Originally Posted by hamster

No, they can't.

Imagine a person walking through a grid of city streets. Suppose that he goes one block north, five blocks east, one block south, five blocks east, etc.

Next, imagine a bird that flies to every second corner visited by the person.

The distance traveled by the bird is less than the distance traveled by the man. He has to walk 1+5+1+5=12 blocks to complete one "period". The bird covers the same route in 2*sqrt(1*1+5*5)=10.2 blocks.

Likewise, the distance traveled by the rider's shoe with respect to the ground is less than the sum of the distance traveled by the bike + the distance traveled by the shoe with respect to the bike. This would be an exact analogy if the shoe were moving straight up and down (like on a stepper machine), but it also holds when the shoe is moving in a circle.

According to my estimates on the first page, if the bicycle travels 10,000 miles and the shoe travels 1,860 miles with respect to the bike, the total distance is approximately 10,000*(1+0.186^2/4) ~ 10,090 miles.