Geometry, Algebra, and Intuition
I have a confession to make: I have always found symbolic algebra more intuitive than geometric pictures. I think you’re supposed to feel the opposite way, and I greatly admire people who think and communicate in pictures, but for me, it’s usually a struggle.
For example, I have seen many pictorial “proofs without words” of the Pythagorean Theorem. I find some of them to be quite beautiful, but I also often find them difficult to unpack, and I never really think “oh, I could have come up with that myself.”
Here’s Pythagoras’ own proof⊕Image by William B. Faulk, lifted from the Pythagorean Theorem Wikipedia Page. It’s worth looking at some of the many other visual proofs given there. :
I like this proof a lot. It’s fairly simple to interpret (more so than some of the other examples in the genre), and quite convincing. We have
Even so, it’s odd to me that this diagram involves four copies of the triangle. This is one of those “I couldn’t have come up with this myself” stumbling blocks.
