Math Series #17
If a circle with circumference rolls around a square with side length , how many times will the circle roll around the square until it reaches the place where it started rolling?
The answer is 5.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
The trick here is that the circle is rolling on the outside of the square, and needs to take a few more turns on the edges of the square to get to the next side. Note that the circle has circumference 1, which means it makes one full turn along each side of the square (4 revolutions). Then note that the circle also takes a quarter turn on each vertex of the square (as shown below), and therefore takes another extra full turn after passing all four vertices of the square. 4 + 1 = 5