There are over 367 known proofs for this, including a proof by differential equations, a proof using similar triangles, a proof by rearrangement, and Euclid's proof which appeared as Proposition 47 in Book 1 of the Elements.
There are over 367 known proofs for this, including a proof by differential equations, a proof using similar triangles, a proof by rearrangement, and Euclid's proof which appeared as Proposition 47 in Book 1 of the Elements. However, there cannot be any (*) trigonometric proof for it because the trigonometric identities are themselves proven using it. By its converse, which is also true, tying 12 equally-spaced knots in a loop of rope may have allowed ancient Egyptians to construct right angles. A more general form of it is the law of cosines, which holds true for all triangles. FTP, name this theorem of Euclidean geometry which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of its legs.
There are over 367 known proofs for this, including a proof by differential equations, a proof using similar triangles, a proof by rearrangement, and Euclid's proof which appeared as Proposition 47 in Book 1 of the Elements.
{Pythagorean} theorem