I'm a programmer and I've recently come back to math hoping to sharpen some of my skills. I did well in math in high school. I also did math competitively. I majored in music in college, so I stopped doing math pretty much after high school.
Lately, I've been distracted by geometry and have been thinking of spending some time getting seriously acquainted with the subject, starting with Euclid and working out from there. My exposure to geometry has been pretty much the standard middle/high school fare. Not very exciting...
Recently though, I've been fascinated by the subject. Is there any good reason for a programmer to study geometry? There are other branches of mathematics that would be more immediately applicable in my life.
Also, would studying geometry help develop proof writing skills? (something I desperately need)
I've also read that studying geometry can help sharpen "mathematical intuition," whatever that is. Is that true?