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Pac-Man Vector Components

Pac-Man Vector Components
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2020-10-29 02:42
VectorCoordinate GeometryGeometric Construction
In collections Vector Operations
This example uses the Pac-Man character to demonstrate vector components. It involves key mathematical concepts such as vectors, coordinates, and geometric triangles. Using GeoGebra commands like Vector, Translate, Rotate, Line, Surface, and Dilate, it dynamically shows the transformation of vector components. Suitable for high school math education and learning vector-related knowledge.

GeoGebra Commands & Parameters

  1. Random(-5, 5) → a
  2. Sequence(i, i, a + 1, 5, 1) → l3
  3. Sequence(i, i, -5, a - 1, 1) → l2
  4. Union(l2, l3) → l4
  5. Vector((xc, yc, zc)) → u
  6. Random(-5, 5) → c
  7. RandomElement(l4) → b
  8. CurveCartesian(x(A) - sin(t), y(A) + cos(t), z(A), t, 0, π) → g
  9. Translate(A, u) → A'
  10. Vector(A, A') → v
  11. Rotate(A - (0, 1.5, 0), If[yc ≥ 0, α, (2 * π) - α], A, Line[A, A + (0, 0, 1)]) → D
  12. Rotate(A + (0, 1.5, 0), If[yc ≥ 0, α, (2 * π) - α], A, Line[A, A + (0, 0, 1)]) → C
  13. Rotate(g, If[yc ≥ 0, α, (2 * π) - α], A, Line[A, A + (0, 0, 1)]) → g'
  14. Rotate(g', If[zc ≥ 0, β, (2 * π) - β], A, If[zc ≥ 0, Line[C, D], Line[D, C]]) → g''
  15. Random(-5, 5) → d
  16. Random(-5, 5) → e
  17. Random(-5, 5) → f
  18. Line(C, D) → j
  19. Surface(g'', (3 * π / 4) + m, Line[C, D]) → k
  20. Dilate(A, If[0 < l ≤ 1, 1 - l, 0], A') → A'_1
  21. Surface(g'', (3 * π / 4) + m, Line[D, C]) → i
  22. Vector(A, A'_1) → w
  23. Translate(i, w) → i'
  24. Translate(k, w) → k'
  25. Sequence(i, i, -5, 5, 1) → l1
  26. Segment(A, Food) → q
  27. Vector((x(Food) - x(A), y(Food) - y(A), z(Food) - z(A))) → r
  28. Midpoint(q) → B
  29. Midpoint(A, B) → E
  30. Midpoint(B, Food) → F
  31. Circle(F, 1 / 2, y = 0) → s
  32. Circle(B, 1 / 2, y = 0) → c_1
  33. Circle(Food, 1 / 2, y = 0) → d_1
  34. Circle(E, 1 / 2, y = 0) → t
  35. Rotate(d_1, q_{1}, Line[Food, Food + (0, 0, 1)]) → e_1
  36. Rotate(s, q_{1}, Line[F, F + (0, 0, 1)]) → f_1
  37. Rotate(c_1, q_{1}, Line[B, B + (0, 0, 1)]) → g_1
  38. Rotate(t, q_{1}, Line[E, E + (0, 0, 1)]) → t'

AI Drawing Prompt Reference

Draw a three-dimensional Pac-Man character with a semicircular body surface, rotated around a vertical axis to demonstrate vector components. The Pac-Man is placed at a random point and translated by a vector to a new position, with an arrow showing the displacement. In front of the Pac-Man, place a series of small spheres along a line segment, representing food pellets, each capable of rotating around its center. Include coordinate axes and a grid background to illustrate vector components and geometric relationships.
The prompt above was compiled from the original drawing commands and is for reference only.