The Coin Paradox

You can easily look this up if you’re a horrible cheater but everyone will hate you if you don’t use [spoiler] tags.

In the top figure, one coin rolls around another coin of equal size.

In the bottom figure, the same coin rolls along a straight line. In each case the rolling coin has made one complete rotation. But the red arc at the top is half the length of the red line at the bottom. Why?

The coin travels half of the circumference in the top, but travels the whole circumference in the bottom.

I liked this.

The top coin is being measured at two different points, the 3 o’clock for a starting point and the 9 o’ clock for an end point. The bottom coin is being measured at the 6 o’clock position for both a starting and end point.