Theory and Geometric application: http://squaringofthecircle.gr/?page_id=99&lang=en
Dear Ioannis,
Your question, with such a huge number sides, although sound from a theoretical point of view, practically is impossible! If one wants to theorise, he can use Vopenka's Alternative Set Theory and say that this huge number od sides is "unlimited"!
Dear Mr Drossos,
Thank you very much for your interest.We would like to notice that our research studies this construction from a theoritical point of view:according to "Theoritical Geometry" of Mr Togas (3rd edition, paragraph 75, page 32) an approach with compass and straigthedge is theoritical.
One can also look at our reasearch page http://squaringofthecircle.gr/?page_id=99&lang=en, page 6 chapter 2 for more information.
Dear Mr. Georgakakis,
The odd-sided regular polygon with the largest number of sides constructible by compass and straightedge has 4,294,967,295 (=3x5x17x257x65537) sides. Gauss showed that such a polygon would have a number equal to a product of distinct Fermat primes. The number you inquire about has repeated odd primes, so it is definitely not constructible. By the way, if anyone ever finds another Fermat prime, the number I cited would jump; there is no known proof that such a prime does not exist.
Dear Mr Singer,
We really appreciate the accurate piece of Information you gave us.
Thank you very much!
The only thing I would like to notice is that our way of polygon Construction uses the summary of number two powers, not the product. It is based on Eukleidian Geometry, on proportional division of a Line.
- Badges
- Science topic
- Similar topics
- Philosophy
- Philosophy Of Science