I'm looking for a topic for a national Math Paper competiton for High School students. The problem is that in the paper I have to study some unsolved before problem. My main interest is mathematical analysis but I know it's difficult to study something there on my level. So far I thought about finding the maximum volume/area of an n-hedron circumscribed on a unit sphere and related problems. I'd be really grateful for any other ideas, preferably not in geometry.
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In previous years the winning papers were for example about: diffrent approach to buffon's needle or finding special matrixes, for which determinant can be easily found in a clever way or studying function f(n), which for given natural n outputs the maximum radius of n spheres that can fit into cube of side length 1 or Sylvester-Galla theorem for circles or k-good graphs and so on... – TheRlee Apr 13 '18 at 17:01
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1Look here www.mathlinks.ro – Dr. Sonnhard Graubner Apr 13 '18 at 17:04
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Perhaps you could do a paper on the packing efficiency of spheres . – The Integrator Apr 13 '18 at 17:36