tag:blogger.com,1999:blog-6587700778834733354.post6377152129264850597..comments2023-11-27T11:16:11.797-05:00Comments on Skeptic but Jewish: Geometry Problem of Regular PolygonsBaruch Spinozahttp://www.blogger.com/profile/11879864721961862810noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-6587700778834733354.post-65069765407502368222011-02-24T18:14:06.717-05:002011-02-24T18:14:06.717-05:00The proof would need a second line to say that an ...The proof would need a second line to say that an equilateral triangle with integer sides cannot have rational area.ehttps://www.blogger.com/profile/04376537400767851942noreply@blogger.comtag:blogger.com,1999:blog-6587700778834733354.post-67722466052907623132011-02-24T17:12:43.774-05:002011-02-24T17:12:43.774-05:00"And the one-line proof is... "
We can..."And the one-line proof is... " <br /><br />We can assume the polygon has integer coordinates, then Pick's theorem would say $A=\frac{B}{2} + I - 1$, i.e. A is rational, but the only regular polygons with rational area with integer sides is a square.Baruch Spinozahttps://www.blogger.com/profile/11879864721961862810noreply@blogger.comtag:blogger.com,1999:blog-6587700778834733354.post-25620203766444591182011-02-23T19:23:05.207-05:002011-02-23T19:23:05.207-05:00And the one-line proof is...And the one-line proof is...ehttps://www.blogger.com/profile/04376537400767851942noreply@blogger.com