Webster's Online Dictionary
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Definition: HYPOTROCHOID

Part of Speech Definition
Noun 1. A curve, traced by a point in the radius, or radius produced, of a circle which rolls upon the concave side of a fixed circle.[Websters].

Source: Webster's Revised Unabridged Dictionary (1913)

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Date "Hypotrochoid" was first used in popular English literature: sometime before 1914. (references)

Note: Hypotrochoid \Hy`po*tro"choid\, noun. [Prefix hypo- trochoid.]. (references)


Extended Definition: HYPOTROCHOID

Hypotrochoid

A hypotrochoid is a roulette traced by a point attached to a circle of radius r rolling around the inside of a fixed circle of radius R, where the point is a distance d from the center of the interior circle.

The red curve is a hypotrochoid drawn as the smaller black circle rolls around inside the larger blue circle (parameters are R = 5.0, r = 3, d = 5).
The red curve is a hypotrochoid drawn as the smaller black circle rolls around inside the larger blue circle (parameters are R = 5.0, r = 3, d = 5).

The parametric equations for a hypotrochoid are:

x = (R - r)\cos\theta + d\cos\left({R - r \over r}\theta\right)
y = (R - r)\sin\theta - d\sin\left({R - r \over r}\theta\right)

Special cases include the hypocycloid with d = r and the ellipse with R = 2r.

The ellipse (drawn in red) may be expressed as a special case of the hypotrochoid; here R = 10, r = 5, d = 1.
The ellipse (drawn in red) may be expressed as a special case of the hypotrochoid; here R = 10, r = 5, d = 1.

The classic Spirograph toy traces out hypotrochoid and epitrochoid curves.

See also

  • epitrochoid
  • Spirograph (toy)

External links

Source: adapted by the editor from Wikipedia, the free encyclopedia; from the article "Hypotrochoid". Image Credit.
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Topics by Level of Interest: HYPOTROCHOID

Topics sorted by level of Interest Level (1=low, 600=high)     Topics sorted Alphabetically Level (1=low, 600=high)
Hypotrochoid 5     Hypotrochoid 5

Source: the editor, created by/for EVE to gauge likely levels of human interest in linguistically triggered topics (compiled across various sources, such as Wikipedia and specialty expression glosses).

Translations: HYPOTROCHOID

Language Translations (or nearest inflections or synonyms, in parentheses)
Slovak hypotrochoida (hypotrochoid). Additional references: Slovak, Slovakia, Hungary, hypotrochoid. (volunteer & more translations)
Slovakian hypotrochoida (hypotrochoid). Additional references: Slovakian, Slovakia, Hungary, hypotrochoid. (volunteer & more translations)
Source: Eve, based on a combination of meta analysis and graph theory (for near and back translations). Top

Constructed Language Translations: HYPOTROCHOID

Language Translations for “hypotrochoid” or closest synonym(s); back translations in parentheses.
Pig Latin ypotrochoidhay (hypotrochoid). Additional references: Pig Latin, hypotrochoid. (volunteer)
Terran B hyotrochoida (hypotrochoid). Additional references: Terran B, hypotrochoid. (volunteer)
Source: compiled by the editor. Top