This is a short (40 minute or less) computer based geometry activity which gets students thinking about polygons "outside the box." In this case, it is looking at how to create a closed polygon by adjusting the angle with the number of sides.
The activity uses "Papert," an online version of the LOGO computer language that can be accessed at the website http://logo.twentygototen.org. This activity describes in detail to small amounts of code needed to unlock the mystery of the "Total Turtle Trip Theorem," which is a documented mathematical theorem that was one of the first "proofs" that was developed from the computer.
This activity includes detailed descriptions of how to use this activity to get students thinking about geometry in new and novel ways!