to the structures of our Brains!…
HERE IS ONE PART THIS IS ALL MISSING….THE RELATIONSHIP BETWEEN THE DIAMETER AND CIRCUMFERENCE OF A CIRCLE IS IMPERFECT, SO 3D REALITY CANNOT BE “PERFECT”, SO THERE WILL ALWAYS BE “DISSONANCE”, AND “EVIL” AND “SUFFERING” AND “DESTRUCTION”, BUT WITHOUT THAT THERE ALSO WOULD NOT BE “EVOLUTION”, “CREATION”, AND “LIFE”!!!!!
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Oh if the crust of the Earth shifted the sun would appear to hold still, and we have evidence it has shifted before, and the obvious reason to me is because the solidifying rock of the crust as it forms holds the magnetic field generated by the spin of molten iron and some other magnetic materials as the heavier ones move down into the center of the Earth, and are expelled back out thanks to explosions which cause volcanoes, which are producing the crust, and causing “continental drift”…
SO, when the magnetic field in the crust builds up enough, it is repelling the field that produced it, and eventually it will have to shift at least 90 up to 180 degrees, and this could cause the sun to seem to hold till or go backwards or in other directions for the time the crust is shifting.
All due to fundamental forces of electricity and magnetism, which are products of the most basic laws of motion, cause and effect, basic Mathematics!
That is how we can actually PROVE the things in the Bible MUST be right, using OBSERVABLE Math and Physics!
Now on that note here are some pages on how to calculate Sine Cosine and Tangent…
https://en.wikipedia.org/wiki/CORDIC
https://mathimages.swarthmore.edu/index.php/Taylor_Series
https://en.wikipedia.org/wiki/Unit_hyperbola
https://en.wikipedia.org/wiki/Hyperbolic_functions
https://www.quantamagazine.org/scientists-pin-down-when-earths-crust-cracked-then-came-to-life-20210325/
https://gizmodo.com/so-much-ice-has-melted-that-the-earth-s-crust-is-shift-1847754514
https://oceanservice.noaa.gov/facts/tectonics.html
https://www.sciencedaily.com/releases/2020/04/200422151310.htm
https://beta.nsf.gov/news/tectonic-plates-started-shifting-earlier-previously-thought
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SO WHAT DOES ALL THIS MEAN MORE SIMPLY…HOW DO WE FIND ANGLES AND LENGTHS OF TRIANGLES WITHOUT A CALCULATOR OR LONG SERIES OF CALCULATIONS (like the Taylor and CORDIC Systems)???
So lest say Sine Cosine and Tangent mean this then… (Still working out “tangent” though)…for SohCahToa, where S=Sine, C=Cosine, T=Tangent (Complex series’ of equations like Taylor or CORDIC as I understand it so far), and h=hypotenuse or longest side of a right triangle, o=shorter side opposite of angle being used (other than h), a=shorter side adjacent (other than h)…
SO THEN,
Sine(angle z)=o/h, must mean:
(o^2 / h^2)x90=(z)
…where: (h)=longest side of right triangle, and (o)=side opposite of angle (z).
And Cosine(angle z)=a/h, must mean:
(a^2 / h^2)x90=(z)
…where: (h)=longest side of right triangle, and (a)=side opposite of angle (z).
Then to find the opposing angle simply take 90-z=(remaining angle).
And you can take SquareRoot(c^2-a^2=b^2)=(b)= The Length of the remaining side if you have the longest and one shorter side on a right triangle.
So then I have to figure out how to make use of just the two shorter side lengths and the 90 degree right angle if you have to find the other three???
Lets use the x=3,y=4,r=5 triangle…
x=3^2=9, y=4^2=16, r=5^2=25
9/25=0.36
16/25=0.64
0.36 * 90=32.4 degrees=angle (A)
0.64 * 90=57.6 degrees=angle (B)
32.4 +57.6 =90 degrees + Right Angle Opposite Hypotenuse (Longest Side) =180 total for any triangle.
SO IMAGINE THIS…
A triangle with 100 degrees on the angle pointing at you, leaving 80 so 40 degrees on each other corner so its symmetrical, and lets say 10 units length on the opposite end….you can see how 10% or 30% or 50% of the 100 degrees points to directly that point in the line like 1 or 3 or 5 on the opposite side (Say the left point is at x=0 and the right is at x=10 then 50 degrees would be x=5 so the length and OPPOSITE angle are directly related in this way, “directly proportional”, “proportion” like 3/4= 3 portions of one whole which is 4 portions).
FROM HERE:
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So what if we have a triangle with side lengths 2,3,4, then what are the angles going to be?
And what if we have angles 40 and 60 leaving 180-(40+60=100)=80 degrees for the third angle, so what are the lengths if the longest side=3 ???
….(the side opposite the largest angle at 80-degrees, directly proportional to the length of the other side, or rather that value squared relative to the other two side lengths squared, are directly proportional to the angles relative to one-another which all add up to 180)…
So, I want to figure out how to apply the above math to triangles NOT having a 90 degree right angle (which is 1/2 or 50% of the total 180 degrees possible, which I think is why SohCahToa and CORDIC and Taylor Series systems work, in part, I think, so far)…
LENGTHS 2,3,4=WHAT ANGLES?…
x=2^2=4
y=3^2=9
r=4^2=16
4/9=0.444…
4/16=0.25
9/16=0.5625
ANGLES 40,60,80=WHAT SIDE LENGTHS IF THE LONGEST ONE=3? (Then try if its 9 for Hypotenuse)?…
40/80=1/2=0.5
40/60=2/3=0.333…
60/80=3/4=0.75
…THOSE DO NOT SEEM TO LINE UP SO FAR LIKE THEY DO FOR RIGHT ANGLES, SO LETS TRY TO BREAK ONE INTO RIGHT ANGLES AND DO SOME MATH TO FIGURE OUT HOW TO COMBINE THESE SIMPLER EQUATIONS…
NOTE HOW: a^2+b^2=c^2
AND, all angles of Triangle add up to 180 degrees, so to divide this triangle into two right triangles, we must choose which corner angle to divide, and which opposite side to divide first…
SO, with Right Triangles the two shorter angles must add up to 90 degrees, so the two new angles created by this dividing line called “height” in common math language here, will be 90 minus whichever remaining angle on that side of the triangle we are working with, like so…
SO THEN WITH ANGLES 40,60,80=WHAT NEW ANGLES ARE CREATED WHEN DIVIDING THE LARGEST ONE AT 80 DEGREES, AND WHEN THE OPPOSITE SIDE LENGTH IS 3 (or 9 also), THEN WHAT ARE THE REMAINING SIDE LENGTHS ALSO???…
90-40=50 degrees for lets say the TOP LEFT SIDE (If 80 degrees is up and 60 to right side)…
90-60=30 degrees for the new angle on the TOP RIGHT SIDE…
SO WHERE DOES THAT LEAVE THE SIDE LENGTHS NOW???
USE A “RATIO” BETWEEN THE TWO NEW ANGLES CREATED (out of 80 degrees=1 whole) TO FIND THE TWO NEW LENGTHS OF THE TWO NEW SIDES OUT OF THE TOTAL OF 3 (equal to 1 whole)…
30/80=0.375
50/80=0.625
Btw: 0.625+0.375=1
SO THEN…
3×0.375=1.125 (out of 3 total, for the side opposite the smaller 30deg angle)
3×0.625=1.875 (for the larger 50 degree angle)
Btw: 1.125+1.87500=3
SO WHAT DO WE HAVE NOW FOR THESE TWO RIGHT TRIANGLES…
FOR THE LEFT TRIANGLE=… Noting the length of either shorter side squared, divided by the longest side length squared, that proportion multiplied by 90 degrees (180 minus the 3rd angle which is 90 in a right triangle), is equal to the angle opposite that shorter sides length (so I can probably change this equation for when one angle is not 90 degrees)…
So, the “proportion” of one short side / the longest side = percent of remaining angle x90 degrees (-90 for the right angle, out of 180 total), SO…
30/90=1/3
60/90=2/3
…SO…
x=(30) degrees angle opposite this side, which is the shortest length since opposite the smallest angle, (leaving 90-30=60 degrees for remaining angle…), at 1.125 long (and 1.125^2=1.265625);
y=(60) degrees angle opposite this side, which is…
This 60 degrees is equal to 2x the smallest 30 degree angle, or 2/3 of 90 so then…
…The shortest side is: 1.125^2=1.265625 …so 2×1.265625=2.53125 …and square root 2.53125= 1.59099026 …So that is the length of the middle size side: 1.59099026;
r=(90) degrees angle opposite this side, and that 90 degrees is equal to SquareRoot of 3x that 1.125^2 then so: 3x(1.125^2)=3.796875 for SQUARE of the Longest side, which is therefore: SqRt(3×1.125=3.696875)=1.94855716, for the length of the Longest side;
SO THAT LEAVES FOR THE LEFT TRIANGLE:
Angle x=30 degrees and opposite Side X=1.125 length;
Angle y=60 degrees and opposite Side Y=1.59099026 length;
Angle r=90 degrees and opposite Side R=1.94855716 length;
NOW LETS CHECK…
1.125^2=1.265625
1.59099026^2=2.53125001
1.94855716^2=3.79687501
…
1.265625+2.53125001=3.79687501
…SO YES THEY DO ADD UP NOW!!!
RIGHT TRIANGLE=…
x=(50) degrees angle opposite this side, which is 1.875 long, (leaving 40…);
y=(40) degrees angle opposite this side, which is long;
r=(90) degrees angle opposite this side, which is long;
1.875^2=3.515625 (Opposite 50 deg angle)
50/90=0.555…
40/90=0.444…
SO, one shorter length squared / the longest length squared, that proportion or percent times the remaining 90 degrees (out of 180 -90 for the right angle) is equal to the angle opposite that shorter length so…
Angle x=50 degrees, Opposite side X=1.875, 1.875^2=3.515625, and this is …gotta finish later…
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If right triangle side Lengths a^2 + b^2 = c^2 … and b=1.875 and 1.56249844=3.515625 …and…
The angles opposite each of those are: A=40, B=50, C=90 …then…
The ratio between the square of the length of one shorter side divided by the square of the longest side, is equal to the ratio between the angle opposite that shorter side divided by the longest 90 degree angle, so…
50/90=0.555…
40/90=0.444…
…THEREFORE…
50(b)/90(c) = 0.555…/1 = 3.515625(b=1.875^2)/
0.555555 x 3.515625=1.95312305
1/0.555555=1.8000018
1.8000018 x 3.515625 = 6.32813133
0.555555 / 3.515625 = 0.158024533
0.444444 x 3.515625 = 1.56249844
1.56249844^2 + 1.56249844 = 4.00389982
Still not getting it right this time.
Last time it was easy, 1/3, 2/3, 30,60,90, this time its 40,50,90, and 4/9 or 0.4444 and 5/9 or 0.55555…
I know the middle length is b=1.875 …and a^2 + b^2 = c^2 … 1.875^2=3.515625 …
…and the ratios are (a)40/(c)90=0.44444…. and (b)50/(c)90=0.55555…
And those ratios between those angles, should equal the lengths (squared) of sides opposite those smaller angles (b is the middle one at 1.875 long), divided by the length (squared) of the longest side…
So…
1.875^2=3.515625 (b^2) …
…and b/c=0.55555 …
Lets see, 1/3=0.33333 and 1/0.333333=3x …. 2/3=0.666666 and 1/0.666666=1.5x …
SO, Opposite 50 deg angle which is angle b, Side =1.875^2=3.515625
50/90=0.555…
40/90=0.444…
Or, 0.555555 + 0.444444 = 1 even…
Side B (Opposite 50 deg angle b)=1.875^2 = 3.515625 …
0.5555555 x 3.515625 = 1.9531248
sqrt 1.9531248 = 1.39754241
0.4444444 x 3.515625 = 1.56249984
sqrt 1.56249984 = 1.24999994
1.9531248 + 1.56249984 = 3.51562464
I THINK THAT WORKED!
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SO NO THAT DID NOT WORK! The ratio between the square of the lengths of two shorter sides of a right triangle DO NOT EXACTLY match the ratio between two or three of the angles, YET! THEY ARE CLOSE, AND I THINK WHAT IS MISSING IS Pi IS NOT INCLUDED IN THIS CALCULATION YET, BUT THE CIRCUMFERENCE AND ANGLES ARE RELATED TO Pi*2*radius (then divide by whatever angle to get circumference)…
…SO I THINK THE SOLUTION, is to add the circumference instead of the smallest side Y from 0-45 degrees (or 0 to 1/4 of a half circle which is 180 degrees, where the radius x Pi gives you the length of that half of the circle), so at 45 degrees that would be .25*Pi*r= 0.785398163…
..(If r=1 like the “Unit Circle”, and btw at 45 degrees x&y=0.707106781 which is the Square Root of 0.5, and 0.5 is Sqrt(0.25), and Sqrt(0.75)=0.866025404)
SO, then instead of r=1+y=0.707106781 ….INSTEAD I THINK if I add .25*Pi*r= 0.785398163 I THINK THAT MIGHT GIVE AN ACCURATE ANSWER???
IF SO THEN AFTER 45 DEGREES UP TO 90 DEGREES I THINK I DO THE SAME WITH THE x AXIS INSTEAD.
I really need to do other things right now but I am obsessed with figuring this out right now and I am so close!!!!
NOW I NEED TO MAKE THE FOLLOWING CHART BELOW, FIND THE PATTERNS, AND HOW TO CORRECT THE MATH, SINCE THE CHANGE IN RATIO BETWEEN SQUARED VALUES OF LENGTHS OF SMALLER SIDES OF THE RIGHT TRIANGLE, DO NOT MATCH THE CHANGE IN RATIO OF THE ANGLES OPPOSITE EACH SIDE LIKE I THOUGHT, BUT THEY ARE CLOSE….SO I THINK I CAN USE THE CIRCUMFERENCE INSTEAD OF THE SMALLER SIDE (OR MAYBE ANOTHER OPTION, THE LONGER SIDE, OR ANOTHER WAY TO COMBINE THEM), AND I THINK I CAN MAKE THIS MATH LINE UP (the first idea was coming CLOSE, but not quite right, more accurate at some spots, and I think I know why, but need to chart all these values and graph the relationships to find how to calculate this better…)…
Btw I was thinking “Radian” meant half a circle but I am wrong, it is the length of the radius along the circumference, so if the radius is 1, then 2xPi= 6.28318531…=Circumference of full 360 degrees circle, so that is 6.28… “Radians” to make one full “Turn” or 360 Degree Circle, using the Radius=1 Unit.
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THIS MIGHT BE MESSED UP HERE (since I made in a text file and it needs a wider format for this chart), BUT HERE, A PARTIALLY COMPLETED CHART OF ANGLES AND SIDE LENGTHS AND MORE DATA I NEED TO FIGURE OUT BETTER WAYS TO CALCULATE SINE AND COSINE AND TANGENT…
____________________________________________________
OK TIME TO MAKE A CHART HERE FOR SINE, COSINE, AND TANGENT VALUES, FROM 0 TO 90 DEGREES IN 5 DEGREE INCREMENTS, WITH X & Y LOCATIONS AND SQUARED VALUES, THE RATIO BETWEEN X^2/Y^2 AND Y^2/X^2, THE CIRCUMFERENCE FROM 0 DEGREES, RATIO BETWEEN SMALLER ANGLES (a & b), RADIUS=1 FOR A “UNIT CIRCLE” SO IT SHOWS PERCENTAGES IN DECIMALS… WHAT ELSE?…
Lets figure for “CIRCUMFERENCE”, it must be 2*Pi(*r=1)=Cir. [since using Radius of (1) just 2Pi=Cir.=6.28318531…so 90 degrees is 1/4 of that, 30deg=1/12th, 10deg=1/36th, deg=1/72nd]…
[…So 360deg or 1 turn = 6.28318531…
6.28318531×0.25= 1.57079633… along circumference for each 90 degrees…
6.28318531/6= 1.04719755… along circumference for each 30 degrees…
6.28318531/72= 0.0872664626… along circumference for each 5 degrees…
Since using “Unit Circle” where “Radius”=(1) that makes a “Radian”=(1) along circumference fyi…
SO X & Y + SIDE LENGTHS MATCHING GRAPH COORDINATES, AND a & b = THE TWO SMALLER ANGLES, WITH a ON TOP OPPOSITE SIDE X, AND b ON BOTTOM LEFT POINTING TO x=0,y=0 OPPOSITE SIDE Y…
…Also NOTE: sqrt(0.25)=0.5 … sqrt(0.5)=0.707106781 … sqrt(0.75)=0.866025404 … and note those points and where they lay in this chart, THAT I think is the key I need to find the Exponential Equation for to correct the equations, when adding squares of two shorter sides of right triangles to equal the square of the hypotenuse it should be multiplied by some exponential using Pi and the radius to find the circumference to use that to correct so the ratio between the squares of these two sides can correctly equal the ratios of the two angles opposite those two sides…
…And 0.25^2=0.0625 … 0.5^2=0.25 … 0.75^2=0.5625…]
__________________________________________________________________________
DEG(b)| SINE OF ANGLE| COSINE OF ANGLE| TANGENT OF ANGLE| _ X _ | _ Y _ |
————————————————————————–
0 | 0 ___________| 1 ___________ | 0 _____________ | _ 1 _ | _ 0 _ |
5 | 0.0871557427 | 0.9961946981 _ | 0.0874886635 __ |0.9962 |0.08716|
10 | 0.1736481777 | 0.984807753 __ | 0.1763269807 __ |0.9848 |0.17365|
15 | 0.2588190451 | 0.9659258263 _ | 0.2679491924 __ |0.966 |0.2588 |
20 | 0.3420201433 | 0.9396926208 _ | 0.3639702343 __ |0.9397 |0.342 |
25 | 0.4226182617 | 0.906307787 __ | 0.4663076582 __ |0.9063 |0.4226 |
30 | 0.5 ________ | 0.8660254038 _ | 0.5773502692 __ |0.866 |0.5 __ |
35 | 0.5735764364 | 0.8191520443 _ | 0.7002075382 __ |0.8192 |0.5736 |
40 | 0.6427876097 | 0.7660444431 _ | 0.8390996312 __ |0.766 |0.6428 |
45 | 0.7071067812 | 0.7071067812 _ | 1 __________ __ |0.7071 |0.7071 |
50 | 0.7660444431 | 0.6427876097 _ | 1.1917535926 __ |0.6428 |0.766 |
55 | 0.8191520443 | 0.5735764364 _ | 1.4281480067 __ |0.5736 |0.8192 |
60 | 0.8660254038 | 0.5 __________ | 1.7320508076 __ |0.5 __ |0.866 |
65 | 0.906307787 | 0.4226182617 _ | 2.1445069205 __ |0.4226 |0.9063 |
70 | 0.9396926208 | 0.3420201433 _ | 2.7474774195 __ |0.342 |0.9397 |
75 | 0.9659258263 | 0.2588190451 _ | 3.7320508076 __ |0.2588 |0.966 |
80 | 0.984807753 | 0.1736481777 _ | 5.6712818196 __ |0.17365|0.9848 |
85 | 0.9961946981 | 0.0871557427 _ | 11.4300523028__ |0.08716|0.9962 |
90 | 1 ___________| 0 ____________ | See below… __ | _ 0 _ | _ 1 _ |
____________________________________________________________________
…CONTINUED…
_________________________________________________________________________________________________________________________________
|DEG(b)| _ X^2 _ | _ Y^2 _ | X^2/Y^2= | Y^2/X^2= | _ a/b= _ | _ b/a= _ |CIRCUMFERENCE|
——————————————————————————
| 0 | 1 | 0 | 1/0=1 | Y^2/X^2=0 | _ 90/0=90 _ | _ 0/90=0 _ | 0=0
| 5 |0.9924144|0.0075968|130.635847|0.0076548667|85/5=17 |5/85=0.058823|180/5=36 so (1/36)*pi=0.0872664626
| 10 |0.9698310|0.0301543|32.1622787|0.0310923243|80/10=8 |10/80=0.125 |(1/18)*pi=0.174532925
| 15 |0.933156 |0.0669774|13.9324011|0.0717751373|75/15=5 |15/75=0.2 |(1/12)*Pi=0.261799388
| 20 |0.8830360|0.116964 |7.54963921|0.132456661 |70/20=3.5 |20/70=0.28571|(1/9)*Pi=0.34906585
| 25 |0.8213796|0.1785907|4.59922941|0.217427728 |65/25=2.6 |25/65=0.38461|180/25=7.2 so (10/72)*Pi=0.436332313
| 30 |0.749956 |0.25 |2.999824 |0.33335289 |60/30=2 |30/60=0.5 |(1/6)*Pi=0.523598776
| 35 |0.6710886|0.3290169|2.0396782 |0.490273415 |55/35=1.57142|35/55=0.63636|180/35=5.142857 so Pi*(1/5.142857)=0.610865255
| 40 |0.586756 |0.4131918|1.42005722|0.704196975 |50/40=1.25 |40/50=0.8 |(1/4.5)*Pi=0.698131701
| 45 |0.4999904|0.4999904| 1 | 1 |45/45=1 |45/45=1 |(1/4)*Pi=0.785398163
| 50 |0.4131918|0.586756 |0.70419697|1.42005722 |40/50=0.8 |50/40=1.25 |180/50=3.6 so (1/3.6)*Pi=0.872664626
| 55 |0.3290169|0.6710886|0.49027341|2.0396782 |35/55=0.63636|55/35=1.57142|180/55=3.2727… so (1/3.2727)*Pi=0.959939088
| 60 |0.25 |0.749956 |0.33335289|2.999824 |30/60=0.5 |60/30=2 |180/60=3 so 1/3*Pi=1.04719755
| 65 |0.1785907|0.8213796|0.21742772|4.59922941 |25/65=0.38461|65/25=2.6 |180/65=2.76923077 so (1/2.76923077)*Pi=1.13446401
| 70 |0.116964 |0.8830360|0.1324566 |7.54963921 |20/70=0.28571|70/20=3.5 |180/70=2.57142857 so (1/2.57142857)*Pi=1.22173048
| 75 |0.0669774|0.933156 |0.07177513|13.9324011 |15/75=0.2 |75/15=5 |180/75=2.4 so (1/2.4)*Pi=1.30899694
| 80 |0.0301543|0.9698310|0.03109232|32.1622787 |10/80=0.125 |80/10=8 |180/80=2.25 so (1/2.25)*Pi=1.3962634
| 85 |0.0075968|0.9924144|0.00765486|130.635847 |5/85=0.058823|85/5=17 |180/85=2.11764706 so (1/2.11764706)*Pi=1.48352986
| 90 | 0 | 1 | 0/1= 0 | Y^2/X^2= 1 | _ 0/90=0 _ | _ 90/0=90 _ |180/90=2 so (1/2)*Pi=1.57079633|
_____________________________________________________________________________
(NOTE Tan(89)=57.2899616308 and Tan(90)=16331239353195370…)
____________________________________________________________________
Here is an online graphing Calculator:
https://www.desmos.com/calculator/2ghtdzya1a
Where I am graphing equations like these for my needs:
4y=x^2
y^4=9(y^2-x^2)
y=(x-1)^2+(y-1)^2
4^2=x^2+y^2
5^2-y^2=x^2
For finding a better solution to sine cosine tangent…
https://www.desmos.com/calculator/vbzzd1m7yz
y=1+(x-1)*2
y=x^2
y=(1+(x-1)*2)*(x^2)
____________________________________________________________________
Here is a right triangle calculator to find angles and side lengths for you:
https://www.omnicalculator.com/math/right-triangle-side-angle
____________________________________________________________________
BTW This webpage helped me find sine in degrees or radians really quickly with a tool in the middle of the page:
https://trigonometricfunctions.com/sin-40-degrees
And Cosine and Tangent:
https://trigonometricfunctions.com/category/sine
https://trigonometricfunctions.com/category/cosine
https://trigonometricfunctions.com/category/tangent
____________________________________________________
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FYI I figured out why that did not work above like I thought, because the way the RATIO BETWEEN ANGLES a and b work in right triangles (between 0 – 90 degrees on the x,y 2D graph), COMPARED TO THE RATIO BETWEEN LENGTHS SQUARED (a^2+b^2=c^2 in 90 degree right triangles on the x,y graph where the “hypotenuse” is the “radius” of a circle being measured), DO NOT CHANGE AT THE SAME RATE… So at 30 degrees (leaving 60 so 1:2 ratio here) the ratio between the square of a and b is: x=0.8667 (or Sqrt(0.75)) and y=0.5 (or Sqrt(0.25)) thus 1:3 ratio. …SO…
I need to figure out how to graph an arch which starts at x,y=0 then with a peak at x=2/3 and y=1/6 then back to y=0 where x=1…
SO WHO WANTS TO LEARN MATH WITH ME NOW???
I can only work on this little bits here and there in between other things right now, so I’m saving links to pages which seem to show what I need to learn here…
I THINK this is the answer I need, how to graph “tilted parabolas”, where the “Focal Point” (in center of curve) is diagonal to the apex (or ‘vertex’ where the two exponential curves meet in center of arch)…
“…
First we’ll start with a Focus point F = (a,b) and a Directrix line D: y = mx + c. Given an arbitrary point P = (x,y) on the parabola we know the (square of the) distance from F is (x-a)^2 + (y-b)^2. But what is the distance to D?
The key is the slope of the line: m. The shortest segment from point P to D will have a slope of -1/m So we take a point on D (d, md + c), plug it into the slope equation and solve for d. …”
http://blog.mathoffthegrid.com/2019/12/tilted-parabolas-skewed-and-symmetrical.html
BUT START HERE FOR A SIMPLER UNDERSTANDING OF HOW TO GRAPH A “PARABOLA” AND HOW TO MANIPULATE OR “translate the parabola” LIKE MOVING UP, DOWN, LEFT, RIGHT, FLIPPING UPSIDE DOWN OR ROTATING 90 DEGREES (“PERPENDICULAR”) TO THE LEFT OR RIGHT…
https://amsi.org.au/ESA_Senior_Years/SeniorTopic2/2a/2a_2content_2.html
This video gives a good example how to find an equation for a parabola with certain points, THIS IS WHAT I AM TRYING TO DO, BUT WITH THE “TILTED PARABOLA” ABOVE…
It must have a peak at x=2/3 and y=1/6 then back to 0 where x=1,y=0.
AND I WANT TO GRAPH A SINE WAVE WITHOUT USING Sin Cos OR Tan ON A CALCULATOR (ONLY Using +-/x and ^ or Sqrt()) because I am trying to find a better way to do exactly that (relate lengths of right triangles to the angles of curves directly, with a simpler equation, THIS equation!)…
This sine wave form graph goes from…
x=0,y=0 to… x=1/3,y=1/6 to… x=0.5,y=0 to… x=2/3,y=-1/6 to…x=1,y=0.
NOTE THE NEGATIVE -1/6 FOR y AT x=2/3…that is important. This graph has three points where y=0 (@ x= 0, 0.5, 1), and TWO PEAKS at Negative and Positive y=1/6.
WHAT IS THE PURPOSE?
This way it should be able to convert directly, exactly, the DIFFERENCE or “Divergence” (If I have that term right), from RATIO between the Angles and therefore Circumference at that angle (from 0 degrees), to the Ratio between the squares of the lengths of x and y at that coordinate on a graph.
In other words…
I believe we can use the result of THIS Equation once we figure it out (one of these two), to convert the RATIO between lengths or coordinates: a^2 and b^2 to the RATIO between angles a and b DIRECTLY, without the long series of equations currently in use (Taylor series or CORDIC as far as I know)
(when dividing one by the other depending on which two angles you are using and which angle you are trying to find, Cos or Sine or Cosine or Cosecant etc…, but the point here is a more efficient way to find that answer then calculators currently use!), and the RATIO between angles a and b (the two smaller ones which add up to 90 degrees).
Here is a discussion on that topic (where I might put this post and ask for help from people who do math for a living):
https://math.stackexchange.com/questions/1516589/non-symmetrical-parabola
This one is an online graphing calculator that seems to work good…
https://www.desmos.com/calculator/hqtxgidxqm
And a triangle angle and length calculator to check results with…
https://www.omnicalculator.com/math/right-triangle-side-angle
… In that^ comment above I put together a chart of #s of ratios at different angles from 0-90 in increments of 5 so I can do this math and check until I find the right way to combine this equation once I find it, with pythagora’s theorem, to find a better way than Taylor’s Series Equations or the CORDIC Method of ESTIMATING by a long chain of calculations, to find angles using lengths of sides in a right triangle an vice-versa…aka “Triangulation” and “Trigonometry” (Which apparently was figured out 2,500+ years ago by Pythagoras and not improved upon but once since then around 80 years ago when computers and radar and so on came into existence!).
And more links I am using to figure this out…
#/media/File:Two_rays_and_one_vertex.png)
https://en.wikipedia.org/wiki/Sine_and_cosine#Series_definitions
https://en.wikipedia.org/wiki/Pythagorean_theorem
https://en.wikipedia.org/wiki/Pythagoreanism
https://www.calculator.net/pythagorean-theorem-calculator.html
https://en.wikipedia.org/wiki/Taylor_series
https://en.wikipedia.org/wiki/CORDIC
https://en.wikipedia.org/wiki/Vertex_(geometry)
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OH THIS TOO: Make the (x) negative (-x) and the graph flips (opposite reflection or mirror image) to the negative side of X or the -X “Quadrant”… and SAME THING if you, flip (y-x+1/2) to (x+y+1/2) … …
Make the 1st y= into -y= and if flips (mirror image) along vertical (y ) axis but stays within same x=1 to x=0 horizontally…
Make the 2nd (y ) neg. and flip the curve (mirror opposite) along (x) but stay in the same square (x=0 to 1)…
Add a negative to the 1/2)^2 part so its -1/2)^2… and it shifts 1 unit to the left Quadrant, without flipping to the mirror image along x (horizontally)…
So still, how DO I combine these equations though?…
…
x^2+y^2=r^2 (r=Radius or Hypotenuse, x & y=coordinates or side lengths of right-triangle)
…
2r=D (Diameter of Circle)
…
DxPi=Circumference of Circle
…
D^2xPi=Area of Circle
…
y= (y – x + 1/2)^2 x -2/3 + 1/6
…
… So we can add another negative (-) to the first three y and x variables here and the 1/2 to change the graph as needed to adjust for the changing variables as the degrees change from 0-360, and correct for the difference between coordinates (or side lengths) x^2/y^2 (Which when added equal Hypotenuse or Radius^2) relative to angles a/b for “triangulation”, depending on how these need to be combined to get CORRECT answers, without long series’ of calculations to APPROXIMATE the right angle and x,y coordinates, circumference, lengths, etc..
https://www.desmos.com/calculator/jza6f9wyii
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So my goal is to find the equation, which directly relates, the ratios between, the two shorter sides of a right triangle, to the longer “Hypotenuse”, WITHOUT Squaring the values, when the Radius or Hypotenuse =1, and the Ratio between the angles at each point, 0 to 90 degrees for the Right Triangle Math…
So far I think that Pi is only useful for relating the ratio between the circumference and diameter, or 2x Radius xPi (Squared for area of Circle).
So I think if we are using the 90 degree measure Pi is not needed, BUT, the last graph DID seem to line up better with the Chart when I changed 1/3 or 2/3 or 3x to 1/Pi etc.
So we need to make a graph with a simple equation to relate…
Y/X or Y^2/X^2 (or Switch X and Y), which are lengths, to angles, a/b or b/a, according to these #s…
___________________________________________________________________
DEG(b)| _ X _ | _ Y _ | _ X/Y=_ | _ Y/X= _ | _ a/b= _ | _ b/a= _ |
—————————————————————————————————————-|
0 | _ 1 _ | _ 0 _ | 1 _______ | 0 ________ |90/0=90 ____ | _ 0/90=0 _ |
1 | 0.9998 |0.017452|57.2885629 |0.0174554911|89/1=89 ____ |1/89=0.011235|
5 | 0.9962 |0.08716 |11.4295548 |0.0874924714|88/2=44 ____ |2/88=0.0227272|
10 | 0.9848 |0.17365 |5.67117766 |0.176330219 |85/5=17 ____ |5/85=0.058823|
15 | 0.966 |0.2588 |3.73261206 |0.267908903 |80/10=8 ____ |10/80=0.125 |
20 | 0.9397 |0.342 |2.74766082 |0.36394594 |75/15=5 ____ |15/75=0.2 |
25 | 0.9063 |0.4226 |2.14458116 |0.466291515 |70/20=3.5 __ |20/70=0.28571|
30 | 0.866 |0.5 __ |1.73200 |0.577367206 |65/25=2.6 __ |25/65=0.38461|
35 | 0.8192 |0.5736 |1.42817294 |0.700195312 |60/30=2 ____ |30/60=0.5 |
40 | 0.766 |0.6428 |1.19166148 |0.839164491 |55/35=1.57142|35/55=0.63636|
45 | 0.7071 |0.7071 |1 |1 |45/45=1 ____ |45/45=1 |
___________________________________________________________________|
So we might use 45 or 90 or 180 or even 360 degrees, divided by the degrees at each major point (like 1 5 10 15 30 45 degrees, after which the math inverts for 60 75 80 85 89 degrees)…
And we might use 2x or 1/2x either R or X or Y or a or b or degrees, or 3x or 1/3 or 1/Pi etc… Until these #s MATCH!
Note the ratios between Sides NOT Squared is x 57.2885629 or 0.0174554911 times the length of the other side at 1 and 89 degrees, whereas the Square roots are 3281.97944 x at 1 and 89 degrees! But clearly the ratio of degrees is 1:89 89:1 or 1/89= 0.0112359551 and 89/90= 0.98888888… so THAT RATIO IS THE EQUATION WE ARE LOOKING FOR HERE, to make a graph match THOSE Values…Just like Pi relates the Circumference to the Diameter, which I am pretty sure we dont need for this part, but if we do, Radius x2 xPi =180 degrees or half the full circle, so 1/2 xR xPi =90 degrees which is 1/2 Pi= 0.159154943… and for 45 degrees 1/4 Pi= (where the math flips or inverts depending how you flip the #s, note btw using a negative “exponent” like ^-2 means you square then divide 1/the result for the “inverse exponent”) 1/4 Pi= 0.0795774715.
So this graph needs to go from 1:1 or 0.5:0.5 at 45 degrees for a and b (where a is adjacent to side or coordinate X and b adjacent to side Y, so the angle a in 0 – 90 matches with the vertical Y Coordinate, or we can switch X & Y or a & b)…FOR THE RATIO BETWEEN ANGLES a & b…AND…
…FOR THE RATIO BETWEEN SIDES LENGTHS, 1:1 at 0.7071 …Which when Squared =0.5, so the Square root of 0.5 is 0.7071 …Note at 30 and 60 degrees X and Y = 0.5 which when squared =0.25, and 0.866 which squared =0.75, which are 1:3 ratio just like 30:90 degrees…
SO, the Ratios between these #s must be at 1 degree, 1:89 for angles, or 1:45 or 1:180 or 1:360 depending how we multiply by the Radius or length of a side before or after squaring it… and for side lengths x 57.2885629 or 0.0174554911 times the length of the other side at 1 and 89 degrees. But both at 1:1 at 45 degrees…AND AT 0 AND 90 DEGREES THEY ARE OPPOSITES, one is 0 and the other 1…
…Until we change at end to go up to 0.9 so it matches 90 degrees math instead of 0-1 for X, so Y goes up to 0.7071 at 0 degrees, then 0.45 + & – on x axis… THEN THAT SHOULD BE THE RIGHT (FAR SIMPLER) EQUATION TO REPLACE THE COMPLEX WAY WE CURRENTLY “TRIANGULATE” WITH SINE COSINE AND TANGENT. Something similar to R^2/X^2 or (R^2/X^2)/Y^2 x 90 with some converting factor to make these ratios line up properly (like 1/89 x 1/57….etc…).
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90 x 2/Pi = 57.2957795 which is CLOSE to the Ratio between lengths X & Y @: 57.2885629 x @: 1 and 89 degrees, but look how far off the next values are…
89 x 2/Pi = 56.6591597
91 x 2/Pi = 57.9323993
89/90 x 2/Pi = 0.629546219
90/89 x 2/Pi = 0.643772804
…IS THIS GIVING ME ANSWERS IN ‘RADIANS’ AND MESSING UP THE MATH RIGHT HERE?????…
45 / .25Pi = 57.2957795
44 / .25Pi = 56.02254
44 * .5Pi = 69.1150384
.5pi * 45= 70.6858347
So far that first value seems the closest, where the graphs should meet at 1 and 89 degrees, to match the angles to the side lengths (Ratios between them, different by 90 degrees x 2/Pi = 57.2957795 which is the shorter side / middle length of X or Y coordinates).
And at 30 and 60 degrees the ratio between SQUARES of the sides are 1/3 (0.25:0.75) and angles are ALSO 1/3 at 30/90 or 90-60=30…etc.. (Inverted on opposite side of 45 where they are both 1:1 at 0.5 when squared or 0.7071 long at 45 degrees on both sides)…but the side lengths at 30 and 60 degrees are 0.5 (0.25 when squared) and 0.866 (0.75 when squared).
SO WHAT IS THE RIGHT EQUATION TO MATCH THESE POINTS????
180/Pi = 57.2957795 THIS LOOKS LIKE PART OF THE ANSWER, where the graph must meet angles to side length ratios at 1 and 89 degrees for angles a and b. So if Radius=1 (“Unit Circle”) and then Diameter=2, then that is the same as R/Pi I think in a way.
That is simpler. CLOSE to the Ratio between lengths X & Y @: 57.2885629. Maybe if we do a more accurate calculation for lengths of x and y when r=1 at 1 and 89 degrees, maybe it will be closer to that fraction?
So we can take 0.5xR or 2Pi or put in 2x or 2/ in various ways to make this graph match these angles to side lengths (the ratio between), so the x or y coordinate shows angles 0-45 or 0-90 by decimals 0.1 – 0.9, and on the other coordinate lengths 0-1 but up to 0.7071 (Squared=0.5 at 45 degrees in the middle of the chart, at y or x=0 or 0.45).
Btw: 1/89= 0.0112359551
…these do not seem to match the X/Y or Y/X Ratios really anywhere though…
90/Pi = 28.6478898
60/Pi = 19.0985932
45/Pi = 14.3239449
30/Pi = 9.54929659
15/Pi = 4.77464829
10/Pi = 3.18309886
5/Pi = 1.59154943
1/Pi = 0.318309886
I WONDER HOW WOULD THIS MATH BE DIFFERENT IF CALCULATING WITH A DIFFERENT “BASE” LIKE “BASE 12”???
And since Nature works on that system, the way there are “Octaves” of light and sound with 12 “Notes” per “Octave” and same “Notes” “Resonate” because the “Wavelengths” are 1/2 or 2x or 3x etc. in length (and same speed for “light” and “sound” in general)….
…So we could use letters A – L to represent the #s 1-12 and O to represent 0 maybe (If below 1 it would be equal to the 12th # or L in lower “Octave”).
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OK SO THIS IS WORKING NOW… At 45 degrees the ratios are both 1:1 at 1/2 degrees and 0.7071 (When R=1) for both side lengths (squared =0.5 both)…
…And at 1 & 89 Degrees the ratio between sides is CLOSE to 180/Pi
180/Pi = 57.2957795
… CLOSE to the Ratio between lengths X & Y @: 57.2885629.
…SO THE RATIO BETWEEN THESE RATIOS (To match the degrees to side lengths at 89 and 1 degrees)…
57.2957795 / 45= 1.27323954
So the ratio between side lengths at 1 & 89 degrees are 1.27… times larger than the degrees from where the ratios between side lengths and degrees match 1:1, in this comparison.
SO THAT MEANS, 45 “degrees” from where ratios between angles and side lengths MATCH, the ratio between side lengths is 57…. and that is about equal to 180/Pi (BECAUSE of Circumference/Diameter=Pi but we are using Radius which is 1/2 Dia thus 1/2 360 deg full circle)…
So 45 deg from center the side lengths “Divergence” is 1.2….etc. times larger than the ratio between degrees, if calculated in this manner, using a center line for the parabola of x=0 so each end hits y=0 at x=0.45 and the peak is at y=0.7071 using this math.
SO WHAT IS THE RIGHT EQUATION NOW?
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NOW I THINK I HAVE THIS FIGURED OUT, THE “FUNDAMENTAL PRINCIPLES” OF “HOW WE EXIST”, WHY IS 4/Pi PRECISELY EQUAL TO THE RATIO BETWEEN X AND Y IN “TRIGONOMETRY”/”TRIANGULATION” WITH “RIGHT TRIANGLES”, AND WHY DO ALL THESE NUMBERS LINE UP IN THESE WAYS… IT IS DUE TO “TRANSVERSE” OR “PERPENDICULAR” FORCES, WHICH ARE EITHER CIRCULAR (SPIRAL, SINE WAVE OR “SINUSOIDAL”) CREATING “LINES OF FORCE” LIKE “MAGNETISM”, OR “LONGITUDINAL” OR “TRANSVERSE”….
So they either relate to Circumference/Diameter=Pi (3.14159…) or to X^2+Y^2=R^2 with right Triangles.
THIS is what I have had in my head for 20+ years, but not been able to Calculate, until I FINALLY learned these “Maxwells Equations” and what these fancy symbols MEAN like “Gradient” and “Divergence” and “Interferometry” and the Sigma (For the series of equations like Taylor Series currently used for Sin Cos Tan, SohCahToa, Trig, in calculators, since 1715 apparently).
SO WHY THESE NUMBERS???
Because with the Right Triangle math, calculating perpendicular forces, NOT including the “exponential” which results from the SPIN of forces causing “Centrifugal” and “Centripetal” “Forces”, which are “Fundamental” and THAT is what CREATES the “Pressure” which causes “Electrical Voltage” to exist and thus Motion aka “Light” and “Electricity” (“Electrons” carrying this “Voltage” or “Pressure” in form of “Momentum”), THIS IS “How We Exist, The Genesis of Relativity”, THIS IS HOW “God” CREATED “The Periodic Table of Elements” RIGHT HERE…
I think it was y^4=(x-y)^2 ..or something like that which produced the figure 8, which are how “Electron Orbital Configurations” produce the “Chemical properties” of “Solid Matter” aka “Natural Elements” of “The Universe”…
https://ptable.com/#Properties
…AND FOR THIS: 4/Pi= X/Y or Y/X at 1 and 89 Degrees out of 90 (1/4 of a total circle, but that is not quite the key)…
BECAUSE, we are measuring 1/4 of the total circle, and these forces MATCH at 45 degrees, 1/2 of the way to 90 degrees out of 360… AND…
We are using the Radius which is therefore 1/2 the length of Diameter, and Circumference/Diameter=Pi so RxPi=180 degrees and 4/Pi= the Ratio between the lengths of sides at 1 and 89 degrees when R=1, when the ratio between lengths and degrees match at 1:1 due to the 45 degrees being symmetrical, and 1/4 of the total circle (so 1/2 due to D/R and then another 1/2 due to R^2=X^2-Y^2), and the ^2 of the X and Y and R (or “Hypotenuse”), is due to the forces of SPINNING “Centrifugal” and “Centripetal” Forces creating “Electromagnetism”, and THAT is WHY all these #s line up in THESE ways!
And THAT is why I now need to make the right equation to graph the relationship DIRECTLY AND EXACTLY between the ratio between degrees 0-45 on either side of the right triangle, and the ratio between 4/Pi, and the ratio between the lengths of sides when R=1 (which you get by dividing R^2/X^2 or /Y^2 and the results should add up to R^2 exactly).
I need to put all this on http://www.HowWeExist.com now that I figured it out, and graph it, test it, make these #s as precise as I can, and provide a new way to calculate angles and “The Fundamental Forces of Nature” which are NOT “Gravity” and “Magnetism” and “Electricity” and “Strong” and “Weak” “Atomic” “Forces” but Pressure and Motion and Resonance vs Dissonance, and “Trigonometry”! THIS MATH HERE! THANK YOU GOD! FINALLY!
So then I have to figure out how to put these #s together on these graphs now…
https://www.desmos.com/calculator/j0zfnq3yl5
And make them match the numbers on my chart:
Which I made using this calculator online:
https://www.omnicalculator.com/math/right-triangle-side-angle
https://www.calculator.net/right-triangle-calculator.html
Oh I should include this to check out more of…
https://math.libretexts.org/Courses/Prince_Georges_Community_College/MAT_1350%3A_Precalculus_Part_I/10%3A_Further_Applications_of_Trigonometry/10.01%3A_Non-right_Triangles_-_Law_of_Sines
https://en.wikipedia.org/wiki/Maxwell's_equations
https://en.wikipedia.org/wiki/Taylor_series
https://en.wikipedia.org/wiki/CORDIC
https://mathworld.wolfram.com/SOHCAHTOA.html
https://ptable.com/#Properties
https://en.wikipedia.org/wiki/File:Electron_orbitals.svg
NOW I THINK I CAN FINALLY “FIX” “Maxwells Equations” AND COMBINE THEM WITH THOSE FROM NEWTON AND EINSTEIN AND CREATE ONE “GRAND UNIFYING FIELD THEORY”, AND MAKE IT MUCH SIMPLER THAN THESE ARE NOW!!!
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For anyone wanting to learn more about the history of math and trigonometry and graphs and so on, “Cartesian Coordinates” and “Euclidean Geometry” and why we have “Pi” and the “Pythagorean Theorem” (a^+b^2=c^2), this page has some good info on that…
https://en.wikipedia.org/wiki/Euclidean_geometry#Triangle_angle_sum
Especially that Triangle Sum part I think is useful. Especially this part about… “Archimedes who proved that a sphere has 2/3 the volume of the circumscribing cylinder.” So instead of Pi^3 its exactly 2/3?
These are the sort of things I am about to do next…
I found that the Square of the Diameter Squared (Same as 2xRadius^2), divided by the Circumference (I was using 4/Pi for this calculation), comes out to 1.273…. and that multiplied by 45 (degrees, max for small angle (a)), is equal, to the ratio between Side Lengths Y/X (or X/Y I need to figure which, depends how you arrange the sides relative to angles), MEANING, that at the furthest point (1 & 89 degrees) on the chart where the lengths and angles are the furthest apart (right before they reach 0 and 1, end of graph), that the Ratio between the Diameter^2/Circumference= X/Y at the maximum “divergence”, away from the middle (45 degrees out of 90 max, in “Euclidean Geometry”) where the ratio between all sides and angles are equal at 1:1 (a&b=45 deg and x&y=0.7071 when R=1, and 0.7071^2=0.5).
SO WHAT I NEED TO DO NEXT, is graph these relationships on the graphing calculator, and get exactly the right ratios so the points on the graph match the values I calculated using a triangle calculator online (using current methods). So far the graph is using:
y=(x^2 / Pi) x 0.45
https://www.desmos.com/calculator/qix82mvqzf
It might have to be something using 89 degrees or half or double that or a square root, I’m sure there will need to be a square (of X^2 or Y^2 or Diameter^2 or Circumference(Pi)^2) to make the graph an “exponential” curve from 1/1 at 45 degrees, up to here:
4/pi x45= 57.2957795
That 57.29…. is approx. the same value as the Ratios between the Length of Y/X or X/Y at 1 & 89 degrees.
So, there is an exponential relationship here between the lengths of the sides, and the diameter (& radius x2 is the same thing) and the Circumference (this attaches to the degrees), which gives that ratio of 1.273…..x45 degrees, which makes the sides and angles and diameter and circumference all DIRECTLY Related! THAT IS THE PART THAT MAKES THE CURRENT COMPLEX MATH FOR SINE COSINE AND TANGENT NO LONGER NECESSARY!
Now I need to practice and check #s until I find the right equations to graph the #s like I have described, 0-0.45 on +&- x,y coordinate graphs, showing Degrees on X and Length of Y or X on the Y (vertical) coordinate, and different graphs to show all the values relationships to one-another.
THEN I CAN FINALLY FINISH THE MAIN GOAL OF SIMPLIFYING ALL THE EQUATIONS IN PHYSICS AND PUTTING THEM ALL TOGETHER, FINALLY!
And I need to put all this on my site as soon as I have time also (but I need to deal with this getting this new court case dismissed and preparing lawsuits for myself and others, making more money, and all this other work too)…
http://www.HowWeExist.com
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And a correction on the equation I think I need… YEAH THIS SEEMS OBVIOUS TO ME NOW!!!! The ratio between the area of a circle and the corresponding circle of same radius, when Radius=1, is: 4/pi= 1.27323954…AND THAT IS THE SAME RATIO BETWEEN THE LENGTHS AND ANGLES, WHEN YOU DO THE MATH RIGHT…Not 0-90 degrees like Euclid devised, but instead by measuring the distance of angles (a) and (b) from where they are at 1:1 ratios (45 degrees on Euclidean Graph), and by using the RATIO between the Radius (or Hypotenuse) times itself, divided by either side length times itself (‘squared’)… OR just the length when you make Radius=1)… That ratio (1.273…) times the length of a side, tells you the ratio of one angle to the max 45 degrees! THAT IS THE DIRECT RELATIONSHIP BETWEEN DIAMETER AND CIRCUMFERENCE OF CIRCLES AND THE LENGTHS AND ANGLES OF TRIANGLES WHICH APPARENTLY NO ONE HAS FIGURED OUT YET!
If 4/pi = X/Y at greatest divergence (1&89 degrees), but the angles and lengths all match at 1/1 at middle 45 degrees (out of 90, using Euclidean Geometry)….then for what I am discussing, I think the value of angle (a) (the one opposite side X lets say for this, so the top angle on the graph), will be equal to…
(Length of X^2) / (Circumference / Diameter or “Pi”) x 45 degrees= …
Then I think that answer must be altered so that….
Angle (a)=45 degrees – (answer)
Angle (b)=(answer) – 45 degrees
And I think THAT answer, might need some conversion…
Since the key I found was that x/y=57.28…. and that equals 4/pi x 45…
…so the ratio of Diameter squared / circumference times max 45 degrees for the smaller angle, I THINK is what that translates to (I need to do the math and work it out)…. so that means the 1.2…something ratio from the square of the circle to the circles area (4/pi) is equal to the ratio between the max length of either side (which equals the hypotenuse or radius) and the min at furthest points…BUT, what that 4 represents I need to figure out…
I THINK it represents the Radius x2 so its equals the diameter, then squared to equal the area of the square, then divided by the area of the corresponding circle of same radius, is what makes the ratio, between length of a side, and max angle for corresponding opposite corner…so that 1.2 something is the correction, to make the ratio of a side length to the hypotenuse (hyp/side) x1.2…, times the degrees used (45 deg), tells the angle of the opposite corner to that side…I THINK….
But I need to work it out. It MIGHT be more like 360/89 or 91 or some other square or cube or inverse number I have to figure out to make the numbers EXACTLY correct. BUT SO FAR THIS IS ALL WORKING!
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A SUMMARY OF “FUNDAMENTAL PRINCIPLES” OF “HOW WE EXIST”, “MATHEMATICAL RATIOS” IN BASIC GEOMETRY, TRIGONOMETRY, CALCULUS, TRIANGULATION:
This article on Volume of Cube Related to Sphere makes a simper connection… 6/Pi=Volume of a Cube/Sphere … so that means Volume of a Sphere/Cube=Pi/6 …
…Whereas the 2 Dimensional Area of a Square/Circle=4/Pi and Circle/Square=4/Pi …
…And the 1 Dimensional Length of the Diameter/Circumference (or outer “Perimeter” for any shape)=1/Pi …and… Circumference/Diameter=Pi=3.141592….
That makes it a lot easier I think than MOST of the answers I have been seeing.
So Here are the REASONS for these Numbers…
The ratio between 1D perimeter and also 2D Area of the Circle and Square is that 4/Pi or Pi/4, but when you go from 2D to 3D you are increasing by a proportion of 3/2 or 1.5x, which is easier to comprehend when using YxYxY=… instead of Y^3 because then you cannot see each variable in the equation (or modify them individually in your equation or graph, so you can only make symmetrical graphs as I understand so far).
So, when using 3 Dimensions, the Volume is the Radius or Diameter Times itself 3 times, so the ratio between the 3D volume and the 2D area is 3/2 or 2/3.
But when using Radius Squared you are using 1/4 of the total square, and then multiplying that by Pi (just over 3, so just over 3/4 or 4/3, also making a 1:3 and 3:1 ratio between these two areas), so 4/3.14159… or 3.141592…/4…
So those are the reasons for a lot of these values, like these:
1/Pi=0.318309886…1D Diameter/Circumference of Circles;
2/Pi=0.636619772…
3/Pi=0.954929659…
4/Pi=1.27323954…=2D Area or 1D Perimeter of Square/Circle (in 2Dimensions);
5/Pi=1.59154943…
6/Pi=1.90985932…=3D Volume of Cube/Sphere;
7/Pi= 2.2281692…
8/Pi= 2.54647909…
…
Pi/8= 0.392699082=A ratio for “Acute Angles” in “Trigonometry”, Up to 45 Degrees, 1/8 of the Total Circle at 360 Degrees;
Pi/7= 0.448798951
Pi/6=0.523598776=3D Volume of Sphere/Cube;
Pi/5=0.628318531
Pi/4=0.785398163…=2D Area or 1D Perimeter of Circle/Square;
Pi/3=1.04719755…
Pi/2=1.57079633…
Pi/1=3.141592…=1D Circumference/Diameter of Circles;
…
Diameter=Radius x2
Radius^2=R x R
Diameter^2=Area of Square
Radius^2=1/4 Diameter^2
Area of Square / 4 = Radius^2
R^2 x4=Area of Square
…
Radius^2 x Pi= Area of Circle
Diameter^2 x 0.7853…=Area of Circle
Area of Circle x 1.273239…=Area of Square
Now, going from 2 Dimensions to 3 Dimensions…
The Area of a 2D Cone inside a 2D Square with same base and height, is 2/1 because the two right triangles on either side equal the one larger triangle in the middle, but when going to 3 dimensions…
Now you are multiplying Radius x Radius x Radius …or… Diameter x Diameter x Diameter…. so NOW we are increasing by a rate of 3/2 or 1.5x, so NOW We have 3rds to deal with…and that odd 3.14…”Pi”… to relate to 1/4ths….
…SO… 1/2 x 2/3 = 1/3, so when comparing the Volume of the Cylinder to the Cone in 3 Dimensions these #s are HOW they work out to 1/3 the Volume of the Cone/Cylinder or Cylinder/Cone=3 ….
Well I have to keep practicing to learn better how to get that equation I’m working on just right, but I ALMOST have it exactly now, and I’m thinking I should finish some more calculations for angles at 44 degrees and the ratios between 45 and 44 and then 44 and 40, to match 1 to 5 degrees on the other side, maybe do 1-2 and 43-44 degrees also (higher #/Lower #=Ratio), then I can compare those ratios which show me the rate of curve I need at those point, the “exponential” value…which SHOULD be that 1.273… I think, or that combined with an x^2 or square root of y (which can be switched with square of X in the equation)…But that helped a lot…
So Volume of 3D Sphere and Cube is:
6/Pi=1.90985932…=3D Volume of Cube/Sphere;
Pi/6=0.523598776=3D Volume of Sphere/Cube;
And for 2D Area of a Circle and Square its:
4/Pi=1.27323954…=2D Area or 1D Perimeter of Square/Circle (in 2Dimensions);
Pi/4=0.785398163…=2D Area or 1D Perimeter of Circle/Square;
And for the ratio between the Diameter and Circumference or Perimeter of Circles and Squares:
Pi/1=3.141592…=1D Circumference/Diameter of Circles;
1/Pi=0.318309886…1D Diameter/Circumference of Circles;
OH NO HOW THE SPHERE WORKS OUT TO 2/3rds THE CYLINDER VOLUME ALSO: The 4/Pi ratio between Square/Circle area, x Diameter to go to a 3rd Dimension for Volume (multiplying total capacity from 2D to 3D so 3/2 or 1/5x), makes a ratio or 2/3 because Volume of a Cube/Sphere is 6/Pi=1.909… or Sphere/Cube=Pi/6=0.5235…
Its that (6/Pi=1.9098) / (4/Pi=1.2732…) =1.5 right there, that is 3/2, or 2/3 or 0.66…, right there.
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