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The hypocycloid is a special kind of hypotrochoid, which is a particular kind of roulette. A hypocycloid with three cusps is known as a deltoid. A hypocycloid curve with four cusps is known as an astroid. The hypocycloid with two "cusps" is a degenerate but still very interesting case, known as the Tusi couple.
In geometry, a deltoid curve, also known as a tricuspoid curve or Steiner curve, is a hypocycloid of three cusps.In other words, it is the roulette created by a point on the circumference of a circle as it rolls without slipping along the inside of a circle with three or one-and-a-half times its radius.
Because of this symmetry, a kite has two equal angles and two pairs of adjacent equal-length sides. Kites are also known as deltoids, [1] but the word deltoid may also refer to a deltoid curve, an unrelated geometric object sometimes studied in connection with quadrilaterals. [2] [3] A kite may also be called a dart, [4] particularly if it is ...
The red curve is a hypotrochoid drawn as the smaller black circle rolls around inside the larger blue circle (parameters are R = 5, r = 3, d = 5).. In geometry, 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 deltoid is a simple closed curve but other hedgehogs may self-intersect, or otherwise behave badly. In particular, there exist anti-symmetric support functions based on the Weierstrass function whose corresponding projective hedgehogs are fractal curves that are continuous but nowhere differentiable and have infinite length.
Astroid, the superellipse with n = 2 ⁄ 3 and a = b, is a hypocycloid with four cusps. Deltoid curve, the hypocycloid of three cusps. Squircle, the superellipse with n = 4 and a = b, looks like "The Four-Cornered Wheel." Reuleaux triangle, "The Three-Cornered Wheel." Superformula, a generalization of the superellipse.
Deltoid (delta-shaped) can refer to: The deltoid muscle, a muscle in the shoulder; Kite (geometry), also known as a deltoid, a type of quadrilateral; A deltoid curve, a three-cusped hypocycloid; A leaf shape; The deltoid tuberosity, a part of the humerus; The deltoid ligament, a ligament in the ankle
Construction of a two-lobed cycloidal rotor. The red curve is an epicycloid and the blue curve is a hypocycloid. A Roots blower is one extreme, a form of cycloid gear where the ratio of the pitch diameter to the generating circle diameter equals twice the number of lobes. In a two-lobed blower, the generating circle is one-fourth the diameter ...