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Visualizing Parametric Equations

Visualizing Parametric Equations
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2016-12-04 23:22
TrigonometryCoordinate GeometryParametric EquationGeometric ConstructionGraphing
This example dynamically demonstrates how parametric equations generate plane curves. It involves core math concepts like parametric equations, coordinate geometry, trigonometry, and geometric transformations. Key GeoGebra commands and objects used include Circle, Rotate, OrthogonalLine, Intersect, Segment, CurveCartesian, and Angle. Suitable for high school students and math enthusiasts learning the application and visualization of parametric equations.

GeoGebra Commands & Parameters

  1. Circle(A, C) → e
  2. Circle(B, D) → f
  3. Rotate(C, (d * b), A) → C'
  4. Rotate(D, ((-a) * b), B) → D'
  5. OrthogonalLine(C', yAxis) → g
  6. OrthogonalLine(D', xAxis) → h
  7. Intersect(h, g) → E
  8. Segment(C', E) → i
  9. Segment(D', E) → j
  10. CurveCartesian(cos((a * t)) + 1, sin((d * t)) + 1, t, 0, b) → c
  11. Segment(A, C) → k
  12. Segment(B, D) → l
  13. Segment(A, C') → m
  14. Segment(B, D') → n
  15. Angle(C, A, C') → α
  16. Angle(D', B, D) → β