From:fc3a501@AMRISC04.math.uni-hamburg.de (Hauke Reddmann)Newsgroups:sci.mathSubject:3 CLASSICAL GEEK PROBLEMS SOLVED!!!Date:26 Apr 1996 12:00:12 GMTOrganization:University of Hamburg -- Germany

THEY SAID IT WAS IMPOSSIBLE. I DID IT. WOW! Mathematicians go PARROTING AND PARROTTING that you can't solve the THREE CLASSICAL GEEK PROBLEMS with compass and straightedge.Well, LOOK AT THIS! 1. Doubling the angle Let the angle be represented by two straight lines through O. Draw any circle K with midpoint O which meets the lines in A and B. Draw a circle with midpoint A through B which meets K in C. OBC is the double of OAB. 2. Trisecting the circle People were so STUPID! They tried and tried to trisect with PARALLEL lines into segments, which INDEED is impossible. But I used SECTORS!! Let the circle K have midpoint O. Pick a point on the periphery as midpoint and draw a circle through O which meets K in A and B. The sector AOB has 1/3 area of circle K. 3. Squaring the cube Here, the DIMENSIONAL problem wasn't recognized. As squaring the cube (volume) with side length x requires a new side length x**2, x can't be a length with a unit, because then x**2 would be an AREA! So at least one unit length u:=1 must be given. Draw two perpendicular lines. At the intersection, mark x to the left and right and u to the top. Construct the circle through that three points in the usual way. It cuts off x**2/u at the bottom. As u was DEFINED 1, this is the sought side lenght. Now give me the NOBEL PRIZE! -- Hauke Reddmann <:-EX8 fc3a501@math.uni-hamburg.de PRIVATE EMAIL fc3a501@rzaixsrv1.rrz.uni-hamburg.de BACKUP reddmann@chemie.uni-hamburg.de SCIENCE ONLY