Pythagorean Numbers

Pythagorean numbers refer to the set of numbers that follow the Pythagorean theorem, which is a fundamental principle in geometry, particularly in the context of right-angled triangles. In a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as an equation relating the lengths of the sides a, b, and c, often written as a² + b² = c². The numbers a, b, and c are known as Pythagorean triples. In Hebrew, the term can be translated as מספרים פיתגוריים. In other languages, it is known as nombres pythagoriciens in French, pythagoreische Zahlen in German, and numeri pitagorici in Italian. These triples have been studied extensively since ancient times and have applications in various fields, including number theory, cryptography, and computer science.