meaning of "trochoid" in english dictionary & in mathematics dictionary?

Question

meaning of "trochoid" in english dictionary in daily life

Answer 1

A trochoid is a curve described by a fixed point as a circle rolls along a straight line. As a circle of radius a rolls without slipping along a line L, the center C moves parallel to L, and every other point P in the rotating plane rigidly attached to the circle traces the curve called the trochoid. Let CP = b. If P lies inside the circle (b < a), on its circumference (b = a), or outside (b > a), the trochoid is described as being curtate, common, or prolate, respectively. Parametric equations of the trochoid, which assume L is the x-axis, are

x = aθ - bsinθ
y = a - bcosθ

where θ is the variable angle through which the circle rolls. A curtate trochoid is traced by a pedal when a bicycle is pedaled along a straight line. A prolate, or extended trochoid is traced by the tip of a paddle when a boat is driven with constant velocity by paddle wheels; this curve contains loops. A common trochoid, also called a cycloid, has cusps at the points where P touches the L.

A hypotrochoid is formed by a wheel rolling around the inside of a fixed circle.

Answer 2

for the math meaning:
http://mathworld.wolfram.com/Trochoid.html
english meaning:
http://dictionary.reference.com/browse/Trochoid

Answer 3

http://en.wikipedia.org/wiki/Trochoid
http://www.m-w.com/dictionary/trochoid