Re: [math-fun] Fwd: There are no equilateral triangles in the Integer Grid.

9 Aug 2017

      In no sense, apparently!

–Dan

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On Aug 9, 2017 04:32, "Dan Asimov" <dasimov@earthlink.net> wrote:

And paradoxically, the conformal bijection

   z |—> -1/(1+z)

of the Riemann sphere

   S^2  =  C u {oo}

to itself that preserves the integer points Z^2 ...

In what sense does this preserve the integer points? F(17) = -1/18

Andy

(i.e., a fractional linear transformation of form

   z |—> (az + b)/(cz + d), a,b,c,d in Z, ad - bc = 1,

i.e., a member of the group

   PSL(2,Z)  =  SL(2,Z) / {+-I})

... is of order three:

   f(f(f(z)))  ==  z
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