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Pac-Man Phantom Parametric Curve

Pac-Man Phantom Parametric Curve
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2020-04-26 20:17
Coordinate GeometryParametric EquationGeometric Construction
This example demonstrates how to draw the Pac-Man shape curve using parametric equations. It involves core mathematical concepts such as parametric curves, natural numbers, tree diagrams, straight lines, dilation, and rhombuses. The construction utilizes GeoGebra commands and objects like Sequence, CurveCartesian, Surface, Sphere, Vector, Circle, Point, Midpoint, Segment, and Rotate. It is suitable for high school students and teachers learning parametric equations, coordinate geometry, and dynamic geometry.

GeoGebra Commands & Parameters

  1. Sequence((x(O) + (R * cos(i + t)), y(O) + (R * sin(i + t)), z(O) + ((h * R) * cos((n * i)))), i, 0, 6.28329, π / dx) → liste1
  2. Sequence(Polygon[A, Element[liste1, i], Element[liste1, i + 1]], i, 0, Length[liste1] + 2) → liste3
  3. CurveCartesian(x(O) + (R * cos(i + t)), y(O) + (R * sin(i + t)), z(O) + ((h * R) * cos((n * i) + t)), i, 0, 6.58329) → a
  4. Sequence((x(A) + (c * cos(k)), y(A) + (c * sin(k)), z(A)), k, 0, (2 * π), π / dx) → l1
  5. Sequence(Polygon[Element[l1, i + 1], Element[liste1, i], Element[liste1, i + 1]], i, 0, Length[liste1] + 2, 1) → liste2
  6. CurveCartesian((x(A) + (c * cos(k + t)), y(A) + (c * sin(k + t)), z(A)), k, 0, (2 * π)) → b
  7. Surface((u * x(a(t))) + ((1 - u) * x(b(t))), (u * y(a(t))) + ((1 - u) * y(b(t))), (u * z(a(t))) + ((1 - u) * z(b(t))), t, 0, (2 * π), u, 0, 1) → d
  8. Surface(x(A) + ((c * cos(u)) * cos(v)), y(A) + ((c * cos(u)) * sin(v)), z(A) + (c * sin(u)), u, 0, π, v, 0, (2 * π)) → e
  9. Sphere(C, 0.4) → f
  10. CurveCartesian(x(A) + (c * cos(u)), y(A), z(A) + (c / 2 * sin(u)), u, 0, π) → i
  11. Surface(i, (2 * π), zAxis) → j
  12. Vector(C, E) → v
  13. Vector(D, F) → w
  14. Circle(C, 0.4, v) → k
  15. Circle(D, 0.4, w) → p
  16. Point(k) → G
  17. Point(p) → H
  18. Midpoint(C, G) → I
  19. Segment(C, E) → l
  20. Rotate(I, g, l) → I'
  21. Circle(I', 0.2, l) → q
  22. Midpoint(H, D) → J
  23. Segment(D, F) → r
  24. Rotate(J, g, r) → J'
  25. Circle(J', 0.2, r) → s