积极 AI Logo 积极 AI

等边三角形动画

等边三角形动画
几何画板及绘图内容加载中，请稍等……
2016-06-29 09:10
测试改名0三角函数几何作图
所属专题 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 CCSS High School: Geometry (Congruence) Volume 2
这个范例演示了等边三角形的动态变化。涉及的核心数学概念包括等边三角形的性质、角度和三角函数。通过使用GeoGebra命令如Line, Ray, Point, Rotate, Angle, Circle等，可以构造出等边三角形的动态变化过程。适合初中及以上学生学习几何变换和动态图形。

GeoGebra 命令及参数

  1. Line(A, B) → f
  2. Ray(A, B) → g
  3. Point(g) → C
  4. Rotate(C, π / 3, A) → C'
  5. Angle(C, A, C') → α
  6. Rotate(A, (-(π / 3)), C) → A'
  7. Angle(A', C, A) → β
  8. Circle(A, C) → c
  9. Circle(C, A) → d
  10. Intersect(c, d, 1) → D
  11. Segment(A, D) → h
  12. Segment(A, C) → i
  13. Segment(C, D) → j
  14. Circle(A, (0.15 * i)) → e
  15. Intersect(e, h, 1) → E
  16. Intersect(e, i, 1) → F
  17. CircleSector(A, F, E) → k
  18. Polygon(A, C, D) → poly1, d_1, a_1, c_1
  19. Dilate(A, If[0 < a ≤ 1, 1 - a, 0], C) → A'_1
  20. Segment(A, A'_1) → l
  21. Dilate(A, If[1 < a ≤ 2, 2 - a, 0], C) → A'_2
  22. Vector(A, A'_2) → u
  23. Translate(k, u) → k'
  24. Rotate(k', If[2 < a ≤ 3, (((a - 2) * 2) * π / 3), (2 * π / 3)], C) → k''
  25. Dilate(C, If[3 < a ≤ 4, 4 - a, 0], D) → C'_1
  26. Vector(C, C'_1) → v
  27. Translate(k'', v) → k'''
  28. Rotate(k''', If[4 < a ≤ 5, (((a - 4) * 2) * π / 3), (2 * π / 3)], D) → p
  29. Dilate(D, If[5 < a ≤ 6, 6 - a, 0], A) → D'
  30. Dilate(D, If[5 < a ≤ 6, 6 - a, 0], C) → D'_1
  31. Segment(D, D') → m
  32. Segment(D, D'_1) → n
  33. Rotate(A, If[6.5 < a ≤ 7.5, ((a - 6.5) * π / 3), π / 3], A) → A'_3
  34. Rotate(A'_1, If[6.5 < a ≤ 7.5, ((a - 6.5) * π / 3), π / 3], A) → G
  35. Segment(A'_3, G) → l'
  36. Rotate(A, If[7.5 < a ≤ 8.5, ((-(a - 7.5)) * π / 3), ((-π)) / 3], C) → A'_4
  37. Rotate(A'_1, If[7.5 < a ≤ 8.5, ((-(a - 7.5)) * π / 3), ((-π)) / 3], C) → H
  38. Segment(A'_4, H) → l'_1