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.”
Appreciation Geometry
Hilbert Curves
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!
Appreciation
Pi Pizza Cutter
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?
- Cut your pie with Pi!
- No Math Test Required For Use.
Click here to see more in Appreciation.
Appreciation
Polar Decorations
I’ve been working a lot with polar coordinates lately, which means holiday decorations like this
put me in mind of polar curves like
Appreciation Geometry
Another Strange Circle
For the fashion-conscious and number-conscious, we have this stylish silver necklace made from the first hundred of so digits of pi. If you have any mathemagicians on your holiday shopping list, you’re welcome. Unfortunately I didn’t have much luck ordering one, as my Japanese is pretty rusty.
I’m actually considering the question “Find a circle whose circumference is pi” for an upcoming exam, just so I could show this as the answer.
Oddly enough, this isn’t even my favorite pi-themed necklace!