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动画137：几何变换与多边形演示

动画137：几何变换与多边形演示
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2016-11-06 12:23
函数解析几何立体几何几何作图
所属专题 Congruence (CO) Cluster Congruence (Vol 1) Geometry Review Congruence (Vol 1) Over 80 Resources Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 S N ATTAR CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 Unit 5: Triangle Congruence Triangle Congruence Theorems 1 Triangle Congruence Book 1
①本范例通过动画演示了立方体、多边形及二次函数图像的变换过程；②涉及的核心数学概念包括向量的平移、旋转、多边形的构造、函数图像的绘制以及参数方程的应用；③作图要点提炼自构造摘要，使用了Rotate（旋转）、Vector（向量）、Translate（平移）、Polygon（多边形）、Line（直线）等GeoGebra命令；④适合高中及以上学段，可用于立体几何、解析几何及函数图像的教学演示。

GeoGebra 命令及参数

  1. Rotate(B, α, A) → B'
  2. Angle(B, A, B') → β
  3. Ray(A, B') → f
  4. Point(f) → C
  5. Rotate(A, (-γ), B) → A'
  6. Angle(A', B, A) → δ
  7. Ray(B, A') → g
  8. Intersect(f, g) → D
  9. Polygon(A, B, D) → poly1, d, a_1, b
  10. Segment(A, B) → h
  11. Segment(D, B) → i
  12. Segment(D, A) → j
  13. Min({h, i, j}) → c
  14. Circle(A, (0.2 * c)) → e
  15. Circle(B, (0.2 * c)) → k
  16. Intersect(e, h) → E,
  17. Intersect(e, j) → F, I
  18. Intersect(k, h) → G,
  19. Intersect(k, i) → H, J
  20. CircleSector(A, E, F) → p
  21. CircleSector(B, H, G) → q
  22. Rotate(K, β, L) → K'
  23. Angle(K, L, K') → ε
  24. Circle(L, h) → r
  25. Ray(L, K) → m
  26. Intersect(r, m, 1) → M
  27. Ray(L, K') → n
  28. Rotate(L, (-γ), M) → L'
  29. Angle(L', M, L) → ζ
  30. Ray(M, L') → s
  31. Intersect(n, s) → N
  32. Dilate(A, If[0 < l ≤ 1, 1 - l, 0], L) → A'_1
  33. Vector(A, A'_1) → u
  34. Translate(p, u) → p'
  35. Line(L, h) → t
  36. Translate(F, u) → F'
  37. Point(t) → O
  38. Angle(M, L, O) → η
  39. Rotate(p', If[1 < l ≤ 2, ((-(l - 1)) * η), (-η)], L) → p''
  40. Point(t) → P
  41. Angle(P, L, M) → θ
  42. Dilate(B, If[2 < l ≤ 3, 3 - l, 0], L) → B'_1
  43. Vector(B, B'_1) → v
  44. Translate(A, v) → A'_2
  45. Translate(B, v) → B'_2
  46. Segment(A'_2, B'_2) → h'
  47. Rotate(A'_2, If[3 < l ≤ 4, ((l - 3) * θ), θ], L) → Q
  48. Rotate(B'_2, If[3 < l ≤ 4, ((l - 3) * θ), θ], L) → R
  49. Segment(Q, R) → h''
  50. Dilate(B, If[4 < l ≤ 5, 5 - l, 0], M) → B'_3
  51. Vector(B, B'_3) → w
  52. Translate(q, w) → q'
  53. Line(M, g) → f_1
  54. Point(f_1) → S
  55. Angle(N, M, S) → τ
  56. Rotate(q', If[5 < l ≤ 6, ((l - 5) * ((2 * π) - τ)), (2 * π) - τ], M) → q''
  57. Dilate(B, If[6 < l ≤ 7, 7 - l, 0], M) → B'_4
  58. Vector(B, B'_4) → u_1
  59. Translate(A, u_1) → A'_3
  60. Translate(B, u_1) → B'_5
  61. Translate(D, u_1) → D'
  62. Polygon(A'_3, B'_5, D') → poly1', d', a'_3, b'_5
  63. Rotate(A'_3, If[7 < l ≤ 8, ((-(l - 7)) * τ), (-τ)], M) → T
  64. Rotate(B'_5, If[7 < l ≤ 8, ((-(l - 7)) * τ), (-τ)], M) → U
  65. Rotate(D', If[7 < l ≤ 8, ((-(l - 7)) * τ), (-τ)], M) → D''
  66. Polygon(T, U, D'') → poly1'', d'', t_1, u_2