Pythagorean triangles with sum of its two legs as Dodecic

Abstract

Number Theory is almost four thousand years old. In ancient clay tablet in Babylon, integral solutions of Pythagorean equations were listed down. Pythagoras theorem has always fascinated young and old mind alike. More than four hundred proofs of the Pythagoras theorem have been discovered so far. Pythagoras theorem is applied in almost every sphere of science- from geometry to Einstein’s theory of relativity. New Pythagorean triangles are being discovered which satisfy certain constraints. Integral solutions of Diophantine equations related to Pythagorean equation are sought by many mathematicians. Applications of these triangles are also being explored in various fields of knowledge. In this paper, we have found nineteen extraordinary Pythagorean Triangles where their sum of two legs are dodecic numbers. These triangles are found by solving the dodecic Diophantine equation using the software Mathematica. Some interesting properties of these Pythagorean Triangles are also observed. Their applications can be explored in cryptography.