# hypocycloid

hy·po·cy·cloidGeom. the curve traced by a point on the circumference of an epicycle that rolls around the inside of a fixed circle

Origin of hypocycloid

hypo- + cycloid## hypocycloid

noun

The plane locus of a point fixed on a circle that rolls on the inside circumference of a fixed circle.

**hypocycloid**

If *a* is the radius of a fixed circle and *b* is the radius of a smaller rotating circle, the parametric equations of the hypocycloid are * x* = ( *a* − *b* ) cos &thgr; + *b* cos ^{[( a − b ) &thgr; ]}_{b}

*y* = ( *a* - *b* ) sin &thgr; - *b * sin [(^{ a - b ) &thgr; ]}_{ b .}