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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.
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With the Cartesian equation it is easier to check whether a point lies on the circle or not. With the parametric version it is easier to obtain points on a plot. In some contexts, parametric equations involving only rational functions (that is fractions of two polynomials) are preferred, if they exist.
Spirograph is a geometric drawing device that produces mathematical roulette curves of the variety technically known as hypotrochoids and epitrochoids.The well-known toy version was developed by British engineer Denys Fisher and first sold in 1965.
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 .
The main trends of research on Wu's method concern systems of polynomial equations of positive dimension and differential algebra where Ritt's results have been made effective. [3] [4] Wu's method has been applied in various scientific fields, like biology, computer vision, robot kinematics and especially automatic proofs in geometry. [5]
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 ...
An animated model of a Tusi couple. The Tusi couple (also known as Tusi's mechanism [1] [2] [3]) is a mathematical device in which a small circle rotates inside a larger circle twice the diameter of the smaller circle.
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