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

Home > Shapes > Geometry
Painted Sphere (Posted on 2007-02-13) Difficulty: 3 of 5
A sphere is painted black and white. Show that there are 3 equidistant points of the same color.

No Solution Yet Submitted by Art M    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Simplify | Comment 5 of 9 |
(In reply to Simplify by Jer)

By "arbitrarily small", you must mean "infinitely small", in which case, all the points are the same point.

On the sphere, the excess of the total angles over 180 degrees, of any equilateral triangle are proportional to the area of the sphere, so the excess of each angle over 60 degrees is also proportional to the area of the triangle.  For example, an equilateral triangle with all 90-degree angles is one octant of the full sphere.  Only as the size of the triange approaches zero does each angle approach 60 degrees. In the construction defined, the triangles have different sizes so the angles are different sizes, none of them 60 degrees, even though the differences be ever so slight.

  Posted by Charlie on 2007-02-13 17:43:43

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