Sunday, September 26, 2010

dynamic geometry challenge?

I have recently been working on a few of the Project Euler problems (I just solved problem 171 {but I'm not telling the answer}) and I started wondering if there could be any dynamic geometry contests of a similar nature. Or any dynamic geometry contests at all. Each Project Euler problem deals with a fairly elementary concept, generally having to do with number theory. The problem may describe some property of a set of integers and you are asked to find the sum of the numbers below a billion having that property, for example. To solve the simple problems, a brute force approach may work, but the more difficult problems require some creativity and skill. I enjoy it immensely.

What could be done to create the same sort of stimulating set of really sound questions that would let people hone skills in the dynamic geometry environment? Questions that are easy to understand but whose answer could not be obtained without a fairly solid construction, the type of questions that would stimulate expertise with tools like Sketchpad.

If dynamic geometry is ultimately no more than an illustration or diagram, perhaps it is never really the best way to solve a problem. Are there (interesting) mathematical problems that can be resolved using Sketchpad which cannot be practically approached in other environments?

3 comments:

  1. I did some programming eons ago and have done nothing of the sort in a long time. Would you be able to recommend which program I should invest my time in to help me (and my students) solve problems of the sort posed at Project Euler?

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  2. @ Anonymous: I have enjoyed the project Euler problems by chipping away at those that intrigue me. I have some experience with Java, so that is what I use. I use the IDE Netbeans, which is a free program from Sun, the makers of Java. It is a helpful program because it responds instantaneously to syntactical errors, which is helpful in the same way that a spell check is helpful to writing. More so really, because a badly spelled sentence can still be understood, while a single incorrect character can wreck a computer program.

    Some of the simplest Project Euler problems can be done using "for", "while" and "if" structures and brute-force programming. The more difficult problems require a more complete understanding of whatever language you choose to use as well as some higher math concepts.

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  3. Thanks, Nate.
    I'll take a look.

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