Cyclometry

[I wuv M4( Satar Jaèoèdoæ)]

I: Its the forums first mathematical textbook!(I believe there was also a textbook on magic here, but that doesn't have to do with real math.) If you don't have at least calculus (up to limits) knowledge please avoid. This branch of mathematics is completely pointless and is not recognized by anyone, so read with caution. Also this has nothing to do with instruments that measure how many revolutions something made. If you see in errors in my math go sue me. I will also treat infinity as a number here, even though it is usaully not counted as a number.

II: ToC

I: Disclaimer
II: ToC
III: Intro
1: Definitions
2: The number circle
3: Function relating to the number circle
4: Graphs on donuts
5: The complex donut with a real hole and other complex stuff
6: Angles and trigonometry

III: I discovered this circle while trying to prove -infinity=+infinity ( and failing), investigating slope/polar graphs, and trying to find away to compress all real numbers into a visible area. This is a branch of mathematics that deals with this circle and its higher dimensions. These also has some relations to a modulus of infinity. Since my keyboard fails at making symbols I will use brackets for them. Limits will be expresses as (limc)f(x)

1: Definitions

[inf]= infinity
\= not equal
[+-]= plus-minus
[+]= Manji

+0= +[inf]^-1
-0= -[inf]^-1=(+0)(-1)\=0(-1)
0 from here is [+-]0=([+-]1)(+0)
0^-1=[+-][inf]
inf from here on is [+-][inf]
If a/= 0 or inf than a/0=inf, a/inf=0
If f(x) has a limit for (lim=+[inf])f(x) than f(+[inf])= (lim+[inf])f(x).
If f(x) has a limit for (lim=-[inf])f(x) than f(-[inf])= (lim-[inf])f(x).
If f(x) dos not have a limit for (lim=+[inf])f(x) than f(+[inf])= the range at +[inf]
If f(x) dos not have a limit for (lim=-[inf])f(x) than f(-[inf])= the range at -[inf]
f(inf)={f(+[inf]),f(-[inf])
(liminf⁺)f(x)=(lim=-[inf])f(x)
(liminf^-)f(x)=(lim=+[inf])f(x)

2:The number circle

Now that you know the definations for this course I can move on to the number circle. The number circle is the the number line condensed into a finite line and then looped into a circle. Here is how to create the circle that can show all real numbers.

Draw a black circle. Then draw a blue diameter. After that draw a red diameter that is perpendicular to the blue diameter. Label one point where the blue diameter 0 and a point were the red diameter intersects the circle 1. On the arc between 0 and 1 is where the numbers between 0 and one go. 1/2 is halfway between 0 and 1, 1/4 is halfway between 0 and 1/2, 1/3 is a one third of the arc from 0 and two thirds the arc from 1. Now it is simple to label the other arcs. Any number reflected across the blue arc gets multiplied by -1 and any number reflected across the red arc gets raised to the -1st power.