Article View: k12.ed.math
Article #519Re: heres a question
From: David G Radcliffe
Date: Tue, 26 Jan 1993 22:31
Date: Tue, 26 Jan 1993 22:31
21 lines
1412 bytes
1412 bytes
Brian Mcdonald (Brian.Mcdonald@p4.f18.n128.z1.fidonet.org) wrote: : how many polygons are there that all its sides are longer than any of its : diagonals : ?????????????????????????peace and i'm outa here There are infinitely many. Consider the polygon ABCD, with A = (-2,0), B = (x,1), C = (0,0), and D = (x,-1). If x > sqrt(3) then all the sides are longer than the diagonals. If you allow polygons to intersect themselves, then you can draw an n-pointed star with this property provided n is odd and greater than 4. Is it possible to find a pentagon which does not intersect itself with this property? Is there an equilateral polygon with 4 or more sides having this property? Can you prove that no convex polygon with 4 or more sides can have this property? Are there other conjectures about this problem which you find interesting? -- David Radcliffe radcliff@csd4.csd.uwm.edu
Technical Details
Message-ID:
<1k4e3mINNp0e@uwm.edu>Path:
arc1-ca.pugleaf.net!sparky!uunet!zeus.ieee.org!overload.lbl.gov!agate!spool.mu.edu!uwm.edu!csd4.csd.uwm.edu!radcliffReferences:
<41295.2B62BCAE@puddle.fidonet.org>Show Full Headers
Complete Article Headers
Path: arc1-ca.pugleaf.net!sparky!uunet!zeus.ieee.org!overload.lbl.gov!agate!spool.mu.edu!uwm.edu!csd4.csd.uwm.edu!radcliff From: radcliff@csd4.csd.uwm.edu (David G Radcliffe) Newsgroups: k12.ed.math Subject: Re: heres a question Date: 26 Jan 1993 22:31:18 GMT Organization: UW-Milwaukee Math Department Lines: 21 Message-ID: <1k4e3mINNp0e@uwm.edu> References: <41295.2B62BCAE@puddle.fidonet.org> NNTP-Posting-Host: 129.89.7.4 X-Newsreader: TIN [version 1.1 PL8]