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TPACK Model Animation Example

TPACK Model Animation Example
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2022-04-06 19:17
TrigonometryParametric Equation
This example demonstrates an animation of the TPACK model. Key mathematical concepts include parametric curves, random variables, and trigonometry. Using GeoGebra commands such as CurveCartesian, Point, and Intersect, dynamic mathematical graphics are constructed. Suitable for mathematics teaching and learning, particularly for teaching parametric equations and trigonometry.

GeoGebra Commands & Parameters

  1. CurveCartesian(((1 / (1 + (0.09 * t)) * sin(t)), (1 / ((0.09 * t) + 1) * cos(t)), t / 4), t, 0, (5 * pi)) → c
  2. Point(xAxis) → I
  3. Intersect(xAxis, yAxis) → J
  4. Polygon(I, J, 3) → pol1, h, i, j, K
  5. Centroid(pol1) → L
  6. Circle(L, 0.5) → e
  7. Segment(I, L) → m
  8. Intersect(e, m, 1) → S
  9. Point(c) → Q
  10. PathParameter(Q) → o
  11. Point(c) → E
  12. Point(c) → D
  13. Point(c) → A
  14. Point(c) → B
  15. Point(c) → C
  16. CurveCartesian((0, v, (1.5 * log(1 / 2, v)) - 0.5), v, 0.1, 1) → b
  17. Rotate(b, α, zAxis) → b'
  18. Mirror(b', zAxis) → b''
  19. Point(zAxis) → F
  20. Point(zAxis) → G
  21. Segment(F, G) → f
  22. Segment(F, G) → g
  23. CurveCartesian((sin(t), cos(t), t / 4), t, 0, (6 * pi)) → a
  24. Point(c) → H
  25. Circle(I, 1.5) → d
  26. Segment(J, L) → l
  27. Segment(K, L) → n
  28. Circle(L, 0.6, space) → p
  29. Intersect(l, p, 1) → M
  30. Intersect(m, p, 1) → N
  31. Intersect(n, p, 1) → O
  32. Vector(J, M) → u
  33. Vector(I, N) → v
  34. Vector(K, L) → w
  35. Translate(d, v) → d'
  36. Segment(J, M) → q
  37. Segment(K, O) → r
  38. Segment(N, I) → s
  39. Point(s) → P
  40. Translate(d, t) → cont
  41. Rotate(cont, 120°, L) → tec
  42. Rotate(tec, 120°, L) → ped
  43. Center(cont) → T
  44. Center(ped) → V
  45. Center(tec) → W
  46. Intersect(cont, ped, 2) → U
  47. Intersect(cont, tec, 1) → Z
  48. Intersect(tec, ped, 1) → A_1
  49. CircleArc(T, U, Z) → c_1
  50. CircleArc(W, Z, A_1) → d_1
  51. CircleArc(V, A_1, U) → e_1

AI Drawing Prompt Reference

Create an animation of the TPACK model with parametric curves. First, draw parametric curve c, then create point I on the x-axis and point J at the intersection with the y-axis, forming polygon pol1 and calculating its centroid L. Draw circle e centered at L, connect I and L with line segment m, and find their intersection S. Create points Q, E, D, A, B, C on curve c, draw parametric curve b and its rotated and mirrored versions b' and b''. Create points F and G on the z-axis, and connect them with line segments f and g. Draw parametric curve a, and connect J and M, K and O, N and I with line segments q, r, s, and point P. Translate circle d to point N, and connect J and M, K and O, N and I with line segments q, r, s, and point P. Translate circle d to point N, rotate and translate curve cont to form tec and ped, and calculate their centers T, V, W, and their intersections U, Z, A_1.
The prompt above was compiled from the original drawing commands and is for reference only.