Can you pin down the value of pi by wrapping polygons tighter and tighter around a circle? You start with a square drawn around a circle of radius 1. Then you double the number of sides to 8, then 16, and so on. Each polygon's perimeter gets closer to the circle's circumference. This process produces a recursive equation that approaches pi from above. The project also shows that this upper-bound formula matches a famous expression published by Francois Viete centuries ago. Finally you derive an algebraic polynomial where one root is pi itself. The other roots are new numbers called the Pi Associates, whose properties remain unexplored.