Alright, in my previous post I began talking about the geometry that a equation of physics is written in, or written for. Now this seems an odd idea for everyone in physics who never studied mathematics very much. And even shocking to mathematicians to say the least.
But the idea is this. In mathematics geometry can be of one of three types. Euclidean, Elliptic and Hyperbolic where each of those three has their own special axioms. The Universe can be either one of these three or a combination of those three, but those three cover every possibility of what geometry and the Space of physics is. In numbers, when you are given two numbers, A and B, there are three possibilities A is less than B, A is greater than B, or A is equal to B. In geometry, there are three possibilities for space; either the geometry is positively curved or negatively curved or flat space geometry.
Now everyone in the last century, the 20th, thought that what I speak of-- the 3 geometries, are confined to just mathematics and is not a integral part of physics. But I am happy to report to you, that the question of geometry and its three types is an integral part of physics and if it is ignored, physics stagnates.
I talked about this in earlier posts, but since I have a whole chapter devoted to a glossary, I would have to list Euclidean Geometry, Elliptic Geometry, Hyperbolic Geometry and list representative equations of each geometry and how that would end up confusing and delaying progress in physics if physicists keep ignoring the origin of those equations.
Equations that are representative of Euclidean Geometry, i.e., line equations of Euclidean geometry:
y = mx + b
Ohm's law: V = i*R
Linear Momentum: p = mv
Hooke's law for spring: F = -k*x
Equations of Elliptic Geometry:
Some of the Maxwell Equations
E = mc^2
E = 1/2mv^2
Malus law: I' = I" cos^2(a)
Basically, any equation that is square or square root. Any equation that is a curved line and not a straight line.
Coulomb law: F*r^2 = charge1*charge2* k
Gravity law of Newton F*r^2 = mass1 * mass2 *k
Equations of Hyperbolic geometry:
Faraday law of Maxwell Equations
Entropy in thermodynamics: S = -k (lnP) Radioactive decay rates: N = N" e^-kt Basically equations involving natural log or "e".
The equations of physics that are based in Euclidean geometry are straight-line equations. The equations based in Elliptic or Hyperbolic geometry are curved line equations.
Now some equations of physics have both Elliptic and Hyperbolic geometry in them for example the Ampere/Maxwell law. Or when you sum all the 4 Maxwell Equations together you have both Elliptic and Hyperbolic geometry combined.
Most of the Equations of physics are written for Elliptic Geometry and the reason should by obvious in that rest-mass is protons and protons are Elliptic geometry.
-- Google's archives are top-heavy in hate-spew from search-engine- bombing. Only Drexel's Math Forum has done a excellent, simple and fair archiving of AP posts for the past 15 years as seen here: