Vi Hart is one of the most brilliant people I've ever found on the internet. She's a recreational mathematician - someone who plays with numbers and ideas for the fun and beauty of it, not to solve specialized problems or prove obscure theorems. She might be the coolest recreational mathematician since Martin Gardner.
Recreational mathematics: "I can quit it any time I want, I swear!"
A lot of her stuff is with geometry. She builds hyperbolic planes and geometric solids out of balloons and beads, fruit and candy and pennies, and more.
But, her coolest stuff is the videos she makes. She just starts with a doodle - a line looping on a paper, or snakes, or a line dividing in two - the sort of things you draw when you're bored in math class. The, she shows how it makes patterns. What happens if you make a spiral of numbers, and circle the primes? You get straight lines - a totally unexpected result.
What if you have a line divide every so often, so that you get 2, then 4, then 8, lines, and so on? You get a neat tree. But if you ignore when two lines join, you get a totally different pattern.
Ms. Hart has lots of neat videos in her Youtube channel; I command you to watch a few.
Very descriptive and nicely-done New York Times Article
The Boston Projection
1 day ago