Thursday, June 15, 2006

REAL Magic Part 3: Mathematics

I am constantly enamored by the amazing power of mathematics. The measure of things can be far more amazing than the magic tricks I use to entertain and educate in elementary school assembly programs and library reading programs.

I once read an article that suggested that there were more combinations for a shuffled deck of cards than there are atoms in The Milky Way galaxy. And if you shuffle cards face up to face down, there are more combinations than there are atoms in the known universe.

That seems impossible, and my quest to find the truth (by first determining the number of combinations of a shuffled deck of cards and then trying to estimate the number of atoms in our planet, solar system, and ultimately the known universe) lead me to the creation of a program for middle school and high school students called Math-A-Magic. You can read about the program at (don't forget the hyphens around the "A").

The power in math that really seems magical is the concept of exponents. Normally scientists and mathematicians use "base 10" exponents, but there are others. You can amaze yourself with simple base-2 exponents. When you double something you are dealing with base-2. Here's an example of the power of base-2.

Fold a piece of paper in half. Fold it in half again. Do it a third time, then a fourth and a fifth. You won't be able to fold that piece of paper in half eight times. It becomes too thick. But what if you could?

Q: What if you could double the thickness of a sheet of paper, say 50 times. How thick would it be?

A: It would stretch from the surface of the Earth, to the surface of the Sun. Don't believe me? Do the math. Measure a stack of 100 sheets of paper and divide by 100 to get the thickness of a single sheet. Get a calculator and enter 1X2. Then X2. Then X2. Keep doing this until you've entered "X 2" 50 times. This is how many thicknesses your imaginary stack would be. Multiply it times your measurement for a thickness of paper and then convert that into miles or kilometers.

Pretty cool, huh?

--Julian Franklin

P.S. The average distance from the surface of the Earth to the surface of the Sun is about 93,000,000 miles (about 150,000,000 kilometers)

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