2008/09/04 by Konstantine Zelator, Zelator, Konstantine · 1 citation
Computer Science · Mathematics · #History and Theory of Mathematics #Mathematics and Applications #Mathematics, Computing, and Information Processing #math.GM
paper · pdf · doi:10.48550/arxiv.0809.0902
26 pages, 6 figures
arxiv created 2008/09/04 · arxiv updated 2009/12/01
This is an exhaustive study of the seventeen elements of Pythagorean triangles, from the point of view of when such an element is an irrational number, a rational number, or an integer. For each of these 17 elements,precice conditions for their integrality,rationality, or irrationality; are given. These 17 elements are:The radius of the incircle, the radius of the circumscribed circle,the three radii of the three exterior circles tangential to the three lines containing the triangles'sides, the lengths of the three heights, the lenghts of the three internal angle bisectors, the lengthe of the three external angle bisectors, and the lengths of the three medians.