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December 28th, 2016, 05:54 AM   #1
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Two Hands Clock

Here a serie of nice Power bijection (what I call Complicate Modulus Algebra)

n=2:



n=3:



And so on using $M_n= (X^n-(X-1)^n)$ ...

With some work it can be pulled into the Rationals too.

The first fact it's trivial (but has lot of conseguences):

Theorem 1: No Irrationals Values / Angles, can be reached with such clocks.

If you can prove your value (f.ex. $A^n+B^n$ ) lead to a root depending by an Irrational, you prove you can't use Integer / Rational, Powers or Roots, to rise it.

Ciao
Stefano

Last edited by complicatemodulus; December 28th, 2016 at 06:02 AM.
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