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Hypocycloid

Hypocycloid
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2020-04-02 10:32
CircleTrigonometryParametric EquationGeometric ConstructionGraphing
This example demonstrates the generation of a hypocycloid, the path traced by a point on the circumference of a small circle rolling inside a fixed larger circle. Key math concepts include circle, parametric equations, trigonometric functions, and geometric construction. The construction leverages GeoGebra commands like Intersect, Segment, CircleArc, Angle, and CurveCartesian. It is suitable for high school mathematics education, illustrating parametric equations, trigonometric applications, and dynamic geometry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Segment(O, A) → f
  3. Segment(O, B) → g
  4. CircleArc(O, A, B) → c
  5. CircleArc(C, P, B) → d
  6. Angle(A, O, B) → α
  7. Angle(D, C, B) → β
  8. Angle(P, C, B) → γ
  9. CurveCartesian(((a - b) * cos(t)) + (b * cos(((a - b) / b * t))), ((a - b) * sin(t)) - (b * sin(((a - b) / b * t))), t, 0, θ) → e
  10. Segment(C, D) → h
  11. Segment(C, P) → i
  12. Segment(O, C) → l
  13. Segment(O, F) → k
  14. Segment(O, E) → j
  15. Segment(F, C) → m
  16. Segment(E, C) → n
  17. Segment(H, P) → p
  18. Segment(G, P) → q