MathPlotAI Logo MathPlotAI

Running Circles around Circles

Running Circles around Circles
Loading the math board and drawing, please wait…
2020-05-15 23:51
CircleTrigonometryComplex NumberParametric EquationGeometric Construction
This example demonstrates how to draw epicycloids and hypocycloids, complex curves generated by circular motion. Key math concepts include circles, complex numbers, curve sketching, and matrix transformations. Construction highlights involve commands like Point, Circle, Vector, Line, and Intersect from GeoGebra. Suitable for high school and above learners to understand parametric equations and locus geometry.

GeoGebra Commands & Parameters

  1. Point((0, 0), u) → A
  2. Point(A, Vector[v_{1} + q]) → B_{1}
  3. Point(A, Vector[v_{2} - q]) → B_{2}
  4. Circle(O, A) → d
  5. Vector(A, B_{1}) → v
  6. Vector(A, B_{2}) → w
  7. Point(A, v_{1}) → B
  8. Circle(A, B) → e
  9. Line(A, O) → f
  10. Intersect(e, f, 1) → C
  11. Intersect(e, f, 2) → D
  12. Circle(D, A) → c
  13. Circle(C, A) → g