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

Home > Shapes
4 cents (Posted on 2014-09-12) Difficulty: 3 of 5
Place four pennies on a table such that each touches at least one other.

For what arrangement will the area of the convex hull of this shape be maximized?

No Solution Yet Submitted by Jer    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Overlooked problem | Comment 1 of 11
This puzzle just came up randomly.  Hard to believe that nobody has commented in 16 months, so I will kick it off.

Instead of pennies, let's use 4 disks of unit radius and 0 thickness.

If laid in a straight line, the convex hull is 12 + Pi

If arranged in a square, the convex hull is also 12 + pi.

If arranged in a diamond shape, the convex hull is 8+ Pi + 2sqrt(3), which is approx .6 less than the other two.

It is hard to imagine a better arrangement, so I am going with a diamond.

Unless, of course, this is a trick question.  If the four are stacked one on top of another, the convex hull is only Pi

  Posted by Steve Herman on 2016-01-30 21:15:26
Please log in:
Remember me:
Sign up! | Forgot password

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

Copyright © 2002 - 2019 by Animus Pactum Consulting. All rights reserved. Privacy Information