Why π is irrational (Part 1 of 5)

8 June 2010

Through the next several posts, I will be taking you through a proof of why π is irrational. The proof was first given by Ivan Niven in 1947 and requires only basic calculus to understand it.
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7 June 2010

I got nerd sniped the other day by a post at The Math Less Traveled about an excellent puzzle/game called Manufactoria. It’s basically a set of puzzles involving queueing theory; it goes through a progression of levels, starting out at the exceptionally easy and progressing to the frustratingly hard. Here’s a screenshot of the thing:
Screenshot of Manufactoria
For now, just have fun playing with it!

Post #3: the Barkhausen effect

19 May 2010

I have an assignment for my electromagnetics class to come up with an “awesome E&M demo” that can be donated to the school’s science department (or make a clock or musical instrument, but I don’t want to do those). So I came up with the idea to make a Barkhausen effect demo. The effect is essentially as follows:

1. Ferromagnetic materials (such as iron) have magnetic “domains”–small regions in which all the magnetic dipoles of neighboring atoms align. In most cases, neighboring domains have different orientations so that the net field is zero.
2. An external magnetic field can change the boundaries of the domains by causing atoms at the boundaries to flip their dipoles.
3. When a migrating domain boundary reaches an impurity in the material (such as, for example, a clump of several atoms of copper in a lump of iron), the boundary bends around the impurity until it pinches off.
4. When the boundary pinches off, the net magnetic field of the lump of metal changes very slightly but very suddenly. The result is a tiny spike in the time-derivative of the magnetic flux through a cross section of the lump of metal.

That’s all there is to the effect. By itself, it’s not noticeable; however, you can wrap some wire around the metal–essentially making an electromagnet–and connect the end to an amplifier and speaker. If you then wiggle a magnet around right next to the metal, you should hear some clicking–that’s the sound of domains flipping and reconnecting.