#08 Eucl Geom = Ellipt Geom + Hyperb Geom; independent and dependent

Now I am fully aware that much of what I wrote in the prior post is above the head of most High School students. Being introduced the first time to the Faraday law in High School, even though it is a demonstration in the classroom.

I write this 10 page book so as to warn the authors of High School geometry textbooks on what they need to change. Such as Jacobs text for High School or Moise's text for college.

I write this 10 pages to warn teachers, authors and students alike what not to teach for geometry so that they later do not have to discard and relearn true geometry. It is far easier to teach someone the true math first, rather than teach them fakery math and later tell them everything they learned before is mostly fakery and here is your relearning of the true geometry.

In my prior post I talked about how Euclidean Geometry had Elliptic and Hyperbolic geometries contained inside itself. That geometry comes in only one type-- Euclidean and that Elliptic and Hyperbolic were dual subsets of Euclidean.

The reason to show the Faraday law as a demonstration is that it is another duality of electricity and magnetism, and whether they are dependent or independent of one another.

In school, in a future class, you will learn the electrons of atoms go around a nucleus in perpetual motion, for they never stop going around and around. The electrons going around is electricity flow of an atom. Now if those electrons of various atoms in a compound are lined up that perpetual electricity becomes a permanent bar magnet. So when you have a permanent bar magnet of iron (show one in class), the reason it is permanently magnetic is because those electrons of iron atoms are permanently going around a nucleus and they are all lined up so that we end up seeing magnetism.

Now as I thrust this bar magnet back and forth into this closed loop of wire, we see a electric current register on this meter (called a galvanometer in physics).

So what is happening? Well, the perpetual motion of electrons in iron atoms causes a permanent bar magnet (if those electrons are lined up). The permanent magnet when thrust through a closed loop wire of copper causes the electrons in copper to move as an electric current.

So we started with electric current of electrons in iron and those became magnetism in iron and by thrusting that magnet into a closed loop of wire we return to another electric current.

So, is magnetism independent of electricity? The answer is no, because from electricity we produce magnetism and from magnetism we produce electricity.. Another law called the Ampere law shows us that a electric current produces a magnetic field.

Electricity exists only with magnetism and magnetism exists only with electricity. Same as Elliptic and Hyperbolic geometry. Neither one is independent of the other. If you had a sphere surface the outside of the sphere surface would be elliptic geometry, but if we were to use the interior of the sphere and remove the poles of the sphere, then that interior surface is hyperbolic geometry. So in Euclidean Geometry, whenever you produce elliptic geometry, you are also producing hyperbolic geometry.

In Old Math (math before 2011), they thought the world of geometry consists of 3 independent and totally different geometries. In new True Math, we see that geometry is only one type-- Euclidean geometry and inside of Euclidean we can construct a subset that is elliptic and another subset that is hyperbolic, both simultaneously existing alongside one another. Just as in Physics, electromagnetism is one phenomenon that is composed of two subsets-- electricity and magnetism.

P.S. Now it maybe advantageous to show the Ampere law in the classroom also..

AP

#08.1 Eucl Geom = Ellipt Geom + Hyperb Geom; independent and dependent existence in math 8th ed.: TRUE CALCULUS

Alright let me point out another analogy between Faraday law of physics and Elliptic geometry added to Hyperbolic geometry makes for Euclidean geometry.

Notice the bar magnet in Faraday law is a magnetic field as a sphere around the bar magnet and notice that the closed loop of wire is like a hyperbolic space. So that when we thrust the bar magnet into the closed loop of wire is like that of joining back the sphere into the hollow core of the cube from which we extracted the sphere to leave a hyperbolic space.

Now I know most of the ideas I set forth are above the heads of most High School students, but what I am attempting to do in these 10 pages is forewarn the teachers and students what should be taught in High School Plane Geometry-- that the points of space that make up plane geometry are a point is separated by empty-space that spans to the next point.

If points are dots, then plane geometry looks like this up close---

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AP