High Quality Content by WIKIPEDIA articles! In geometry, a centered trochoid is the roulette formed by a circle rolling along another circle. That is, the path traced by a point attached to a circle as the circle rolls without slipping along a fixed circle. The term encompasses both epitrochoid and hypotrochoid. The center of this curve is defined to be the center of the fixed circle. Alternatively, a centered trochoid can be defined as the path traced by the sum of two vectors, each moving at a uniform speed in a circle. Most authors use epitrochoid to mean a roulette of a circle rolling around the outside of another circle, hypotrochoid to mean a roulette of a circle rolling around the inside of another circle, and trochoid to mean a roulette of a circle rolling along a line. However, some authors (for example following F. Morley) use "trochoid" to mean a roulette of a circle rolling along another circle, though this is inconsistent with the more common terminology. The term Centered trochoid as adopted by combines epitrochoid and hypotrochoid into a single concept to streamline mathematical exposition and remains consistent with the existing standard.

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