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

Home > Shapes > Geometry
Integer points on circles. (Posted on 2011-02-28) Difficulty: 3 of 5
If a circle is centered on the origin and has radius r, it may pass through some points with integer coordinates. In fact, by symmetry, this will be a multiple of 4.

Find the smallest radius that will pass through 4n integer points where n=1,2,3,4,5.

Feel free to go further.

See The Solution Submitted by Jer    
Rating: 3.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts n = 5 (spoiler) | Comment 7 of 14 |
Playing around with Excel, I came up with a radius of 25*sqrt(2) = about 35.35534.  It passes through (5,35), (17,31), (25,25),(31,17) and (35,3).

5^2+35^2 = 17^2+31^2 = 25^2 + 25^2 = 1250.  I didn't see a lower value available, but maybe I missed something (plus, I was only looking for multiples of sqrt(2).

/*************************/

No, wait!  I wrote too soon.  25 works.
It passes through (0,25), (15,20),(20,15),(7,24) and (24,7).
25^2 = 15^2+20^2 = 7^2 + 24^2 =  625.
And now I really don't see a minimum.

I guess I'll tackle n = 4 next. 

  Posted by Steve Herman on 2011-03-01 03:07:21
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