The Definition of Pi

thingiverse

Many pi-day "things" are about the symbol itself or its decimal representation. I designed this as a back-to-basics alternative to those: a manipulative to demonstrate the definition of pi as the ratio of a circle's circumference to its diameter. Start the wheel at 0 with the D upright -- its marked diameter will be horizontal and a bump on the track will mesh with a bite out of the wheel. The track is labelled in multiples of the wheel's diameter (0, D, 2D, 3D, 4D). Roll the wheel forward, and when the bite comes around again, it meshes with a second bump on the track at pi-times-the-diameter, a little way past the 3xD marker. Easy as Pi! Bonus for estimating/approximating: the track has a smaller tick-mark every D/7...you can see that the bump at (pi x D) very nearly lines up with the tick-mark at Dx(3+1/7)=Dx22/7, which is a once-popular approximation of pi.