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

Home > Shapes
Circle Cover Conclusion (Posted on 2016-07-07) Difficulty: 3 of 5
A circle of unit radius is completely covered by four identical regular hexagons.

What is the smallest area of each hexagon?

No Solution Yet Submitted by K Sengupta    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Interpretation 2: Overlap Comment 2 of 2 |
Consider my previous solution.  Take the two hexagons that don't overlap, rotate them 30 degrees.  Then slide them towards each other until the two vertices of each touch sides of each of the other two hexagons.

Considering hexagons of unit side length:  the distance from the midpoint of the side the non-overlapping hexagons to the center of the rotated ones is (9-2√(3))/6.

The radius of the circle that fits is then √((43-12√(3))/12)≈1.306

If the circle has unit radius, the hexagon side length is the reciprocal of this: √(12/(43-12√(3)))≈.7350
And hexagon area (648+774√(3))/1417≈1.4034
  Posted by Jer on 2016-07-07 14:13:26
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 (3)
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