While walking around the park taking bleak, wintry pictures, I happened upon a boy with a perfect-snowball-making device. I asked him if he would make one for me so I could photograph it. “I like taking pictures of math, ” I said. He produced the following sphere for me.
I then asked if he would hold the snowball in his hand so I could photograph that, too. He responded matter-of-factly, “Then I’ll throw it at you”. It seemed like a reasonable deal, so I agreed.
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I wonder if my students sometimes think to themselves, “I bet Mr. Honner will like this, because he’ll be able to blog about it.”
This is a cool sculpture inspired by a Hilbert curve, made from what looks to be left-over metal piping.
http://blog.makezine.com/math_monday_3d_hilbert_curve_in_ste/
A Hilbert Curve is constructed through an iterative process that is repeatedly self-similar. You start with a simple, bent path around the inside of a square, and then you take each straight part of that path and bend it to make it look what you started with. And repeat. Ad infinitum.
Given the infinite self-similarity (and some other properties), the Hilbert curve is a kind of fractal. A nice visual illustration can be found at Wikipedia: http://en.wikipedia.org/wiki/Hilbert_curve.
What’s especially interesting about Hilbert curves is that they essentially “fill up” the plane. This is seemingly paradoxical, in that you have a one-dimensional object (a path) that ends up equivalent to a two-dimensional object (a plane). For this reason, these are also referred to as space-filling curves.
I already have one plant that might be a fractal; I’ll be on the look-out for a space-filling vine!
If you are in need of a last-minute gift for the mathematician in your life, might I suggest the Pi Pizza Cutter!
http://www.thinkgeek.com/homeoffice/kitchen/e616/
I assume that this works in both degree and radian mode.
Who can resist a product with such excellent tag-lines?
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I’ve been working a lot with polar coordinates lately, which means holiday decorations like this
put me in mind of polar curves like
