All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Shapes
Cutting polygons (Posted on 2006-09-24) Difficulty: 3 of 5
Describe how every simple polygon can be tranformed into any other simple polygon with the same area by dissecting it with straight cuts and rearranging the pieces.

See The Solution Submitted by JLo    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): spoiler | Comment 5 of 9 |
(In reply to re: spoiler by brianjn)

 
Use Art M's procedure to convert simple polygon P_1
into square S_1 and simple polygon P_2 into square S_2.
The squares are congruent by definition. 
Apply the cuts making up square S_1 to square S_2.
Now square S_2 is made up of pieces that can form
simple polygon P_1 or simple polygon P_2.
To convert a rectangle into a square see
  www.cut-the-knot.org/Curriculum/Geometry/SquareRectangle.shtml
To combine two squares into one see Proof #2 under
  www.cut-the-knot.org/pythagoras/index.shtml
 

Edited on September 26, 2006, 4:14 pm
  Posted by Bractals on 2006-09-26 16:11:24

Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (11)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information