Cycloid

A mathematical construct specified by a pair of parametric equations. Specific case of the more generic cyclohedron. Related 2D forms include hypercycloid and curtate cycloid, which are also generalizations.

For a cycloid based on a circle of radius r with rotation angle a, the parametric equations are as follows:

x=r(a-sin(a))
y=r(1-cos(a))

An interesting property of this construct is that the area under the first dome-shape (a=0 to a=2pi) is equal to 8r.

A kind of scale appearing in many modern bony fishes (order Osteichthys), typically ones with soft ray fins (i.e., without spines) such as trout. Cycloid scales tend to be smooth and either round or oval. They can be used to age a fish, since each year a growth ring (circulus) is formed around the scale as it grows.

Cycloid scales appeared after ganoid scales and before ctenoid scales.

Cy"cloid (s?"kloid), n. [Cyclo- + -oid: cf. F. cycloide.] Geom.

A curve generated by a point in the plane of a circle when the circle is rolled along a straight line, keeping always in the same plane.

⇒ The common cycloid is the curve described when the generating point (p) is on the circumference of the generating circle; the curtate cycloid, when that point lies without the circumference; the prolate or inflected cycloid, when the generating point (p) lies within that circumference.

 

© Webster 1913.

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Cy"cloid, a. Zool.

Of or pertaining to the Cycloidei.

Cycloid scale Zool., a fish scale which is thin and shows concentric lines of growth, without serrations on the margin.

 

© Webster 1913.

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Cy"cloid, n. Zool.

One of the Cycloidei.

 

© Webster 1913.