Parabolic Cooking

As I read about parabolas on the mathisfun page, I couldn't help but be fascinated by the "Reflector" example. It displays many different rays, all bouncing off the inside of a parabola, coming together in a "focus point." This had never been covered in class, so it was quite new to me. It certainly made sense though. The lightbulb in a flashlight lies at the focus point, and is surrounded by a parabolic mirror.

Anyways, I realized that if a parabolic mirror were placed in the sun, it would direct all of the suns rays to its focus point. The heat would be intense at this point, because all of the energy is focused at that point. I realized that this is sort of the concept behind a solar oven. However, a traditional solar oven is much less efficient than a parabolic mirror, as it uses flat pieces of tin foil which a) don't reflect as much light b) reflect the light over a much more broad area. A parabolic mirror, forming a sort of dish, would be a super efficient solar oven. A small surface could be install at the surface point, It could be used to bake items which require lesser amounts of heat, such as chocolate chip cookies. This oven could be installed in any spot outside, on a pivot, allowing the dish to be rotated towards the sun. A parabolic mirror would not only work great as an oven, but it could be used by anyone and never require any extra energy.

Tesselations... in 3D!

After reading the Jamm'n Peaches blog, I was intrigued. I decided to look into it further, and after a bit of reading I learned of something quite interesting. Not only is tessellation possible on a two-dimensional plane, but also in three-dimensional space! Such tessellations are referred to as "honeycombs." Interestingly enough, there are many shapes that are able to tesselate in 3D: truncated octahedrons, rhombic dodecahedrons, and of course, prisms. But these prisms, just like their two-dimensional counterparts, must be either a square, a triangle, or a hexagon. The rules for space-filling tessellation are similar to that of two-dimensional tessellations; instead of leaving no area unfilled, honeycombs call for no space to go unfilled. Many of these tessellations can be found in nature. However, one tessellation is found all around us: the cubic tessellation. They can be found from hotels all the way to shelves.

http://en.wikipedia.org/wiki/Tessellation
http://en.wikipedia.org/wiki/Honeycomb_(geometry)

Math Jokes!

Math isn't always the most fun subject. It is good to insert a bit of humor into it! Here are some math jokes to lighten the mood.

Why should you never drink root beer out of a square glass? You'll end up with just beer!

Why do you never see mathematicians at the beach? They don't have the sine and cosine, so they can't get a tan!

If only the US had 53 states. Then we would truly be one nation, indivisible. (53 is prime).

And finally,