Descartes' Smart Start...
by Debbie Sands (15, JFK High School, NY)

Long ago two young friends named Isaac Beeckman and René Descartes lived in a small town in France. One day, the boys were bored of their usual games and wanted to play something new and exciting.

As René and Isaac sat on the grass thinking about what to do, René thought of a fantastic idea.

"Let's play pirates. One of us will hide something and the other person will go try and find it."

"Okay," said Isaac.

"I'll hide something first," René exclaimed.

So René ran into the woods behind Descartes' house, buried some gold coins in the dirt, and returned back to Isaac.

"Alright, now let's go find what you hid," said Isaac.

The boys sprinted into the woods and searched high and low for the gold coins. However, they could not find the spot where René had hid them.

"I know why we cannot find the coins I buried. We need some sort of system to keep track of the exact place where we hide things."

"You're right. I'll come back tomorrow and we can try again."

That night, René lay in his bed staring at the flies crawling over the tiles on his bedroom ceiling and thinking about the buried coins. All of a sudden, René thought of another fantastic idea.

"I can find out the fly's exact position using the crisscrossing lines on the tiles. So I'll call the sideways side the x-axis and the up and down side the y-axis. The center of the tile will be called the origin at (0.0). Locations of points on the tile can be plotted when one point from each of the axis are used. Using this idea, I can make a map to help Isaac and me find the buried coins."

The next day, Isaac returned to the Descartes' house as he had promised and René practically flew to meet him to explain his plan. So the boys took paper and a quill and ink from Mr. Descartes' desk and drew a picture using René's coordinate system.

The boys hid some new gold coins in the ground and used the trees and plants around them as the axis. The boys figured out the coordinates of where they buried the coins and lo and behold, they found the exact location of the money.

Isaac was amazed at his friend's creativity and could not believe the system actually worked. They played the game repeatedly and each time the boys found the coins exactly where they had buried them.

At the end of the day, the boys walked back to Descartes' house for supper, worn out from all the fun they had had.

"Wow René, you really have something there with this graphing idea of yours."

"Nah, it's just a game."

Little did René Descartes know, this simple game would eventually become the basis for modern calculus and geometry.