Pythagorean Theorem and Triangles

Today, young children sometimes first hear of the famous Pythagorean theorem from the mouth of the Scarecrow, when he finally gets a brain in MGM's 1939 film version of The Wizard of Oz. Alas, the Scarecrow's recitation of the famous theorem is completely wrong!
The Pythagorean theorem states that for any triangle, the square of the hypothenuse c is equal to the sum of the squares on the two (shorter) "leg" lengths a and b - which is written a^2 + b^2 = c^2. The theorem has more published proofs than any other, and Elisha Scott Loomie's book Pythagorean proposition contained 367 proofs.
Pythagorean triangles (PTs) are right triangles with integer sides. The " 3-4-5" PT - with legs of length 3 and 4, and a hypothenuse of length 5 - is the only PT with three sides as consecutive numbers and the only triangle with integers sides, the sum of whose sides (12) is equal to double its area (6).  After the 3-4-5 PT, the next triangle with consecutive leg lengths 21-20-29. The tenth such triangle is much larger: 27304197-273004196-38613965.
In 1643, French mathematician Pierre de Fermat (1601-1665) asked for a PT, such that both the hypothenuse c and the sum (a + b) had values that were square numbers. it was startling to find that the smallest three numbers satisfying these conditions are 4,565,486,027,761, 1, 061, 652,293,520, and 4,687,298,610,289. It turns out that the second such triangle would be so "large" that if its numbers were represented as feet, the triangle's legs would project from Earth to beyond sun!
Although Pythagoras is often credited wit the formulation of the Pythagorean theorem, evidence suggests that the theorem was developed by Hindu mathematician Baudhayana centuries earlier around 800 B.C. in his book Baudhayana Sulba Sutra. Pythagorean triangles were probably known  even earlier to Babylonians.