teacher note Teacher Note: Turtle Geometry

The turtle is actually useful for exploring a wide variety of ideas in geometry. The book Turtle Geometry does a wonderful job of showing how turtles can be used to explore a wide variety of geometric, mathematical, and scientific ideas (e.g., using turtles to model insect behavior). The example pattern below is drawn from that book.

a scan of the cover of the book about turtle geometry

Figure 1: A scan of Mark’s copy of the book

Total Turtle Trip Theorem

That last piece of code is actually a pattern for a wide variety of geometric shapes. Here’s a triangle. It may not be obvious why we turn 120 in this program, but it will be soon.

And here’s a pentagon.

The Total Turtle Trip Theorem states that the turtle will draw a closed figure with n sides when the sum of the angles turned is a multiple of 360. In the triangle example 3 * 120 = 360 and in the pentagon example 5 * 72 = 360.

Change the ?? in line 7 below to the amount to turn each time to draw a 12 sided polygon, which is called a dodecagon. If you get it right the turtle will draw a 12 sided closed polygon.

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