积极 AI Logo 积极 AI

动画75：几何变换与函数演示

动画75：几何变换与函数演示
几何画板及绘图内容加载中，请稍等……
2016-06-27 09:06
向量函数解析几何变换几何作图
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
①本范例通过动画演示平行四边形、等腰三角形及圆扇形等图形的变换与组合；②涉及核心数学概念包括全等、相似、比例、二次函数、坐标几何等；③构造中运用了Line, Slope, PointIn, Vector, Translate, Segment, Circle, Intersect, CircleSector, Dilate, CircleArc, Rotate, Polygon等命令及对象；④适合高中数学教学，用于理解几何变换与函数图像关系。

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. Circle(A, (0.2 * Min[d, h])) → p
  12. Intersect(p, d, 1) → F
  13. Intersect(p, h, 1) → G
  14. Circle(B, (0.2 * Min[d, h])) → q
  15. Intersect(q, h, 1) → H
  16. Intersect(q, f, 1) → I
  17. CircleSector(A, G, F) → r
  18. CircleSector(B, I, H) → s
  19. Dilate(A, If[0 < k ≤ 1, 1 - k, 0], C') → A'_2
  20. Vector(A, A'_2) → v
  21. Translate(r, v) → r'
  22. CircleArc(A, G, F) → t
  23. Rotate(r', If[1 < k ≤ 2, ((k - 1) * π), 3.141592653589793], C') → r''
  24. Dilate(B, If[2 < k ≤ 3, 3 - k, 0], C) → B'_1
  25. Vector(B, B'_1) → w
  26. Translate(s, w) → s'
  27. Rotate(s', If[3 < k ≤ 4, ((k - 3) * π), 3.141592653589793], C) → s''
  28. CircleArc(B, I, H) → d_1
  29. Polygon(A, B, C', C) → poly1, a_1, b_1, c', c_1