There are some areas of maths that anyone can speculate about or simply enjoy the beauty of without having to dig too deep into the underlying theory. Here are a few that have grabbed me.
My interest in Polyhedra started in my early teens when I came across a fascinating book called simply "Polyhedra" in my school library. Using the nets provided in this book, I made several models from coloured card which I hung from my bedroom ceiling. I've since sawed and planed my way through a dozen or so hardwood polyhedra, beautiful to look at and to hold, some of them still decorate my home.
- Kepler's Rhombic Dodecahedron
- This link takes you to a nice rotating model of this space-filling solid. The rest of the site is a rag-bag of interesting articles and java applets.
- Mark Newbold's Stereo 3D POV-Ray Polyhedra
- Mark's site has a lot of good sterograms of polyhedra, both anaglyph (red-blue glasses) and crossed-eye types.
- Wolfram World
- Previously known as Eric Weisstein's World of Mathematics. A very extensive maths site that's a bit hard to navigate, but worth it. Some nice rotatable Java applet polyhedra.
- The Geometry Junkyard Software
- Another fascinating collection. It's a pity that there are so many broken links.
If you want to explore beyond the simple symmetry of the cube, the following pages contain a collection of rotatable animated polyhedra, all of them powered by Martin Kraus's LiveGraphics3D Java Applet.
- Cubes & Octahedra
- Polyhedral transformations of the cube and octahedron.
- Stella Octangula
- Polyhedral transformations of the stella octangula (two tetrahedra in a cube).
- Rhombic dodecahedra
- Polyhedral transformations of rhombic dodecahedra.
- Polyhedral transformations of dodecahedra.
- Wire frame polyhedra
- Wire frame models of dodecahedra and icosahedra.
Whether you are trying to figure out the pattern of the primes, or just wondering how to factorise huge composite numbers and crack encryption, there is something challenging about this the most basic aspect of number theory.
- The Prime Pages
- Everything everything you wanted to know about primes, if you can find it.
- Fermat's Last Theorem - Fermat's One Proof
- Does what it says on the tin - all about Fermat's last theorem.
- Riemann Zeta Function graphics
- Some useful graphics which may (or may not) help in understanding this area of prime theory.
- Millennium Prize Problems
- Brief description of the Riemann hypothesis etc.
- The music of primes
- More about the Riemann hypothesis and prime numbers, with graphs to help visualize the problem.
Moirés are the interference patterns which emerge when two or more regularly spaced or repeating patterns are superimposed. They often engage my attention in an almost subliminal way - I notice the movement out of the corner of my eye and then there is nothing there. Just look through two layers of chain-link fence, or trellis, or netting, and you'll see what I mean.