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任意边构建等边三角形动态演示

任意边构建等边三角形动态演示
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2019-10-17 08:28
测试改名0多边形向量参数方程几何作图
①本范例动态演示在任意图形边构建等边三角形的过程与性质；②涉及核心数学概念包括等边三角形构造、旋转、向量、参数方程、几何变换等；③作图要点运用了Segment、Rotate、Angle、Point、Polygon、Midpoint、Dilate、Vector、Translate、Line等GeoGebra命令与对象；④适合高中及以上数学教学与几何作图探索。

GeoGebra 命令及参数

  1. Segment(A, B) → f
  2. Rotate(B, (a * π / 180), A) → B'
  3. Angle(B, A, B') → α
  4. Ray(A, B') → g
  5. Point(g) → C
  6. Segment(B, C) → h
  7. Segment(A, C) → i
  8. Polygon(A, B, C) → poly1, c, a_1, b
  9. Polygon(C, B, 3) → poly2, j, k, l, D
  10. Polygon(A, C, 3) → poly3, m, n, p, E
  11. Rotate(A, If[0 < d ≤ 1, (d * π / 3), π / 3], A) → A'
  12. Rotate(C, If[0 < d ≤ 1, (d * π / 3), π / 3], A) → C'
  13. Segment(A', C') → i'
  14. Rotate(B, If[0 < d ≤ 1, (d * π / 3), π / 3], C) → B'_1
  15. Rotate(C, If[0 < d ≤ 1, (d * π / 3), π / 3], C) → C'_1
  16. Segment(B'_1, C'_1) → h'
  17. Rotate(B'_1, If[1 < d ≤ 2, ((d - 1) * π / 3), π / 3], D) → I
  18. Rotate(C'_1, If[1 < d ≤ 2, ((d - 1) * π / 3), π / 3], D) → J
  19. Segment(I, J) → h''
  20. Rotate(A', If[1 < d ≤ 2, ((d - 1) * π / 3), π / 3], E) → A''
  21. Rotate(C', If[1 < d ≤ 2, ((d - 1) * π / 3), π / 3], E) → C''
  22. Segment(A'', C'') → i''
  23. Midpoint(E, D) → L
  24. Dilate(D, If[4 < d ≤ 5, 5 - d, 0], L) → D'
  25. Dilate(L, If[5 < d ≤ 6, 6 - d, 0], E) → L'
  26. Rotate(D, If[6 < d ≤ 7, ((-(d - 6)) * π), (-π)], L) → D'_1
  27. Rotate(D', If[6 < d ≤ 7, ((-(d - 6)) * π), (-π)], L) → D''
  28. Dilate(A, If[3 < d ≤ 4, 4 - d, 0], D) → A'_1
  29. Dilate(D, If[5 < d ≤ 6, 6 - d, 0], B) → D'_2
  30. Vector(D, D'_2) → u
  31. Translate(A, u) → A'_2
  32. Translate(A'_1, u) → F
  33. Segment(A'_2, F) → q'
  34. Line(E, B) → s
  35. Segment(A, B) → q
  36. Rotate(A, If[2 < d ≤ 3, ((d - 2) * π / 3), π / 3], A) → A'_3
  37. Rotate(B, If[2 < d ≤ 3, ((d - 2) * π / 3), π / 3], A) → B'_2
  38. Segment(A'_3, B'_2) → q'_1
  39. Rotate(A'_3, If[3 < d ≤ 4, ((d - 3) * π / 3), π / 3], B'_2) → G
  40. Rotate(B'_2, If[3 < d ≤ 4, ((d - 3) * π / 3), π / 3], B'_2) → H
  41. Segment(G, H) → r
  42. Polygon(A, B'_2, B) → t1, b_1, a_2, b'_2
  43. Dilate(C, If[5 < d ≤ 6, 6 - d, 0], E) → C'_2
  44. Vector(C, C'_2) → v
  45. Translate(B'_1, v) → K
  46. Translate(C'_1, v) → M
  47. Segment(K, M) → h''_1
  48. Dilate(C, If[6 < d ≤ 7, 7 - d, 0], D) → C'_3
  49. Vector(C, C'_3) → w
  50. Translate(A'', w) → A'''
  51. Translate(C'', w) → C'''
  52. Segment(A''', C''') → i'''
  53. Polygon(E, C, D, B'_2) → q1, e, c_1, d_1, b'_1