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A cyclocycloid is a roulette traced by a point attached to a circle of radius r rolling around, a fixed circle of radius R, where the point is at a distance d from the center of the exterior circle. The red curve is a cyclocycloid (in this case an hypocycloid ) drawn as the smaller black circle rolls around inside the larger blue circle ...
Construction of the limaçon r = 2 + cos(π – θ) with polar coordinates' origin at (x, y) = ( 1 / 2 , 0). In geometry, a limaçon or limacon / ˈ l ɪ m ə s ɒ n /, also known as a limaçon of Pascal or Pascal's Snail, is defined as a roulette curve formed by the path of a point fixed to a circle when that circle rolls around the outside of a circle of equal radius.
It is the curve traced out by a point fixed to a circle (where the point may be on, inside, or outside the circle) as it rolls along a straight line. [1] If the point is on the circle, the trochoid is called common (also known as a cycloid ); if the point is inside the circle, the trochoid is curtate ; and if the point is outside the circle ...
An epitrochoid (red) with fixed circle's radius R = 3, rolling circle's radius r = 1 and distance d = 1/2 from the rolling circle's center to the generating point A hypotrochoid (red) with R = 5, r = 3, d = 5. In geometry, a centered trochoid is the roulette formed by a circle rolling along another circle. That is, it is the path traced by a ...
In mathematics, an annulus (pl.: annuli or annuluses) is the region between two concentric circles. Informally, it is shaped like a ring or a hardware washer. The word "annulus" is borrowed from the Latin word anulus or annulus meaning 'little ring'. The adjectival form is annular (as in annular eclipse).
The curve that has a catacaustic forming a circle. Approximates the Archimedean spiral. [11] Atomic spiral: 2002 = This spiral has two asymptotes; one is the circle of radius 1 and the other is the line = [12] Galactic spiral: 2019
The completed body of constant width is then the intersection of the interiors of an infinite family of circles, of two types: the ones tangent to the supporting lines, and more circles of the same radius centered at each point of the given arc. This construction is universal: all curves of constant width may be constructed in this way. [3]
Hence, given the radius, r, center, P c, a point on the circle, P 0 and a unit normal of the plane containing the circle, ^, one parametric equation of the circle starting from the point P 0 and proceeding in a positively oriented (i.e., right-handed) sense about ^ is the following: