Cornered 

If you reduce the turtle's turn size, the polygon becomes more and more circlelike. But what if you increase the turtle's turn size? Click Go. This time, the turtle makes a hexagon. You might have expected a triangle, since an equilateral triangle has three 60degree angles. But those are the angles inside the triangle. The turtle's turns are the "outside angles." 

How would you make other regular polygons  squares, triangles, pentagons? For a pentagon, the turtle needs to make five turns of 72 degrees. For a square, four turns of 90 degrees. For a triangle, three turns of 120. By the time the turtle finishes each polygon, it has turned through a total of 360 degrees. Why 360? In a certain sense, it was arbitrary to choose 360 as the number of degrees in a circle. But not completely arbitrary. It's a better choice, for instance, than 241. The number 360 has many factors. It's the smallest number divisible by 2, 3, 4, 5, 6, 8, 9, and 10. Oh well, it misses 7. If you had 2520 degrees in a circle, you could include 7, but each degree would be awfully small. And don't even think about dividing by 11. 

Go to the next page or the previous page or the contents page. Mitchel Resnick and Brian Silverman Epistemology and Learning Group MIT Media Laboratory Last modified: November 17, 2003 