This is a cool collection of graphs of relations using software called GrafEq:
http://www.xamuel.com/graphs-of-implicit-equations/
For example, at the right is the graph of
There are several other cool graphs displayed here.
It is worth noting that Wolfram Alpha can graph these relations, too. For example, here is the above equation:; while Wolfram Alpha captures the spirit of the graph, the image is not as detailed or attractive as the GrafEq version.
Is this the world’s only computable license plate?
A little zooming in may be helpful.
For the record, this is approximately 5.999086179.
A lot of nervous energy was building up while I was waiting in the wings at the 2012 TEDxNYED conference.
Luckily, I found some polygons to play around with, so I converted my anxiety into mathematical art.
This is a nice list of famous unsolved math problems from Wolfram MathWorld:
http://mathworld.wolfram.com/UnsolvedProblems.html
There are some well-known problems here, like the Goldbach Conjecture and the Collatz Conjecture, and some lesser-known open problems like finding an Euler Brick with an integral space diagonal.
It’s especially nice that several of these challenges are easy to explain to non-mathematicians. For example, the Goldbach Conjecture asks “Can every even number be written as the sum of two prime numbers?” Somewhat surprisingly, after nearly 300 years, the best answer we have is probably.
I think I’ll make this page next year’s summer homework assignment.
This is an amazing collection of interactive diagrams of mathematical knots:
Click on any of the hundred or so knots here to go to a flash-based interactive diagram of the knot that can be rotated and manipulated.