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Dynamic Geometry Animation 185: Parallelogram with Differential Equation and Lin

Dynamic Geometry Animation 185: Parallelogram with Differential Equation and Lin
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2017-02-09 23:42
PolygonAngleFunctionTransformationSlider Animation
In collections Congruence (CO) Cluster Congruence (Vol 2) CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Gail LeBlancCCSS High School: Geometry (Congruence) Volume 2
This example demonstrates a dynamic geometric animation driven by differential equations and linear functions, where a parallelogram, angles, and line segments continuously evolve under slider control, producing complex transformations. Core mathematical concepts include parallelogram properties, angle and segment relationships, differential equations (such as step functions), and the influence of linear functions on geometric parameters. The construction uses GeoGebra commands such as Rotate, Angle, Ray, Line, Point, Intersect, Segment, Min, Circle, Dilate, CircleSector, Vector, Polygon, and Translate, involving objects like points A, B, C, D, E, F, G, H, I, J, K, S and auxiliary elements (a, α, f, g, h, etc.). Suitable for high school and above to explore dynamic geometry and function modeling, and for teachers to demonstrate how parameter changes affect geometric structures.

GeoGebra Commands & Parameters

  1. Rotate(B, a°, A) → B'
  2. Angle(B, A, B') → α
  3. Ray(A, B) → f
  4. Ray(A, B') → g
  5. Line(B, g) → h
  6. Point(g) → C
  7. Line(C, f) → i
  8. Intersect(h, i) → D
  9. Segment(C, D) → j
  10. Segment(A, B) → k
  11. Segment(B, D) → l
  12. Segment(A, C) → m
  13. Min(m, k) → b
  14. Circle(C, (0.2 * b)) → d
  15. Circle(A, (0.2 * b)) → e
  16. Circle(B, (0.2 * b)) → p
  17. Circle(D, (0.2 * b)) → c
  18. Intersect(e, k, 1) → E
  19. Intersect(e, m, 1) → F
  20. Intersect(p, k, 1) → G
  21. Intersect(p, l, 1) → H
  22. Intersect(d, g, 2) → I
  23. Ray(C, I) → q
  24. Intersect(c, h, 2) → J
  25. Ray(D, J) → r
  26. Intersect(c, i, 2) → K
  27. Ray(D, K) → s
  28. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], B) → A'
  29. Segment(A, A') → t
  30. Rotate(E, If[1 < o ≤ 2, ((o - 1) * α), α], A) → E'
  31. CircleSector(A, E, E') → c_1
  32. Dilate(A, If[2 < o ≤ 3, 3 - o, 0], C) → A'_1
  33. Vector(A, A'_1) → u
  34. Segment(A, A'_1) → f_1
  35. Dilate(C, If[3 < o ≤ 4, 4 - o, 0], D) → C'
  36. Vector(C, C') → v
  37. Segment(C, C') → g_1
  38. Dilate(D, If[4 < o ≤ 5, 5 - o, 0], B) → D'
  39. Segment(D, D') → h_1
  40. Polygon(A, B, D, C) → poly1, a_1, b_1, d_2, c_2
  41. Dilate(A, If[5.5 < o ≤ 6.5, 6.5 - o, 0], C) → A'_2
  42. Vector(A, A'_2) → w
  43. Translate(A, w) → A'_3
  44. Translate(A', w) → A''
  45. Dilate(A, If[6.5 < o ≤ 7.5, 7.5 - o, 0], B) → A'_4
  46. Vector(A, A'_4) → u_1
  47. Translate(A, u_1) → A'_5
  48. Translate(A'_1, u_1) → L
  49. Intersect(d, i) → M, N
  50. Intersect(d, g) → O, P
  51. Angle(A, C, N) → β
  52. Rotate(N, If[6.5 < o ≤ 7.5, ((-(o - 6.5)) * β), (-β)], C) → N'
  53. Dilate(C, If[7.5 < o ≤ 8.5, 8.5 - o, 0], B) → C'_1
  54. Vector(C, C'_1) → v_1
  55. Intersect(d, f_1) → Q,
  56. Intersect(d, g_1) → R,
  57. Rotate(R, If[5 < o ≤ 6, ((-(o - 5)) * (π - α)), (-(π - α))], C) → R'
  58. CircleSector(C, R', R) → d_1
  59. Dilate(A, If[6 < o ≤ 7, 7 - o, 0], D) → A'_6
  60. Vector(A, A'_6) → w_1
  61. Translate(c_1, w_1) → e_1
  62. Rotate(e_1, If[7 < o ≤ 8, ((-(o - 7)) * π), (-π)], D) → k_1
  63. Dilate(C, If[8 < o ≤ 9, 9 - o, 0], B) → C'_2
  64. Vector(C, C'_2) → i_1
  65. Translate(d_1, i_1) → p_1
  66. Rotate(p_1, If[9 < o ≤ 10, ((-(o - 9)) * π), (-π)], B) → q_1
  67. Dilate(A, If[11 < o ≤ 12, 12 - o, 0], C) → A'_7
  68. Vector(A, A'_7) → j_1
  69. Translate(c_1, j_1) → r_1
  70. Dilate(C, If[12 < o ≤ 13, 13 - o, 0], D) → C'_3
  71. Vector(C, C'_3) → l_1
  72. Translate(r_1, l_1) → s_1