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基于向量与旋转变换的等边三角形与平行四边形动态构造演示

基于向量与旋转变换的等边三角形与平行四边形动态构造演示
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2016-06-14 21:30
测试改名0圆多边形向量变换
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
本范例演示利用向量平移与旋转变换构建等边三角形及平行四边形的动态几何关系。涉及的核心数学概念包括向量运算、几何变换、多边形性质及外接圆概念。作图要点在于使用 GeoGebra 命令如 Vector, Translate, Rotate, Dilate, Polygon 等，结合点 A, B, C 及其变换点 A', B', C' 进行精确构造。适合中学几何教学或数学竞赛中的图形变换探究，帮助学生直观理解空间结构。

GeoGebra 命令及参数

  1. Line(A, B) → a
  2. Slope(a) → m
  3. PointIn(c) → C
  4. Line(C, a) → e
  5. Vector(A, B) → u
  6. Translate(C, u) → C'
  7. Segment(B, C') → f
  8. Segment(C, C') → g
  9. Segment(A, B) → h
  10. Segment(A, C) → d
  11. Midpoint(A, C') → D
  12. Dilate(A, If[0 < k ≤ 1, 1 - k, 0], D) → A'
  13. Segment(A, A') → i
  14. Dilate(D, If[1 < k ≤ 2, 2 - k, 0], C') → D'
  15. Segment(D, D') → l
  16. Dilate(C, If[2 < k ≤ 3, 3 - k, 0], D) → C'_1
  17. Segment(C, C'_1) → j
  18. Dilate(D, If[3 < k ≤ 4, 4 - k, 0], B) → D'_1
  19. Segment(D, D'_1) → n
  20. Rotate(D, If[5 < k ≤ 6, ((k - 5) * π), 3.141592653589793], D) → D'_2
  21. Rotate(D', If[4 < k ≤ 5, ((k - 4) * π), 3.141592653589793], D) → D''
  22. Segment(D'_2, D'') → l'
  23. Rotate(D, If[6 < k ≤ 7, ((k - 6) * π), 3.141592653589793], D) → D'_3
  24. Rotate(D'_1, If[5 < k ≤ 6, ((k - 5) * π), 3.141592653589793], D) → E
  25. Segment(D'_3, E) → n'
  26. Rotate(A, If[6 < k ≤ 7, ((-(k - 6)) * π), -3.141592653589793], D) → A'_1
  27. Rotate(B, If[6 < k ≤ 7, ((-(k - 6)) * π), -3.141592653589793], D) → B'
  28. Polygon(A, B, C', C) → poly1, a_1, b_1, c', c_1