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Yesterday I proved my first theorem! It's quite dumb and all, but it says that for any number of sides n, the polygon with most area you can inscribe in a circumference is a regular polygon. I haven't found a proof for anything like this, but I'd like to know whether somebody has proved it ever before.

I expect it to be proven, but if not, what could I do with the proof? Is there somewhere I can check for proofs to theorems online, maybe?

ChemiCalChems
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  • There is no maximum area of an $n$-gon. Is the perimeter fixed? – Umberto P. Apr 22 '17 at 14:56
  • I didn't say the maximum area was fixed. I said that the polygon of n sides with maximum area, is for any n, regular. And no, the perimeter is not fixed. The only limitation is that the polygon must be inscribed. – ChemiCalChems Apr 22 '17 at 14:58
  • try a search in google, proofwiki or just in math.stackexchange (check this or also this). – Masacroso Apr 22 '17 at 15:02
  • @Masacroso yep, that got me. – ChemiCalChems Apr 22 '17 at 15:08
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    Congratulations for proving something. Even if it's already known - and expect that to be the case for things you prove for quite some time, a lot of very smart people have proved a lot of stuff over a long time - it's always an achievement to prove something on one's own. – Daniel Fischer Apr 22 '17 at 15:15
  • I googled "maximum area of n-gon inscribed in circle" and got a long list of good stuff, including this theorem asked and answered on this site..... I have found that to find something on this site, it's often easier to google it. – DanielWainfleet Apr 22 '17 at 17:45

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You can try and google it. Otherwise you should go onto MatSciNet or a similar database (accessible through a university library) and do a search, that is search for listed pear reviewed papers that may have already addressed the problem.

AnyAD
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  • I'm not yet in university yet, is there any other way? I've tried googling it, but nothing seems to be coming up. – ChemiCalChems Apr 22 '17 at 15:00
  • If you don't get any helpful replies, I am happy to do a quick search for you. Let me know. – AnyAD Apr 22 '17 at 15:04
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    It was proven here already. Oh well. At least I've learned some LaTex. – ChemiCalChems Apr 22 '17 at 15:09
  • You can also check books on geometry in a university library (no need to be a student), for example Coxeter Geometry. There will be pdfs online as well. I'd say that someone will have addressed the problem already. Good luck. – AnyAD Apr 22 '17 at 15:12