What does hypocycloid mean?
A hypocycloid is a geometric curve produced when a circle rolls inside another circle and a fixed point on the rolling circle traces its path. The term belongs to formal mathematics and is especially associated with planar geometry, though related curves also occur in mechanics and the study of gears and planetary motion. The shape depends on the relative sizes of the two circles and the location of the tracing point. When the rolling circle has half the radius of the fixed circle, the curve is a deltoid; when it has one-third the radius, it is an astroid. A hypocycloid should not be confused with an epicycloid, which is generated by a circle rolling around the outside of another circle. The word combines Greek roots meaning “under” and “circle-form,” accurately describing the rolling configuration. Although uncommon in everyday speech, the term names an important family of mathematically elegant curves.
nounA hypocycloid is a plane curve traced by a point on the circumference of a circle as that circle rolls internally along the inside of another, usually fixed, circle. Its familiar special cases include the deltoid and astroid.
- A curve traced by a point on a circle as the circle rolls internally along the inside of another circle.
"The path of a marked point on a small circle rolling inside a larger circle forms a hypocycloid."
"The deltoid is a three-cusped hypocycloid generated by a circle rolling inside a circle of twice the radius."
"In the study of planetary motion, an epitrochoid or hypocycloid can provide a model for paths traced by rolling circles."
The plural is hypocycloids when referring to more than one curve of this type.
"The study compares several hypocycloids generated by different circle radii."
Roll a small circle inside a larger one and mark its edge: the resulting curve can be a deltoid, an astroid, or another beautiful hypocycloid.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does hypocycloid come from?
The word combines the Greek prefix hypo-, meaning “under,” with cycloid, a term derived from Greek kyklos, “circle,” and eidos, “form” or “shape.” It was developed in the language of geometric mathematics to describe the curve traced by a circle rolling inside another circle. Its related terms include epicycloid, for the corresponding outside-rolling curve, and hypotrochoid, a more general term for curves traced by points on a circle rolling internally around another circle.
How hypocycloid is actually used
This is a specialized mathematical term used in geometry, mechanics, and related technical contexts. It is not normally used in general conversation.
Easily confused with hypocycloid
A hypocycloid is traced by a circle rolling inside another circle, whereas an epicycloid is traced by a circle rolling outside another circle.