Thanks! Jim On Thu, Apr 16, 2020 at 7:24 AM Adam P. Goucher <apgoucher@gmx.com> wrote:
It seems that the Conway-Gordon theorem is another example: the authors prove that, given 6 points in general position in R^3, the number of ways [out of (6 choose 3)/2 == 10] to partition them into two *linked* triangles is necessarily odd.
https://twitter.com/JSEllenberg/status/1250585677202325505
Sent: Friday, January 31, 2020 at 6:45 PM From: "James Aaronson" <jamesaaaronson@gmail.com> To: "math-fun" <math-fun@mailman.xmission.com> Subject: Re: [math-fun] Existence from parity
For the Square Peg Problem https://en.wikipedia.org/wiki/Inscribed_square_problem, if the curve is piecewise smooth, the argument shows that there is an odd number of inscribed squares (generically).
https://www.ams.org/notices/201404/rnoti-p346.pdf
James
On Wed, Jan 29, 2020 at 2:45 PM James Propp <jamespropp@gmail.com> wrote:
What are people’s favorite examples of existence proofs that show that a set is not empty by showing that its cardinality is odd?
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