Problem 1387. Points on a circle.

Created by James

Solve Later

This problem is related to 1283, Points on a Sphere. In this case, instead of a sphere, you have a circle. Given a radius R, calculate the number of points on the circumference of the circle that have two integer coordinates. For a circle of radius 5, you would have 12 points:

(0, 5) and (0, -5)
(5, 0) and (-5, 0)
(4, 3) and (4, -3)
(-4, 3) and (-4, -3)
(3, 4) and (3, -4)
(-3, 4) and (-3, -4)

Some radii are quite large, so watch out. Good luck!

Solve

Solution Stats

107 Solutions
23 Solvers

Last Solution submitted on Jan 16, 2025

Last 200 Solutions

Problem Comments

4 Comments

4 Comments

Show 1 older comment

Chris Cleveland on 14 Jul 2017

Great problem! Learned a bunch from others solutions as well.

HH on 3 Dec 2017

In the problem statement, I think you meant '3' and '4', rather than '1' and '2', in the respective +/- combinations.

James on 4 Dec 2017

Thanks for catching my stupidity on that one, HH. It's fixed now.

Rafael S.T. Vieira on 23 Jun 2020

The tip for this question is the sum of squares function, which I use in my solution. There are many possible solutions to this problem, but the huge circle radii limit what we can employ, so be careful.

Solution Comments

Show comments

Problem Recent Solvers23

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 1387. Points on a circle.

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers23

Suggested Problems

More from this Author80

Problem Tags

Community Treasure Hunt

Problem 1387. Points on a circle.

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers23

Suggested Problems

More from this Author80

Problem Tags

Community Treasure Hunt

Players