Saturday, February 24, 2007

Math by Design

"I've never done so much math to build something!" this usually clownish 8th grade boy exclaimed upon finishing his intricate string art design.
He had to learn a lot to get to this point. The effect was cumulative, and now I saw that it was also powerful.
Can you fashion a 3 dimensional design that fools the eye and amazes your friends? Before you answer, let's see if you can do the math my 8th grade struggling math students had to master.
1. Be able to use a compass to draw a perfect circle on a 12" x 12" piece of paper.
2. Find the center of the circle.
3. Find and draw the diameter of this circle.
4. Figure out how many degrees apart 24 points on the outside of the circle would have to be apart.
5. Using a protractor, mark those 24 points accurately on the outside of the circle.
6. Figure out the area of this circle (remember the formula? πr2).
7. Figure out the circumference of this circle (remember that formula? πd).
8. What shape is formed by a 3 point design? How many of them are formed? (answer: 3 octagons)
9. What shape is formed by a 4 point design? How many of them are formed? (answer: 4 hexagons)
10. What shape is formed by a 6 point design? How many of them are formed? (answer: 6 squares)
11. What shape is formed by an 8 point design? How many of them are formed? (do you see the pattern yet? Can you guess?)
12. Now you're ready to create your own string art design on paper. Then you follow your own pattern created by coordinates on this geometric plane with string, nails, and a 12" x12" piece of plywood. That's what we did.
Following directions that someone else gives you, as long as they are clear, concise, and easy to follow, leads to satisfaction. Following the directions that you create yourself is tricky. We may find that we're not as clear or concise as we should be, and we tend to make it more difficult on ourselves. No two designs look alike. Some are more difficult than others to replicate. But here's the cool part. Once you discover the patterns found in your unique design, the directions are easier to follow and following them leads to more than satisfcation - it leads to ephiphany!
"I never knew I could do so much math and still have so much fun!"
I wish I could bottle a person's ephiphany to share with others, but I know that ephiphanies are personal - no two look alike.
By the way, the answer to number 11 is 8 triangles!