# 193 geometry/revolutions.p

## Description

This article is from the Puzzles FAQ,
by Chris Cole chris@questrel.questrel.com and Matthew Daly
mwdaly@pobox.com with numerous contributions by others.

# 193 geometry/revolutions.p

A circle with radius 1 rolls without slipping once around a circle with radius

3. How many revolutions does the smaller circle make?

geometry/revolutions.s

4 if the smaller circle rolls on the outside of the larger circle; 2 if

it rolls on the inside.

Imagine you are rolling a wheel by pushing it along the equator of the

earth. Suppose the circumference of the wheel is one third of that of

the earth. By the time you return to your starting point, the wheel

finishes 3 revolutions relative to you. But do not forget you yourself

also finishes 1 revolution in the same direction. As a result, the

number of absolute revolutions is 3+1=4.

But if the small circle is rolling inside the large circle, the answer

is then 3-1=2, because in this case the wheel makes a counter-revolution

as you walk once around.

Continue to: