hypocycloid

American  

[hahy-puh-sahy-kloid] / ˌhaɪ pəˈsaɪ klɔɪd /

noun

Geometry.

1. a curve generated by the motion of a point on the circumference of a circle that rolls internally, without slipping, on a given circle.

---

hypocycloid British  

/ ˌhaɪpəˈsaɪklɔɪd /

noun

1. a curve described by a point on the circumference of a circle as the circle rolls around the inside of a fixed coplanar circle Compare epicycloid cycloid

---

hypocycloid Scientific  

/ hī′pō-sī′kloid′ /

1. The curve described by a point on the circumference of a circle as the circle rolls on the inside of the circumference of a second, fixed circle.

---

Other Word Forms

• hypocycloidal adjective

Etymology

Origin of hypocycloid

First recorded in 1835–45; hypo- + cycloid

Example Sentences

A hypocycloid is a special kind of hypotrochoid in which the point tracing out the curve is on the edge of the circle, not the interior.

From Scientific American

In epicycloidal teeth the curve forming the face of the tooth is designated an epicycloid, and that forming the flank an hypocycloid.

From Project Gutenberg

The curve generated by rolling on the concave side is called a 'hypocycloid'.

From Project Gutenberg

A quick check shows why the 3-point hypocycloid works and the other fails: a line dropped from the very top of the hypocycloid will across horizontally at the bottom curve.

From New York Times

If the radius of the rolling circle be one-half of the fixed circle, the hypocycloid becomes a diameter of this circle; this may be confirmed from the equation to the hypocycloid.

From Project Gutenberg