Definition

1. Noun:
   • A small circle whose center moves around the circumference of a larger circle: In historical astronomy, an epicycle was a geometric model used to explain the apparent retrograde motion of planets. The planet was thought to move on this small circle (the epicycle), the center of which itself moved along the circumference of a larger circle (the deferent) centered on or near the Earth.
   • A circle that rolls around (inside or outside) another circle; generates an epicycloid or hypocycloid: In geometry, an epicycle is a circle whose center moves along the circumference of another fixed circle. If it rolls on the outside, it generates an epicycloid; if it rolls on the inside, it generates a hypocycloid.

Usage Examples

• Noun:
  • Ptolemy's geocentric model used epicycles to account for the complex observed paths of the planets.
  • In geometry class, we learned how an epicycle rolling on the outside of a fixed circle creates a beautiful epicycloid curve.

Advanced Usage

• "Epicyclic motion": Refers to the compound motion described by an epicycle, often used in discussions of historical astronomy or gear systems (epicyclic gears).
  • The ancient model of epicyclic motion was eventually replaced by Kepler's elliptical orbits.

Variants and Related Words

• Epicyclic (adj): Of or relating to an epicycle or epicyclic motion.
  • An epicyclic gear train can provide high reduction ratios in a compact space.
• Epicycloid (n): A curve traced by a point on the circumference of a circle (the epicycle) rolling externally around another fixed circle.
• Hypocycloid (n): A curve traced by a point on the circumference of a circle (the epicycle) rolling internally around another fixed circle.

Synonyms

• Orbital circle (in the historical astronomical context).
• Rolling circle (in the geometric context).

Related Phrases

• "Deferent and epicycle": A phrase describing the two key components of the Ptolemaic system.
  • The Ptolemaic system combined a deferent and an epicycle to model a planet's path.

Noun

1. a circle that rolls around (inside or outside) another circle; generates an epicycloid or hypocycloid