A “wobbler” consists of two intersecting circles in perpendicular planes. When you roll it along the ground, it wobbles left and right as it moves forward. I saw these 18″ diameter pine disks for sale at a lumber store and thought they would make a wonderfully large wobbler.
The construction simply involves cutting a slot in each disk and forcing the parts together for a friction fit. These disks are 1″ thick, so the slot is exactly 1″ wide. It can be shown that if the depth of the slot is 29% of the way into the center, then the center of gravity remains at a constant height as it rolls, so it will wobble down the slightest incline.
I wrote a description of wobblers made from coins in MAKE Volume 15.
On a smaller scale, CDs also work well. Simply slot them on a saw and friction-fit them together. For all surfaces to be reflective, put two CDs face-to-face to make each circle.
See all of George Hart’s Math Monday columns