积极 AI Logo 积极 AI

动画演示等距三角形与旋转

动画演示等距三角形与旋转
几何画板及绘图内容加载中，请稍等……
2017-06-04 10:04
测试改名0多边形变换几何作图
①本范例通过动画演示等距三角形的构造与旋转变换；②涉及核心数学概念包括全等、等边三角形、旋转、几何变换；③作图要点运用了Polygon（多边形）、Segment（线段）、Rotate（旋转）、Min（最小值）、Line（直线）、Intersect（交点）、Dilate（缩放）等GeoGebra命令；④适合高中数学教学，用于理解几何变换与图形性质。

GeoGebra 命令及参数

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Polygon(C, B, 3) → poly2, d, e, f, D
  3. Polygon(A, C, 3) → poly3, g, h, i, E
  4. Polygon(B, A, 3) → poly4, j, k, l, F
  5. Segment(A, B) → m
  6. Segment(B, C) → n
  7. Segment(C, A) → p
  8. Rotate(B, If[0 < o ≤ 1, (o * π / 3), 1.0471975511965976], B) → B'
  9. Rotate(C, If[0 < o ≤ 1, ((-o) * π / 3), -1.0472], B) → C'
  10. Segment(B', C') → n'
  11. Rotate(B, If[1 < o ≤ 2, ((o - 1) * π / 3), 1.0472], C) → B'_1
  12. Rotate(C, If[0 < o ≤ 1, (o * π / 3), 1.0471975511965976], C) → C'_1
  13. Segment(B'_1, C'_1) → n'_1
  14. Rotate(C, If[2 < o ≤ 3, ((-(o - 2)) * π / 3), -1.0471975511965976], C) → C'_2
  15. Rotate(A, If[2 < o ≤ 3, ((-(o - 2)) * π / 3), -1.0471975511965976], C) → A'
  16. Segment(C'_2, A') → p'
  17. Rotate(C, If[3 < o ≤ 4, ((o - 3) * π / 3), 1.0471975511965976], A) → C'_3
  18. Rotate(A, If[3 < o ≤ 4, ((o - 3) * π / 3), 1.0471975511965976], A) → A'_1
  19. Segment(C'_3, A'_1) → p'_1
  20. Rotate(A, If[4 < o ≤ 5, ((-(o - 4)) * π / 3), -1.0471975511965976], A) → A'_2
  21. Rotate(B, If[4 < o ≤ 5, ((-(o - 4)) * π / 3), -1.0471975511965976], A) → B'_2
  22. Segment(A'_2, B'_2) → m'
  23. Rotate(A, If[5 < o ≤ 6, ((o - 5) * π / 3), 1.0471975511965976], B) → A'_3
  24. Rotate(B, If[5 < o ≤ 6, ((o - 5) * π / 3), 1.0471975511965976], B) → B'_3
  25. Segment(A'_3, B'_3) → m'_1
  26. Min(list1) → t
  27. Rotate(B, π / 3, C) → B'_7
  28. Rotate(A, π / 3, B) → A'_7
  29. Rotate(C, π / 3, A) → C'_7
  30. Line(B'_7, A) → f_1
  31. Line(C, A'_7) → t_1
  32. Line(C'_7, B) → d_1
  33. Intersect(t_1, d_1) → M
  34. Dilate(B'_7, If[6 < o ≤ 7, 7 - o, 0], A) → G
  35. Segment(B'_7, G) → q
  36. Dilate(C'_7, If[7 < o ≤ 8, 8 - o, 0], M) → H
  37. Segment(C'_7, H) → r
  38. Dilate(M, If[8 < o ≤ 9, 9 - o, 0], B) → M'
  39. Segment(M, M') → s
  40. Dilate(A'_7, If[9 < o ≤ 10, 10 - o, 0], M) → I
  41. Segment(A'_7, I) → g_1
  42. Dilate(M, If[10 < o ≤ 11, 11 - o, 0], C) → M'_1
  43. Segment(M, M'_1) → h_1