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

Home > Shapes > Geometry
Points On A Circle (Posted on 2004-08-14) Difficulty: 4 of 5
I placed six points on the circumference of a circle such that the distance between any two of the points is an integer. What is the smallest such circle I could use?

What if each distance must be unique?

No Solution Yet Submitted by ThoughtProvoker    
Rating: 4.4286 (7 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution First part (Solution) | Comment 7 of 17 |

If the distances (straight lines, not curves) don't have to be distinct, then the smallest circle appears to be one of radius 12.5 units, with the six points as follows (centered on the origin of the xy-axes):

Point 1: (12.5 , 0)
Point 2: (10.54 , 6.72)
Point 3: (-3.5 , 12)
Point 4: (-12.5 , 0)
Point 5: (-10.54 , -6.72)
Point 6: (3.5, -12)
 
Distances:
Points 1 to 2:  7
Points 1 to 3:  20
Points 1 to 4:  25
Points 1 to 5:  24
Points 1 to 6:  15
Points 2 to 3:  15
Points 2 to 4:  24
Points 2 to 5:  25
Points 2 to 6:  20
Points 3 to 4:  15
Points 3 to 5:  20
Points 3 to 6:  25
Points 4 to 5:  7
Points 4 to 6:  20
Points 5 to 6:  15
 
 

  Posted by Penny on 2004-08-15 21:39:33
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 (15)
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