# cycloid

cycloid
1. resembling a circle; circular.
2. (of the scale of a fish) smooth-edged, more or less circular in form, and having concentric striations.
3. (of a fish) having such scales.
4. Psychiatry. of or noting a personality type characterized by wide fluctuation in mood within the normal range.
n.
5. a cycloid fish.
6. Geom. a curve generated by a point on the circumference of a circle that rolls, without slipping, on a straight line.
[1655-65; < Gk kykloeidés like a circle. See CYCL-, -OID]

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the curve generated by a point on the circumference of a circle that rolls along a straight line. If r is the radius of the circle and θ (theta) is the angular displacement of the circle, then the polar equations of the curve are x = r(θ - sin θ) and y = r(1 - cos θ).

The points of the curve that touch the straight line are separated along the line by a distance equal to 2πr, which is the circumference of the circle, indicating one complete revolution of the circle. The curve is periodic, which means that it repeats in an identical pattern for each cycle, or length of the line, that is equal to 2πr.

One variant of the simple cycloid is the curtate cycloid, for which the curve falls below the line at the cusps, making retrograde loops in which the curve moves in the direction opposite to that of the rolling circle.

The prolate cycloid is similar to the simple cycloid except that the curve has no cusps and does not intersect the line. The prolate is formed by a point on a radius less than that of the rolling circle, such as a point on the spoke of a wheel.

For the case of a circle rolled along outside the circumference of another circle, an epicycloid is formed. For a circle rolled along inside the circumference of another circle, a hypocycloid is formed. See also brachistochrone.

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Universalium. 2010.

### Look at other dictionaries:

• Cycloid — Cy cloid (s? kloid), n. [Cyclo + oid: cf. F. cyclo[ i]de.] (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. [1913 Webster] Note: The common cycloid is …   The Collaborative International Dictionary of English

• Cycloid — Cy cloid, a. (Zo[ o]l.) Of or pertaining to the Cycloidei. [1913 Webster] {Cycloid scale} (Zo[ o]l.), a fish scale which is thin and shows concentric lines of growth, without serrations on the margin. [1913 Webster] …   The Collaborative International Dictionary of English

• Cycloid — Cy cloid, n. (Zo[ o]l.) One of the Cycloidei. [1913 Webster] …   The Collaborative International Dictionary of English

• cycloid — [sī′kloid΄] n. [Gr kykloeidēs, circular < kyklos (see WHEEL) + eidēs, OID] Geom. a curve traced by any point on a radius, or an extension of the radius, of a circle which rolls without slipping through one complete revolution along a straight… …   English World dictionary

• Cycloid — For other uses, see Cycloid (disambiguation). A cycloid generated by a rolling circle A cycloid is the curve traced by a point on the rim of a circular wheel as the wheel rolls along a straight line. It is an example of a roulette, a curve… …   Wikipedia

• cycloid — Suggesting cyclothymia; a term applied to a person who tends to have periods of marked swings of mood, but within normal limits. [cyclo + G. eidos, resembling] * * * cy·cloid sī .klȯid n a cycloid individual cycloid adj relating to, having, or… …   Medical dictionary

• cycloid — I. noun Etymology: French cycloïde, from Greek kykloeidēs circular, from kyklos Date: 1661 a curve that is generated by a point on the circumference of a circle as it rolls along a straight line • cycloidal adjective II. adjective Date: 1847 1.… …   New Collegiate Dictionary

• cycloid — Brachystochrone Bra*chys to*chrone, n. [Incorrect for brachistochrone, fr. Gr. bra chistos shortest (superl. of brachy s short) + ? time : cf. F. brachistochrone. ] (Math.) A curve, in which a body, starting from a given point, and descending… …   The Collaborative International Dictionary of English

• cycloid — 1. noun a) The locus of a point on the circumference of a circle that rolls without slipping on a fixed straight line. b) A fish having cycloid scales …   Wiktionary

• cycloid — /ˈsaɪklɔɪd/ (say suykloyd) adjective 1. resembling a circle; circular. 2. (of fishes scales) smooth edged, more or less circular in form, with concentric striations. 3. having such scales, as a fish. 4. Psychology (of a personality type)… …