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

Home > Shapes
The art of fencing (Posted on 2006-12-27) Difficulty: 5 of 5
Three neighbours buy a piece of land that they want to cultivate as a garden. The land has the shape of a square. To avoid that their petunias and pumpkins get in the way of each other, they decide to split the garden into three cells of equal area. To keep things simple, the border between two adjacent cells should be a straight line. Under these constraints, can you help them to divide their garden such that the total length of the fence is minimized? How would you divide the garden for five, six, seven or eight neighbours?

No Solution Yet Submitted by JLo    
Rating: 3.0000 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Hints/Tips idea | Comment 1 of 6

In minimum fencing problems like this there should be a central point where the three lines meet at 120-degree angles. Soap bubbles stretched over a frame in a 3-D simulation of a 2-D problem will seek this 120-degree angle, or rather, set of angles.

So the only determination to be made is where this central meeting point is, and what orientation the three vanes (fences) have.


  Posted by Charlie on 2006-12-27 14:50:58
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 (8)
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