Pythagorean Triangles

Abstract

This book is a mathematical study of Pythagorean triangles- right angles with natural sides. The Pythagorean Theorem was fundamental to many theorems of Elementary Geometry and foremost offers a solution (in integers) to the indefinite equation of three unknowns: X2 + Y2 = Z2. This text discusses different types of Pythagorean triangles including primitive Pythagorean triangles, triangles with the same areas and perimeters, and rational triangles. Even though this book does not contain any information about the symbol tetractys, it offers insight into Pythagorean triangles and mathematics: the smallest Pythagorean triangle (x,y,z), for example, must have arms that are relatively prime; and such a triangle is also called a primitive triangle (x,y,z), where the numbers x and y must be odd or even i.e. both x and y cannot be odd/even .