What does hypotrochoid mean?
A hypotrochoid is a mathematical curve produced when a smaller circle rolls inside a larger circle and a fixed point on the smaller circle traces its path. Depending on the relative sizes of the circles and the position of the tracing point, the resulting curve can form loops, rosettes, or other repeating patterns. The term belongs primarily to geometry, mechanics, and technical drawing, where such curves are used in the design of gears, engraving patterns, and decorative mechanisms. It is related to the hypocycloid, the special case in which the tracing point lies on the circumference of the rolling circle. Although a hypotrochoid is sometimes described simply as a type of trochoid, the word normally signals the specific configuration in which the rolling circle remains inside the larger circle.
nounA hypotrochoid is a curve traced by a point attached to a circle that rolls inside another circle. Its form depends on the radii of the two circles and the distance of the tracing point from the center of the rolling circle.
- A planar curve generated by a point attached to a circle that rolls without slipping inside a larger circle.
"The designer used a hypotrochoid to create the intricate pattern engraved on the dial."
"The hypotrochoid becomes progressively more intricate as the rolling circle completes more revolutions."
"A computer-controlled pen traced a hypotrochoid across the sheet of paper."
The plural is used when referring to multiple such curves or to the mathematical family more generally.
"Several hypotrochoids can be generated by changing the ratio of the circles' radii."
A hypotrochoid turns one circle rolling inside another into a surprisingly intricate family of mathematical curves.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does hypotrochoid come from?
The word combines the Greek prefix hypo-, meaning 'under', with trochoid, from Greek trokhos, meaning 'wheel'. The term developed in the vocabulary of geometry to distinguish curves traced by a circle rolling inside another circle from epitrochoids, which are traced by a circle rolling outside another. Its mathematical relatives include the hypocycloid and epicycloid, all named for their rolling arrangements.
How hypotrochoid is actually used
The term is specialized and is normally used in mathematics, engineering, and technical drawing.