Cycling in circles in France

Watching cyclists struggle through the Tour de France from our armchairs (or should it be deckchairs?) is great fun, but as Burkard Polster and Marty Ross have discovered, it would be even more fun if the cyclists cycled in circles.

If you draw a closed convex loop on the ground and cycle so that your back wheel follows the loop, your front wheel will trace out a larger loop. It turns out that the area in between the two loops is always the same, regardless of the shapes and sizes of the two loops: if the length between the two wheel hubs of your bike is L, then the area between the loops is always π L². Go to the The Age Education Resource Centre to find out why...