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Lost in Space

When the turtle goes FORWARD 1 RIGHT 1, it moves ahead one "turtle step," then turns right by one degree. Each day, in its journey around the sun, the earth also turns right by about one degree. But the "earth step" that it takes each day is much bigger than a turtle step; it moves forward more than 1.5 million miles. Clearly, the size of the circle depends on the size of the step.

Click Go. As you can see, the circle is smaller than the one on the previous page.

Why is it smaller? After each step, the turtle turns twice as much as the one on the previous page (RIGHT 2 instead of RIGHT 1). So it only needs to take half as many steps to get around. The resulting circle has half the circumference and half the radius of the one on the previous page.

Try other numbers. For example, what happens with FORWARD 2 RIGHT 2?

Some readers might be bothered by a "trick" in our examples. The turtles aren't really making circles; they are making regular polygons with a large number of sides. The FORWARD 2 RIGHT 2 command draws a polygon with 180 sides; the FORWARD 1 RIGHT 1 command draws a polygon with 360 sides. What if you kept reducing the step size and turn size? You would get polygons with more and more sides, looking more and more like circles. In fact, by reducing the step size and turn size, you can get as close to making a real circle as you want.

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Last modified: November 17, 2003
by Rupert Russell