lpetrich
Contributor
Pythagorean theorem - Pythagoras's Theorem - a theorem with numerous proofs, a theorem that has been at least partially recognized for many centuries in the literate parts of the world. Though named after Pythagoras - Pythagoras (Stanford Encyclopedia of Philosophy), it is doubtful whether he himself came up with a proof of it, and it must be noted that it is difficult to distinguish fact from fiction about him. Was he a vegetarian? Did he eat the meat of sacrificed animals? Did he sacrifice animals? However, the surviving sources on him agree that he forbade the eating of beans. His followers formed a sort of religious cult or philosophical school, Pythagoreanism - Pythagoreanism (Stanford Encyclopedia of Philosophy), and Plato was greatly influenced by that.
For side lengths a, b, c of a right triangle, where a and b are the lengths of the sides next to the right angle and c the length of the side opposite that angle, the hypotenuse, it is
a2 + b2 = c2
For a spherical surface with radius R,
cos(a/R)*cos(b/R) = cos(c/R)
For a hyperbolic surface with radius factor R,
cosh(a/R)*cosh(b/R) = cosh(c/R)
For side lengths a, b, c of a right triangle, where a and b are the lengths of the sides next to the right angle and c the length of the side opposite that angle, the hypotenuse, it is
a2 + b2 = c2
For a spherical surface with radius R,
cos(a/R)*cos(b/R) = cos(c/R)
For a hyperbolic surface with radius factor R,
cosh(a/R)*cosh(b/R) = cosh(c/R)