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等边三角形构建关系的动态演示

等边三角形构建关系的动态演示
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2017-08-18 19:59
测试改名0多边形角三角函数几何作图
①本范例动态演示了从任意三角形两边构建两个等边三角形时产生的特殊关系；②涉及核心数学概念包括全等、等边三角形、几何分布、对数、差值与斜率、三角函数；③作图要点：使用Segment、Rotate、Angle、Ray、Point、Polygon、Midpoint、Dilate等GeoGebra命令构建图形；④适合高中及以上数学学习者和教师用于探索几何变换与关系。

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(C, A) → F
  24. Midpoint(B, C) → G
  25. Dilate(C, If[2 < d ≤ 3, 3 - d, 0], F) → C'_2
  26. Dilate(C, If[2 < d ≤ 3, 3 - d, 0], G) → C'_3
  27. Segment(C, C'_2) → q
  28. Segment(C, C'_3) → r
  29. Rotate(C, If[3 < d ≤ 4, ((d - 3) * π), π], F) → C'_4
  30. Rotate(C'_2, If[3 < d ≤ 4, ((d - 3) * π), π], F) → H
  31. Segment(C'_4, H) → q'
  32. Rotate(C, If[3 < d ≤ 4, ((-(d - 3)) * π), (-π)], G) → C'_5
  33. Rotate(C'_3, If[3 < d ≤ 4, ((-(d - 3)) * π), (-π)], G) → K
  34. Segment(C'_5, K) → r'
  35. Midpoint(E, D) → L
  36. Polygon(F, G, L) → poly4, l_1, f_1, g_1
  37. Dilate(D, If[4 < d ≤ 5, 5 - d, 0], L) → D'
  38. Dilate(L, If[5 < d ≤ 6, 6 - d, 0], E) → L'
  39. Segment(D, D') → s
  40. Segment(L, L') → t
  41. Rotate(D, If[6 < d ≤ 7, ((-(d - 6)) * π), (-π)], L) → D'_1
  42. Rotate(D', If[6 < d ≤ 7, ((-(d - 6)) * π), (-π)], L) → D''
  43. Segment(D'_1, D'') → s'
  44. Dilate(L, If[7 < d ≤ 8, 8 - d, 0], G) → L'_1
  45. Segment(L, L'_1) → e
  46. Rotate(L, If[8 < d ≤ 9, ((d - 8) * π / 3), π / 3], G) → L'_2
  47. Rotate(L'_1, If[8 < d ≤ 9, ((d - 8) * π / 3), π / 3], G) → M
  48. Segment(L'_2, M) → e'
  49. Rotate(L'_2, If[9 < d ≤ 10, ((d - 9) * π / 3), π / 3], F) → N
  50. Rotate(M, If[9 < d ≤ 10, ((d - 9) * π / 3), π / 3], F) → M'
  51. Segment(N, M') → e''