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

Home > Just Math > Calculus
Cut Wire (Posted on 2005-05-20) Difficulty: 3 of 5
A piece of wire is to be cut into two pieces (one bent into the shape of a regular p-gon and the other a regular q-gon).

If

1) p = 2*q,
2) 2*perimeter(q-gon) = 3*perimeter(p-gon), and
3) the sum of the two areas is minimized;

then what is the value of q?

See The Solution Submitted by Bractals    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution solution | Comment 2 of 6 |

The idea is to minimize the sum of the two areas by choosing q, which must be at least 3, making p at least 6.

The total perimeter is fixed, equal to the total length of the piece of wire.  The q-gon gets 3/5 of the length of the wire, while the p-gon gets 2/5.

As the number of sides is increased, with the same given perimeter, the area enclosed increases, so we want to make the number of sides as small as possible: that makes the value of q 3.


  Posted by Charlie on 2005-05-20 19:15:03
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 (2)
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