On 08 Jul 2013, at 23:22, Johnathan Corgan wrote:

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On 07/08/2013 02:16 PM, Jason Resch wrote:This one is very interesting, but the fact that Pi was a poorchoice forthe constant makes the equation considerably more ugly than it should be. There is a growing movement to usurp the number Pi with the much more important constant "2*Pi"(see: http://www.math.utah.edu/~palais/pi.html ). If we call thatnewnumber tau (t). Then Euler's identity becomes: e^(t * i) = 1I think part of the appeal of the original formulation is realizingthatthe result of an exponentiation of a positive number can be a negativenumber. While this is unremarkable with complex exponents, manypeopleare only used to seeing real (or even just integer) exponents.

`I like and often give the following exercise: compute i^i. Is it real`

`or imaginary?`

`Since sometimes my most amazing result in math is the Turing`

`universality of the diophantine polynomials.`

`My favorite simple result is the irrationality of sqr(2). A good`

`exercise, using the fundamental theorem of arithmetic (existence and`

`uniqueness of decomposition of numbers in prime factors) generalizes`

`this for sqr(n) for any n not being a square. A result often`

`attributed to Theaetetus.`

`Of course the existence of universal numbers is also an amazing,`

`stunning results, especially if you know how weak are the pretense of`

`"universality" for mathematical notions. This needs Church thesis,`

`which I consider as the most amazing thesis in cognitive science.`

Bruno

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