Join the Elsevier boycott! Over 6700 top scholars have already done it. And let your colleagues know! Download a copy of the Elsevier boycott poster and print it out — or else just download and print this image:
Archimedean tilings are beautiful patterns whose possibility is predicted — but not guaranteed — by solutions to a simple equation. I'll explain what that equation says, where it comes from, and what happens when things don't quite work!
If you plot all the roots of polynomials whose coefficients are 1 and -1, say polynomials of some large degree like 24, you get a picture like this:
How can we understand the amazing patterns here? Read The Beauty of Roots for some answers!
Sometimes you can learn a lot from an old piece of clay. This is a Babylonian clay tablet from around 1700 BC. It contains an amazingly good approximation to the square root of 2. How could they have calculated it? To find out, see my article with Richard Elwes.
The Azimuth Project gang is working on some simple models that can be viewed on your web browser. For a basic one, try this.
There's a complexity barrier built into the very laws of logic: roughly speaking, while lots of things are more complex than this, we can't prove any specific thing is more complex than this. And this barrier is surprisingly low! Just how low? Read my article on Surprises in Logic.
This article also explains what happens when we combine the complexity barrier idea with the famous 'unexpected hanging paradox'.
In week318 of This Week's Finds, start learning about "Milankovitch cycles": periodic changes in the Earth's orbit and tilt that may help cause the ice ages. It's not easy to see how they affect the climate:
However, I'll show you some evidence that they do!
No crystal in nature can be shaped like a regular dodecahedron, or a regular icosahedron. But iron pyrite can form a "pseudo-icosahedron", and Johan Kjellman pointed out this nice example:
For more, read my page on fool's gold.
By the way, Stewart Dickson has created a stellated dodecahedron that acts as a 3d version of the Pythagorean pentagram! I talked about the Pythagorean pentagram in "week265". Here's a picture of it, drawn by James Dolan:
If you take a pentagram and keep drawing lines through points that are already present, you can form this picture, packed with pentagrams that are related by various powers of the golden ratio. Here's another view, created by Stewart Dickson:
If you like math and chemistry, try reading about chemistry and the Desargues graph:
On a different note, here's a really easy introduction to the octonions and their role in string theory:
For common questions about physics, you can't beat this:
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© 2011 John Baez
baez@math.removethis.ucr.andthis.edu