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Answer for the clue "An epicycloid in which the rolling circle equals the fixed circle ", 8 letters:
cardioid

Word definitions for cardioid in dictionaries

WordNet Word definitions in WordNet
n. an epicycloid in which the rolling circle equals the fixed circle

Wikipedia Word definitions in Wikipedia
A cardioid (from the Greek καρδία "heart") is a plane curve traced by a point on the perimeter of a circle that is rolling around a fixed circle of the same radius. It is therefore a type of limaçon and can also be defined as an epicycloid having a single ...

The Collaborative International Dictionary Word definitions in The Collaborative International Dictionary
Cardioid \Car"di*oid\, n. [Gr. kardio-eidh`s heart-shaped; kardi`a heart + e'i^dos shape.] (Math.) An algebraic curve, so called from its resemblance to a heart.

Wiktionary Word definitions in Wiktionary
a. Having this characteristic shape n. (context geometry English) An epicycloid with exactly one cusp; the plane curve with polar equation rho = 1 + cos,theta - having a shape supposedly heart-shaped

Usage examples of cardioid.

He dropped to his knees and inventoried the canvas bag, which contained everything an astute documentarian ought to have: the Betacam, the Ampex deck, the Nicad battery pack, two extra cassettes, a cardioid mike with sponge wind guard, steno notebook, pens.

A piece of cheese, with one of those built-in cardioid mikes, but it was adequate for spoken-word, ideal for oral history.

Rosette and seahorse and seething cloud, nebulosities on the brink of determinate form, cardioid traceries of the heart the patterns wrapped around him until he became a fractal tapestry, alive, every element in constant motion.

He dropped to his knees and inventoried the canvas bag, which contained every­thing an astute documentarian ought to have: the Betacam, the Ampex deck, the Nicad battery pack, two extra cassettes, a cardioid mike with sponge wind guard, steno notebook, pens.