My Math Forum Self-intersecting Polygons and Simple Polygons
 User Name Remember Me? Password

 Algebra Pre-Algebra and Basic Algebra Math Forum

 July 27th, 2009, 05:46 PM #1 Newbie   Joined: May 2009 Posts: 14 Thanks: 0 Self-intersecting Polygons and Simple Polygons Intuitively this seems true to me, but I am not certain and haven't been able to find any source specifically addressing it. Any help would be appreciated. Can we take every self-intersecting polygon and, ignoring the angles, form a simple (non-self-intersecting) polygon with the same side lengths as the self-intersecting polygon (and with side lengths that remain in the same order)? For instance, lets say we have a self-intersecting 4-gon (quadrilateral) that looks like an hourglass. Intuitively we might imagine that the lengths are rigid rods and the connections are small ball-bearings. Can we pick it up, twist it and lay it back down so that it no longer looks like an hourglass, but instead a simple quadrilateral that lays flat on the ground? Its strange, I don't even see this addressed in Coxeter's writings that I have, perhaps because it is so elementary (my Dear Watson). -Eric
 July 27th, 2009, 10:11 PM #2 Global Moderator   Joined: Dec 2006 Posts: 20,937 Thanks: 2210 It's trivial to prove for a quadrilateral; just "unfold" it.
 July 28th, 2009, 09:28 AM #3 Newbie   Joined: May 2009 Posts: 14 Thanks: 0 Re: Self-intersecting Polygons and Simple Polygons The quadrilateral was an instance, I was curious about any self intersecting n-gon.

Search tags for this page

### is a intersecting hourglass a polygon

Click on a term to search for related topics.
 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post benice Art 0 July 4th, 2013 09:27 PM automan12 Algebra 0 May 30th, 2013 12:32 AM benice Art 4 May 25th, 2012 09:44 PM mathdigger Algebra 1 September 14th, 2010 08:42 AM leonhardeuler Real Analysis 2 September 5th, 2007 07:22 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top

Copyright © 2019 My Math Forum. All rights reserved.