2008/03/25 by Konstantine Zelator, Konstantine "Hermes" Zelator, Zelator, Konstantine "Hermes"
Engineering · Mathematics · #11A #11D #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #FOS: Mathematics #General Mathematics (math.GM) #History and Theory of Mathematics #Mathematics and Applications #math.GM #msc:11A #msc:11D
paper · pdf · doi:10.48550/arxiv.0803.3605
27 pages
arxiv created 2008/03/25 · openalex publication_date 2008/03/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
There are four characteristic circles for each triangle on a plane. All for are tangential to the three straight lines containing the triangles' three sides. Three are exterior circles, the fourth is the in-circle. When the triangle is Pythagorean, the four diameters are integers. Consider a Pythagorean triangle with the property that one leglength is a perfect(or integer)square, and with one of the four diameters also a integer square.Of the eight resulting combinations, we prove that only six are possible or can occur. We then completely parametrically describe the six families; each corresponding to one of the six combinations.