Right, but this is different from some of the pairing proofs we talked about before. The paper is here : http://people.reed.edu/~ormsbyk/138/ConwayGordon.pdf <http://people.reed.edu/~ormsbyk/138/ConwayGordon.pdf> They show that the sum mod 2 of the number of linked pairs of triangles is the same for all embeddings since it’s invariant under crossing changes, and then they show that it is 1 for a particular embedding. C
On Apr 16, 2020, at 5:24 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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