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

Home > Shapes
Covering a rectangle by circles (Posted on 2012-01-30) Difficulty: 2 of 5
Prove, that if a given rectangle can be covered by 100 circles each of r=2, then it can be covered by 400 circles each of r=1.

See The Solution Submitted by Ady TZIDON    
Rating: 4.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): Possible solution | Comment 4 of 6 |
(In reply to re: Possible solution by Steve Herman)

I assumed what was meant was that the circles 'covered' the rectangle in the sense of the densest possible packing i.e. there would still be some (minimal) gaps. This would make the rectangle bigger than the total area of the circles.

I have to admit I hadn't considered the alternative of 'completely covered', but on brief reflection I'm not sure it matters; in the first case there is a constant 'efficiency' factor, x, less than 1; in the second there is an equivalent 'inefficiency' factor, say y, greater than 1. This factor still cancels leaving 400pi.

To put it another way, in the first case the circles are inscribed within the corresponding hexagons, in the second case, the hexagons  are circumscribed by the circles.

Edited on January 31, 2012, 11:31 am
  Posted by broll on 2012-01-31 11:02:56

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 (4)
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