this post was submitted on 19 Dec 2023
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A^2 + B^2 = C^2 is known as the Pythagorean theorem. This theorem explains the proportionality of the 3 sides of a right triangle (a triangle with 1 corner angle = 90 degrees). If you know the length of 2 sides (in his example, the wall beams) you can find out the length of the third (in his example, this would be the supporting strut spanning the beams that meet at a 90 degree angle). If their example is explaining a beam that spans the room from 1 corner to the other, you still use this formula as a rectangle is 2 right triangles that meet along their hypotenuse (the longest leg of a right triangle, or the length you are solving for in this problem). The 2 known sides are the length/width of the room, and you solve for the 3rd side, your diagonal beam
Did Pythagoras even know about sin, cos and tan? I am reluctant to call A^2 +B^2 =C^2 trigonometry.
Hipparchus, the alleged founder of trigonometry, was alive 350 years after Pythagoras (500BC to 150BC).
Completely fair point, that I do not think I have the knowledge to speak on. On the Trigonometry Wikipedia page, he pops up a few times, and many trig identities are known as pythagorean identities. Perhaps its not fully trig, but was used as a basis to help discover trig? Without having the understanding pythagorus gave mathematicians regarding triangles, I would think it would be pretty hard to begin developing deeper math regarding said triangles
Squaring using 3+4=5 is one of the oldest relationships used by masons. don't need a ruler, just a piece of string or straight edge. Pythagoras described the relationship on paper