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动画演示几何变换与轨迹 by Tim Brzezinski

动画演示几何变换与轨迹 by Tim Brzezinski
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2016-06-15 23:40
圆多边形几何作图轨迹
所属专题 Congruence (CO) Cluster Congruence (Vol 1) Congruence (Vol 1) Over 80 Resources CCSS High School: Geometry (Congruence) Volume 1 S N ATTAR Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 Congruence: Volume 1 - Chapter 1 Congruence: Volume 1 - Chapter 1 Congruence V1C1 Check
①本范例通过动画演示圆、梯形等图形的变换与轨迹；②涉及核心数学概念包括角度、圆、多边形、解析几何、极限、几何作图等；③作图要点提炼自构造摘要，使用了Circle, Segment, Point, Ray, Midpoint, OrthogonalLine, Intersect, Rotate, Angle, Vector, CircleSector, Dilate, Translate等GeoGebra命令与对象；④适合高中及以上数学学习者，用于理解几何变换、轨迹及高等数学概念的应用。

GeoGebra 命令及参数

  1. Circle(A, B) → c
  2. Segment(A, B) → a
  3. Point(b) → C
  4. Ray(A, C) → d
  5. Point(d) → D
  6. Circle(D, a) → e
  7. Midpoint(A, D) → E
  8. OrthogonalLine(E, b) → f
  9. Point(f) → F
  10. Ray(E, F) → g
  11. Point(g) → G
  12. Intersect(c, b) → H, I
  13. Intersect(e, b) → J, K
  14. Rotate(I, α, A) → I'
  15. Angle(I, A, I') → β
  16. Rotate(K, π - β, D) → K'
  17. Angle(K, D, K') → γ
  18. Circle(A, (0.4 * a)) → h
  19. Circle(D, (0.4 * a)) → k
  20. Segment(A, I') → i
  21. Segment(D, K') → j
  22. Intersect(h, b, 2) → L
  23. Intersect(h, i, 1) → M
  24. Intersect(k, b, 2) → N
  25. Intersect(k, j, 1) → O
  26. Circle(G, a) → p
  27. Intersect(p, l, 2) → P
  28. Intersect(p, l, 1) → Q
  29. Intersect(p, g, 1) → R
  30. Vector(G, P) → u
  31. CircleSector(A, L, M) → q
  32. CircleSector(D, N, O) → r
  33. Dilate(A, If[0 < m ≤ 1, 1 - m, 0], G) → A'
  34. Vector(A, A') → w
  35. Translate(q, w) → q'
  36. Dilate(D, If[2 < m ≤ 3, 3 - m, 0], G) → D'
  37. Vector(D, D') → n
  38. Translate(r, n) → r'
  39. Vector(G, Q) → s
  40. Vector(A, I') → u_1
  41. Vector(A, I) → t
  42. Vector(D, K) → v_1
  43. Vector(D, K') → w_1
  44. Rotate(q', If[1 < m ≤ 2, ((m - 1) * (π - α)), π - α], G) → q''

AI 绘图提示语参考

绘制一个动态几何演示图：以固定线段为半径作两个圆，其中一个圆上取动点，从该点引射线并在射线上取点，以该点为圆心、原线段长为半径作第三个圆。构造中点与垂线，在垂线上取点并作射线，交各圆于多个交点。通过旋转、平移和缩放操作，展示圆扇形和轨迹的变换，并添加向量表示移动方向。整体呈现圆、多边形、角、轨迹等几何元素的联动动画。
以上提示语为根据原始绘图命令整理而来，仅供参考。