## Hypocycloid

In geometry, 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. It is comparable to the cycloid but instead of the circle rolling along a line, it rolls within a circle.

Various sizes of circles generates different hypocycloids. Let the radius of the fixed circle be a, the radius of the rolling circle be b.

The parametric equation of the hypocycloid is:

{(a + b)*Cos[t] + b*Cos[(a + b)/b*t], (a + b)*Sin[t] + b*Sin[(a + b)/b*t]}

If we use this equation we can obtain different types of hypocycloid because the parameters a Continua >

## Epicycloid

The epicycloid is the locus of a point on the circumference of a circle that rolls without slipping on the circumference of another circle.

The red curve is an epicycloid traced as the small circle (radius = 2) rolls around the outside of the large circle (radius = 4). The epicycloid can have both a parametric equation and a polar equation.

The parametric equation is:

X = r (k + 1) cos (t) – r cos ( (k + 1) t)

Y = r (k + 1) sin (t) – r sin ( (k + 1) t)

If we use these equations we can obtain Continua >