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. As the radius of the larger circle is increased, the hypocycloid …

Dec 3, 2025 · A hypocycloid is therefore a hypotrochoid with h=b. To derive the equations of the hypocycloid, call the angle by which a point on the small circle rotates about its center theta, and the …

Hypocycloid: A hypocycloid is traced by a fixed point on a circle of radius r rolling around the inside of a circle of radius R. Use the slider to adjust the ratio R/r – this controls the shape of the curve.

The hypocycloid is the envelope of a diameter of a circle with radius equal to twice that of (C), rolling without slipping on, and outside, (C0).

Illustrated definition of Hypocycloid: The curve made by a point on the circumference of a circle rolling around the inside of a larger circle. We get...

Feb 20, 2024 · If the point is not located on the rolling circle, but outside (or inside) it, the curve is said to be a lengthened (shortened) hypocycloid, or hypotrochoid. If $m=2$ the hypocycloid is a segment of a …

Interactive demo of a smaller circle rolling inside of larger circle to create a hypocycloid

May 25, 1999 · A 3-cusped hypocycloid is called a Deltoid or Tricuspoid, and a 4-cusped hypocycloid is called an Astroid. If is rational, the curve closes on itself and has cusps.

The meaning of HYPOCYCLOID is a curve traced by a point on the circumference of a circle rolling internally on the circumference of a fixed circle.

A hypocycloid is the curve traced by a fixed point on a smaller circle that rolls without slipping inside a larger circle. Its parametric equations can be derived and analyzed using calculus.