WOLFRAM|DEMONSTRATIONS PROJECT

Rolling a Coin around a Coin

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rolling circle radius
0.7
rolling circle angle
0
point distance
1.35
The red circle rolls on the outside of the black circle of radius 1. (The blue point shows how it rolls.) An invisible point at distance
q
from the center of the black circle is attached to the red circle, tracing out a path as the red circle rolls; such curves are called epitrochoids.
When the circles have the same radius, you can see that the blue point is oriented in the same direction after half a revolution. Therefore a coin rolling completely around another coin of the same size goes through two complete revolutions.