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A hypocycloid is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle.
Depending on the ratio of the radii of the inner and outer circles, the fixed point traces different curves.
We can use two circles of radii ratio 2:1 to draw a straight line segment. In the nineteenth century the problem of converting circular motion to rectilinear and vice versa was crucial to the design of steam engines: the to-and-fro movement of the piston had to be converted to a rotation of the wheels. The 2:1 hypocycloid was one of numerous solutions proposed.
