Mixed Moss

The other day I shut my eyes and this is what I saw.

Imagine a polygon with equilateral sides. How many sides, you ask? X number of sides; we don’t know yet. Now imagine that you are going to hold the area inside the polygon constant. Now, you are going to change the number of sides (that is, X). Imagine it has three sides. It’s a triangle. Now imagine it has four sides and is a square. Now imagine five, and then six, and then seven. Go on sliding the number that’s filling in for X as high up the number line as you can imagine.

Each time the number gets bigger, the length of the sides gets shorter because we are holding the area inside the polygon constant. So as the number X approaches infinity, the length of each side approaches zero. What happens? Eventually, each side will turn into, not a line, but a point. And the shape will become a circle.

Now imagine that X was swinging through a cycle on the number line. It was sliding back and forth on the line, from three sides to infinity sides and back again, over and over again. That is what I saw when I shut my eyes: a circle sliding into a triangle and back again, through all the other different polygon shapes.

And that is really the only interesting thing I have to say today. Go read Erica’s vox, it’s  more interesting and original than mine!

This entry was posted on Monday, November 27th, 2006 at 12:03 pm and is filed under Uncategorized. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.