I am just wondering if there is any, what are some math contest like the math Olympiad that involves solving non-euclidean geometric problems (shortest path, area...)?
Thanks!
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1$\begingroup$ don't know about contests. Note that one may, in the hyperbolic plane, use a compass and straightedge to construct a circle and "square" of the same area. Here a square has four equal sides, four equal angles. That cannot be done in the ordinary plane. I should admit that the same task is easy on the surface of a sphere of radius $1,$ $\endgroup$– Will JagyCommented Nov 16, 2021 at 5:36
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$\begingroup$ The Superbrain Mathematics Competition only makes use of material commonly known to all Irish students who have completed secondary school in Ireland including the higher level mathematics examination, hence no non-Euclidean geometry. $\endgroup$– Ben McKayCommented Nov 16, 2021 at 13:33
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$\begingroup$ @BenMcKay: I don't understand your comment: the question asks about competitions that do include, not about competitions that do not include such problems. It's like asking for recommendations for Chinese restaurants, and then somebody answers that "Bella Italia" only serves Italian cuisine. $\endgroup$– Alex M.Commented Dec 30, 2021 at 9:04
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$\begingroup$ @AlexM.: I worried that Dian Sheng might work his way through all of our old problems to check that there aren't any non-Euclidean ones. I hoped I was saving him time. In a restaurant, the menu is easy to check quickly, and the name of the restaurant might give a clue to the cuisine. For competition problems, it is not so easy to check all of them. For example, are there any Superbrain problems about group theory or about algebraic geometry or about the Poincare inequality? That is not so easy to answer, just from the name Superbrain. $\endgroup$– Ben McKayCommented Dec 30, 2021 at 11:20
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1 Answer
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The William Lowell Putnam competition says this
The Putnam Competition covers a range of material in undergraduate mathematics, including elementary concepts from linear algebra, modern algebra, analysis, and number theory.
So it seems it does not include "noneuclidean geometry" problems.
answered Nov 16, 2021 at 11:58
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$\begingroup$ I don't understand this answer: the question asks about competitions that do include, not about competitions that do not include such problems. It's like asking for recommendations for Chinese restaurants, and then somebody answers that "Bella Italia" only serves Italian cuisine. $\endgroup$– Alex M.Commented Dec 30, 2021 at 9:02