Henry Ernest Dudeney/Modern Puzzles/209 - A Wheel Fallacy

by : $209$

 * A Wheel Fallacy
 * Here is a curious fallacy that I have found to be very perplexing to many people.


 * The wheel shown in the diagram makes one complete revolution in passing from $A$ to $B$.
 * It is therefore obvious that the line $AB$ is exactly equal in length to the circumference of the wheel.


 * Dudeney-Modern-Puzzles-209.png


 * Now the inner circle (the large hub in the diagram) also makes one complete revolution along the dotted line $CD$ and,
 * since the line CD is equal to the line $AB$, the circumference of the larger and smaller circles are the same.


 * This is clearly not true.
 * Wherein lies the fallacy?