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

Home > Shapes > Geometry
Triangulation of Numbers (Posted on 2008-03-18) Difficulty: 3 of 5
       W------------------------X
       |                      * |
       |    A              *    |          
       |                O       |
       |             *  * *  B  |	 
       |          *     *  *    |
       |       *        *   *   |
       |    *           *    *  |
       | *      D       *  C  * |
       Z----------------Q-------Y
What is the minimum area of rectangle WXYZ if all lengths are whole numbers, as are the areas of the similar triangles, denoted by A, B, C & D?

See The Solution Submitted by brianjn    
Rating: 3.6667 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: solution | Comment 4 of 7 |
(In reply to solution by Charlie)

Charlie wrote: "The guess is that each triangle is similar to a 3,4,5 right triangle....

......  I don't have a proof that this is a minimum, however, so the following program checks for solutions with an area of ......."

I am certain that in preparing this I found an unproven statement which reflected that a 3,4,5 right triangle had the minimum integral area.  My source would have been wikipedia but I couldn't relocate that in a hurry. 

However, the breadth of Maths, and it applications, rests upon certain axioms of which a statement like "The smallest integral area for a right triangle having sides of integral length is a 3,4,5".  We can't prove them, but we know intuitively the truth.

I am impressed that you took time out to bother testing against your given true belief. 


  Posted by brianjn on 2008-03-19 08:16:23
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 (12)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information