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动画演示几何平均与圆柱体交集

动画演示几何平均与圆柱体交集
几何画板及绘图内容加载中，请稍等……
2017-03-04 21:54
立体几何几何作图
所属专题 Congruence (CO) Cluster Congruence (Vol 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
①本范例通过动画演示几何平均在圆柱体与圆锥体交集中的变化现象；②涉及核心数学概念包括几何平均、均值、圆柱体、百分比、交集、圆锥截面、立体几何；③作图要点提炼自构造摘要，使用了Ray, Point, Midpoint, Circle, Semicircle, OrthogonalLine, Intersect, Segment, Line, Angle, Rotate, CircleArc, Dilate, CircleSector, Vector, Translate等GeoGebra命令与对象；④适合高中及以上学生及数学爱好者用于理解立体几何与圆锥曲线的动态关系及几何平均的应用。

GeoGebra 命令及参数

  1. Ray(A, (1, 0)) → f
  2. Point(f) → B
  3. Ray(B, C) → g
  4. Point(g) → D
  5. Midpoint(A, D) → E
  6. Circle(E, D) → c
  7. Semicircle(A, D) → d
  8. OrthogonalLine(B, f) → h
  9. Intersect(d, h, 1) → F
  10. Segment(A, F) → i
  11. Line(D, F) → j
  12. Segment(F, D) → k
  13. Angle(A, F, D) → α
  14. Circle(F, 2) → e
  15. Intersect(e, j, 2) → G
  16. Angle(G, F, A) → β
  17. Circle(A, (0.15 * Min[i, k])) → p
  18. Circle(D, Radius[p]) → q
  19. Intersect(p, y = 0) → H, I
  20. Intersect(p, i, 1) → J
  21. Intersect(q, l, 1) → K
  22. Intersect(q, k, 1) → L
  23. Rotate(D, If[0 < a ≤ 1, (a * π), π], E) → D'
  24. CircleArc(E, D, D') → r
  25. Dilate(B, If[1 < a ≤ 2, 2 - a, 0], F) → F'
  26. Segment(B, F') → m
  27. Angle(F, B, A) → γ
  28. CircleSector(A, I, J) → s
  29. CircleSector(D, L, K) → t
  30. Dilate(A, If[3 < a ≤ 4, 4 - a, 0], F) → A'
  31. Dilate(D, If[3 < a ≤ 4, 4 - a, 0], F) → D'_1
  32. Segment(A, A') → n
  33. Segment(D, D'_1) → b
  34. Angle(B, A, F) → δ
  35. Angle(F, D, B) → ε
  36. Rotate(I, If[4 < a ≤ 5, ((a - 4) * δ), δ], A) → I'
  37. Rotate(K, If[4 < a ≤ 5, ((-(a - 4)) * ε), (-ε)], D) → K'
  38. CircleSector(D, K', K) → c_1
  39. CircleSector(A, I, I') → d_1
  40. Ray(F, G) → f_1
  41. Dilate(A, If[6 < a ≤ 7, 7 - a, 0], F) → A'_1
  42. Vector(A, A'_1) → u
  43. Translate(d_1, u) → e_1
  44. Rotate(e_1, If[7 < a ≤ 8, ((-(a - 7)) * π / 2), ((-π)) / 2], F) → g_1
  45. Dilate(D, If[8 < a ≤ 9, 9 - a, 0], F) → D'_2
  46. Vector(D, D'_2) → v
  47. Translate(c_1, v) → h_1
  48. Rotate(h_1, If[9 < a ≤ 10, ((a - 9) * π / 2), π / 2], F) → k_1
  49. Segment(A, B) → i_1
  50. Segment(B, D) → j_1