December 28th, 2016, 06:54 AM  #1 
Senior Member Joined: Dec 2012 Posts: 924 Thanks: 23  Two Hands Clock
Here a serie of nice Power bijection (what I call Complicate Modulus Algebra) n=2: n=3: And so on using $M_n= (X^n(X1)^n)$ ... 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 07:02 AM. 

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