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Hypotrochoid : ウィキペディア英語版
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 parametric equations for a hypotrochoid are:
:x (\theta) = (R - r)\cos\theta + d\cos\left(\theta\right)
:y (\theta) = (R - r)\sin\theta - d\sin\left(\theta\right).
Where \theta is the angle formed by the horizontal and the center of the rolling circle (note that these are not polar equations because \theta is not the polar angle).
Special cases include the hypocycloid with ''d'' = ''r'' and the ellipse with ''R'' = 2''r''.
The classic Spirograph toy traces out hypotrochoid and epitrochoid curves.
==See also==

* List of periodic functions
* Epitrochoid
* Cycloid
* Hypocycloid
* Epicycloid
* Spirograph

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
ウィキペディアで「Hypotrochoid」の詳細全文を読む



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