What does astroid mean?
An astroid is a distinctive curve in mathematics: a hypocycloid with four cusps, generated by a fixed point on the circumference of a small circle as it rolls without slipping around the inside of a larger circle whose radius is four times as great. Its Cartesian equation, x^(2/3) + y^(2/3) = a^(2/3), gives it a graceful, star-like silhouette with points aligned along the axes, which is reflected in its name, drawn from the Greek word for star. The astroid appears naturally in problems about envelopes — for example, the family of positions of a sliding ladder encloses an astroid-shaped region — and it turns up in optics and engineering wherever such rolling motions occur. Although 'astroid' is occasionally encountered meaning asteroid, that use is rare; today the word belongs almost entirely to the vocabulary of geometry, where it names one of the most familiar and attractive of the classical cycloidal curves.
nounIn geometry, a four-cusped hypocycloid — the curve traced by a point on the circumference of a circle rolling inside another circle four times its diameter. More rarely, the word is used to mean an asteroid, though this sense is nonstandard.
- A four-cusped hypocycloid curve formed by a circle of radius r rolling inside a circle of radius 4r; it has the equation x^(2/3) + y^(2/3) = a^(2/3).
- (Rare, nonstandard) An asteroid — a small rocky celestial body orbiting the sun.
"The path of a point on a wheel rolling inside a larger circle traces out an astroid with four elegant cusps."
"A ladder sliding down a wall has an envelope shaped like an astroid."
"Early astronomers occasionally wrote astroid where modern usage prefers asteroid."
Standard regular plural, used when referring to multiple instances or members of the curve family.
"Different choices of scaling parameter produce a family of similar astroids."
The astroid gets its name from its star-like shape — yet it lives entirely on paper, traced by one circle rolling inside another exactly four times its size.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does astroid come from?
The word astroid derives ultimately from the Greek astron, meaning 'star', combined with the suffix -oid ('having the form of'), so it literally means 'star-shaped'. It entered English mathematical usage in the 19th century, when geometers were systematically naming the family of cycloidal curves. It shares this Greek root with words such as asteroid, astrology, astronomy, and asterisk.
How astroid is actually used
Primarily a technical term used in mathematics and physics. The astronomical sense is rare and generally avoided in careful writing, where 'asteroid' is standard.
Easily confused with astroid
An asteroid is a rocky body orbiting the sun in space; an astroid is a four-pointed mathematical curve studied in geometry.