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A Swirl of Spirals

A Swirl of Spirals
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2019-04-03 17:40
VectorCoordinate GeometryParametric Equation
This example demonstrates a combination of spiral lines in polar coordinates. Key mathematical concepts include polar coordinates, parametric equations, and vectors. Using commands like CurveCartesian and Point, complex geometric shapes can be constructed. Suitable for high school mathematics education, particularly in coordinate geometry and parametric equations.

GeoGebra Commands & Parameters

  1. CurveCartesian((k_L^(t) * cos(t)), (k_L^(t) * sin(t)), t, 0, (10 * π)) → LogS
  2. Point(LogS) → A
  3. CurveCartesian(((k_A * t) * cos(t)), ((k_A * t) * sin(t)), t, 0, (10 * π)) → Arch
  4. Point(Arch) → B
  5. CurveCartesian(cos(t) / sqrt(t / k_C), sin(t) / sqrt(t / k_C), t, 0.01, (10 * π)) → Cotes
  6. Point(Cotes) → C
  7. CurveCartesian(((-sqrt(t)) * cos(t)), ((-sqrt(t)) * sin(t)), t, 0, (10 * π)) → FermatN
  8. CurveCartesian((cos(t) * sqrt((k_F * t))), (sin(t) * sqrt((k_F * t))), t, 0, (10 * π)) → FermatP
  9. Point(FermatP) → D