I Learned the Pythagorean Theorem

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. 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.

I probably had a weird introduction to Pythagorean triples in my childhood -- through my Meccano kit. 3,4,5 was of course the most common one. Other bases that worked were 6,8,9 and 12. The 12 was the more interesting one. You brace a right angle with 3,4,5 and then examine which other holes align.

I would be happy to know if others had a similar experience. I date myself though.

This kit was Russian made and had just excellent finish, tiny chrome plated nuts and bolts.I haven't thought about it in a while.

Now I need to look for it at my parent's house.

The day I learned the Pythagorean theorem, I also learned the Triangle inequality. From then on every corner parking lot or diagonal sidewalk through a park became a shortcut to be taken, and enjoyed.

Little wonder that the way I got through the more boring homework assignments in 100 and 200 level CS classes later on was to turn in the most efficient version of the answer instead of the most expedient.