Pythagoras Theorem – A crucial link between geometry and numbers

Pythagoras Theorem (PT) is the most remarkable contribution to mathematics of Pythagoras (ca. 570 BC – ca. 495 BC). Pythagoras Theorem helps translate the structure of nature into numbers. Among other things, his theorem brought about a crucial link between geometry and numbers. Let us look at the following identities:
9 + 16 = 25; 49 + 576 = 625; 25 + 144 = 169 and 64 + 225 = 289. They appear to be quite innocuous. But a more careful look into them could establish that these can be written as 3² + 4² = 5²; 7² + 24² = 25²;
5² + 12² = 13² and 8² + 15² = 17². In other words, trios like (3, 4, 5); (7, 24, 25); (5, 12, 13) and (8, 15, 17) can be the lengths of the three sides of a right-angled triangle, the largest one among them being the hypotenuse as according to PT, if the perpendicular sides and the hypotenuse of a right-angled triangle are respectively a, b and c, then a² + b² = c².