One Good Turn 

360 is not the only choice. Mathematicians often use "radians" rather than degrees. There are about 6.283 radians in a circle. The exact number of radians in a circle is the same as the ratio of the circumference of a circle to its radius. This ratio is the same for all circles, regardless of the size. Here's a different choice. We will make TURN 1 turn a full circle. Click Go. On each turn, the turtle turns a fifth of
the way around. So five turns make a pentagon. Similarly, FORWARD 80 

Now, try FORWARD 80 TURN 2 / 5. This makes another fivesided figure. But it's not a pentagon; it's a fivesided "star polygon." The turtle crosses its path before returning to its starting position. The turtle makes two full turns while drawing the star polygon. In general,
Numbers that can be represented as T / N are called rational numbers. So if the input to TURN is any rational number, then the turtle will eventually get back to its starting position, having drawn a figure with N points. Some numbers (such as the number of radians in a circle) can not be represented as T / N. If the turtle turns "irrationally," it will never return its starting position. 

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 