Counting Pythagorean circles
Abstract
This article deals with right-angled triangles that have positive integer sides. The three lengths of these sides may be reduced to expressions in two (positive integer) parameters. In turn, the radii of their inscribed and excircles can be expressed in terms of the parameters. Using these and the properties of multiplicative functions, the number of such triangles with a given arbitrary integer inradius may be determined. This is repeated for the excircle on the shortest side.
Fields of Study & Subjects
Analytic Number Theory Research
Algebraic Geometry and Number Theory
Mathematics and Applications
Publication details
- Journal / source
- The Mathematical Gazette
- Volume
- 110
- Issue
- 577
- Pages
- 37–48
- Publication date
- 2 January 2026
- Language
- EN