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This was something I worked on a while back but never got around to posting. This is my rendition of Ansel Adams’ Rose and Driftwood.

I didn’t have any driftwood, so my desk had to suffice. Also, origami roses are kind of difficult to make. I was quite proud of how mine turned out. Here’s the real thing for comparison.

A stereographic projection is a mapping that projects a sphere onto a plane. Stereographic projections occur in many areas of math. In fact, this past summer when I was studying minimal surfaces, we used a stereographic projection in the proof of Berstein’s Theorem (a major result in minimal surface theory). More recently, in the topology class I am currently enrolled in, a stereographic projection is used to show that the unit circle is the one point compactification of the real line.

Stereographic projections have a wide variety of uses in the math world, so what? Well, it turns out there are some pretty cool applications of them outside the pure math world. The most practical example is in the making of world maps. Since the Earth is a sphere, in order to project the Earth onto a flat piece of paper, to make a map, a stereographic projection is used.

But this is what’s really cool…

We can go the other way, project a plane onto a sphere. So imagine this, you take a picture, which is flat. We can project that image onto a sphere to get something that looks like this

photo courtesy of wikipedia

On Christmas eve my family and I went around looking at Christmas lights. This is the Balian House in Altadena. We used to go and look at the Christmas lights here when I was much younger and it’s actually exactly as I remember. Apparently the Balian family used to (or still does) own an ice cream company and this was the house they lived in. I’m not sure if anyone lives here now. I think the family just owns it and they still decorate it for Christmas.

The Balian House

The day after Christmas my family went shopping, I decided to go to the Huntington Library in San Marino. It was very crowded. I especially like the Japanese garden they have.

Japanese Garden

Zen Garden

 

Click here for more pictures. Click here for the mathematics about the picture.