Geometry, Algebra, and Intuition

Jason Merrill:

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 proofImage 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.: