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Geometric Construction: Spirograph

Geometric Construction: Spirograph
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2019-12-27 00:50
CircleTrigonometryCoordinate GeometryParametric Equation
This example demonstrates the process of drawing a Spirograph using geometric relationships between two circles. It involves core mathematical concepts such as circles, rotation, parametric equations, and coordinate geometry. Key GeoGebra commands used include Circle, Rotate, Intersect, Ray, and Segment. Suitable for high school and above students to explore parametric equations and geometric transformations.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Circle(O, R) → c
  3. Intersect(c, xAxis, 2) → B
  4. Rotate(B, α, O) → T
  5. Ray(O, T) → f
  6. Circle(T, r) → d
  7. Intersect(d, f, 1) → A
  8. Circle(A, r) → e
  9. Circle(A, p) → g
  10. Intersect(g, f, 2) → C
  11. Rotate(C, (-((k * α))), A) → C'
  12. Segment(A, C') → h