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Analytic Geometry2D

Special Plane Curves - Theory & Concepts - Analytic Geometry Spirograph

Analysis of advanced planar curves including cycloids, epicycloids, hypocycloids, and lemniscates.

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Spirograph & Cycloid Simulator

Trace epicycloid and hypocycloid curves by rolling a circle along the outside or inside of a fixed circle

Fixed Radius R3.0
Rolling Radius r1.0
Angle: 0°
{x(θ)=(R−r)cos⁡θ+rcos⁡(R−rrθ)y(θ)=(R−r)sin⁡θ−rsin⁡(R−rrθ)\begin{cases} x(\theta) = (R-r)\cos\theta + r\cos\left(\frac{R-r}{r}\theta\right) \\ y(\theta) = (R-r)\sin\theta - r\sin\left(\frac{R-r}{r}\theta\right) \end{cases}

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