![]() ![]() The parametric equations for a hypotrochoid are: x ( θ ) = ( R − r ) cos θ + d cos ( R − r r θ ) where LCM is least common multiple. hypotrochoid: noun a plane curve traced by a point on the radius or extended radius but not on the circumference of a circle rolling on the inside of a fixed circle compare epitrochoid. y (theta) (R - r)sin (theta) - dsin ( (R-r)/rtheta) The definition on Wikipedia of a hypotrochoid can further explain: 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. Numerically solve and graphically display tangent lines and integrals. ![]() #Graphmatica equation for hypotrochoids plus#Graph Cartesian functions, relations, and inequalities, plus polar, parametric, and ordinary differential equations. These equations yield a HYPOCYCLOID when bc and a HYPOTROCHOID when c differs from b. 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).Ī 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. a powerful, easy-to-use, equation plotter with numerical and calculus features. EPICYCLOIDS, HYPOCYLOIDS, EPITROCHOIDS, AND HYPOTROCHOIDS There are four related classic curves which are generated by one circle rolling about the outside or inside of stationary second circle. ![]()
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