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I have explained the Pythagorean Theorem to many people. It is part of an explanation that I give that simple does not mean easy. Math is simple in a way that w
by btilly 11mo ago
I have explained the Pythagorean Theorem to many people. It is part of an explanation that I give that simple does not mean easy. Math is simple in a way that we are not wired for. And so a key to not being frustrated is to realize that there is nothing wrong with us that we sometimes struggle to understand simple things.
As part of it, I show how simple the Pythagorean theorem is to prove. The same proof as https://etc.usf.edu/clipart/43500/43501/pythag3_43501.htm https://etc.usf.edu/clipart/43500/43501/pythag3_43501.htm. It can literally be drawn on the napkin.
You start with two squares of size a+b. You cut one into a square of size a, a square of size b, and 4 right-angled triangles a-b-c. You cut the other into 4 right angled triangles and a square of size c. When you eliminate the triangles (that have equal area), we're left with a^2 + b^2 = c^2.
The point being that it can be very hard to come up with such a simple thing. And it can sometimes take a while to truly accept it. Because we messy humans are wired for certain kinds of complex - like recognizing voices - and not for always getting simple right.
- srean 11mo agoThe other old 'proof without words' is this one https://en.wikipedia.org/wiki/Xuan_tu https://en.wikipedia.org/wiki/Xuan_tu