MathPlotAI Logo MathPlotAI

Cardiod (Epicycloid, Hypocycloid) via Rolling Coin

Cardiod (Epicycloid, Hypocycloid) via Rolling Coin
Loading the math board and drawing, please wait…
2019-09-11 03:26
CircleTrigonometryCoordinate Geometry
This example demonstrates the generation of a cardioid (epicycloid, hypocycloid) through a rolling coin. Key mathematical concepts include circles, geometric transformations, and trigonometric functions. Using GeoGebra commands such as Intersect, Circle, Rotate, and CurveCartesian, the trajectory of the cardioid is constructed. Suitable for high school mathematics education, particularly in coordinate geometry and trigonometry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, R) → c
  3. Rotate(C, (-(pi / 2)), B) → C_2
  4. CurveCartesian(((R + r) * cos(θ)) + (r * cos(((1 + R / r) * θ))), ((R + r) * sin(θ)) + (r * sin(((1 + R / r) * θ))), θ, 0, ((2 * pi) * orbits)) → a
  5. Circle(B, abs(r)) → d
  6. Corner(5) → dims
  7. Element(windims, 1) → g
  8. Textfield(ratio) → InputBox1