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Jan. 30th, 2008 @ 09:55 pm More of the Best, Programming and Otherwise
Current Mood: chipper
Programming:Other:
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L33t
Oct. 21st, 2006 @ 12:53 am Soccer Ball Theorem Proof
Current Mood: thoughtful
Tags:
Here's the answer to that homework problem I mentioned earlier. To restate the problem:

A ball is sewn together from pentagonal and hexagonal pieces of material. Each edge of each polygon lines up exactly with an edge of another polygon. Three polygons meet at each corner of each polygon. Prove that the ball must contain exactly 12 pentagons.

The answer to this problem is simple... )
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Skilled
Oct. 18th, 2006 @ 12:55 am The Soccer Ball Theorem
Current Mood: contemplative
Current Music: This Week in Tech #73
Tags: ,
The following problem was on my homework (paraphrased):

A ball is sewn together from pentagonal and hexagonal pieces of material. Each edge of each polygon lines up exactly with an edge of another polygon. Three polygons meet at each corner of each polygon. Prove that the ball must contain exactly 12 pentagons.

It's quite the beautiful proof.

Hint )
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Skilled
Sep. 8th, 2004 @ 12:09 am To Work
Current Mood: busy
Tags:
L33tminion: To work! ... Oh, sorry, I though you were proposing a toast...

Sam: *shakes head*


I didn't have any classes this morning (although I did get some work done), but the afternoon was very busy. After software design, which was unexceptional, was the cohort, where we split into teams and began work on our project for the quarter, bottle rockets. We're going to use this as a center point for our curriculum, allowing us to apply to what we learned (physics, calculus, Matlab, mathematical modeling, experimental design, the scientific method, teamwork, design, etc.).

Afterwords, I attended a guest lecture given by Dr. Arthur Benjamin, a professor of Applied Mathematics from Harvey Mudd University (and a mathematical genius and exceptional human calculator).

More on the lecture (interesting, but long)... )
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L33t
Jul. 19th, 2004 @ 09:58 pm Soap Bubble Science
Current Mood: happy
Tags: ,
Yesterday's lecture on chaos theory was interesting, but today's lecture, which was on the physical properties of soap films, was by far the best lecture this session. The lecture showed how properties of soap bubbles can be used to demonstrate solutions to minimization problems.

More Details on the Lecture )

The professor also gave the following problem. How can you construct a square of side length a given two points a units apart using only a compass (no straight edge)? I've thought about this for a little, but so far I haven't figured it out. I might work on it a little later.

Today in lab, I finished working on the first draft for our final report. Tomorrow we will finish the report and begin work on our presentation.
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L33t
Jul. 6th, 2004 @ 06:54 pm Calm Before the Research
Current Mood: energetic
Tags: ,
Today was pretty relaxing. I got my kit of stuff, which includes a map and a really nice hat.

The group spent the morning attending lectures on the different research projects, and the afternoon interviewing with the project coordinators who will make the project assignments.

I interviewed with the Mathematics and Computer Science Coordinator. My top 5 project choices were:
1. Image Completion Using Multiscale Interpolation (Computer Vision)
2. Using Genetic Algorithms to Solve a Simplified Version of the Protein Folding Problem (Genetic Algorithms)
3. Reconstructing Motions from Data Recorded from a Sensor Glove (Data Recording)
4. Identifying Objects in a Database from an Image Despite Arbitrary Lighting (Computer Vision)
5. Proving that a Simplified Version of a Game of Minesweeper is NP-Complete (Complexity Theory)

The interviewer seemed impressed by my ComSci knowledge (I think I am the only serious Computer Science person in the program, or at least one of a few) and offered me number 3 as I was telling him my choices (It wasn't mentioned in the lectures, and I only had four projects chosen at the time).

After my interview, I took a walk to get my glasses fixed (I lost a nosepiece). The walk was long, and I wasn't sure of the directions, but I was finally sucessful. The walk would have been really nice, except that it is so hot and humid here (remember: hat, water bottle, sunscreen). At least the buildings are all air-conditioned.

Extended Weather Forcast )

Tonight, a party. And project assignments will be revealed.
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L33t
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