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几何平均数演示 by chlafrance02

几何平均数演示 by chlafrance02
几何画板及绘图内容加载中，请稍等……
2018-02-17 01:40
圆函数三角函数几何作图
①本范例通过动态演示半圆与线段关系，直观展示几何平均数的几何意义；②涉及核心概念包括几何平均数、切线函数、几何变换、期望值、内切圆、幂函数；③作图要点：使用Segment, Semicircle, Point, OrthogonalLine, Intersect, Line, Rotate, Angle, Polygon, TableText, Midpoint, Textfield, CircleArc等命令构建图形；④适合高中数学教学，用于理解几何平均数的计算与性质。

GeoGebra 命令及参数

  1. Segment(Z, A_1) → t_1
  2. Semicircle(Z, A_1) → d_1
  3. Point(d_1) → B_1
  4. OrthogonalLine(B_1, t_1) → a_1
  5. Intersect(t_1, a_1) → C_1
  6. Segment(C_1, A_1) → h_2
  7. Segment(Z, C_1) → g_2
  8. Line(A, B) → f
  9. OrthogonalLine(C, f) → g
  10. Rotate(A, (-(90°)), C) → A'
  11. Angle(A', C, A) → α
  12. Line(C, A') → h
  13. Intersect(f, h) → D
  14. Intersect(f, g) → E
  15. Polygon(A, C, E) → poly1, e, a, c
  16. Polygon(E, C, D) → poly2, d, e_1, c_1
  17. Segment(E, C) → i
  18. Segment(E, C) → j
  19. Segment(A, E) → k
  20. Segment(E, D) → l
  21. TableText({{A1, B1, C1, D1, E1}, {A2, B2, C2, D2, E2}, {A3, B3, C3, D3, E3}, {A4, B4, C4, D4, E4}, {A5, B5, C5, D5, E5}, {A6, B6, C6, D6, E6}, {A7, B7, C7, D7, E7}}, "|_") → text4
  22. TableText({{A9, B9, C9, D9, E9}, {A10, B10, C10, D10, E10}, {A11, B11, C11, D11, E11}, {A12, B12, C12, D12, E12}, {A13, B13, C13, D13, E13}, {A14, B14, C14, D14, E14}, {A15, B15, C15, D15, E15}, {A16, B16, C16, D16, E16}, {A17, B17, C17, D17, E17}, {A18, B18, C18, D18, E18}, {A19, B19, C19, D19, E19}}, "|_") → text6
  23. Semicircle(F, G) → p
  24. Point(p) → H
  25. Segment(F, G) → n
  26. Midpoint(n) → I
  27. Polygon(H, F, G) → poly3, g_1, h_1, f_1
  28. Semicircle(R, S) → r
  29. Point(r) → T
  30. Polygon(R, T, S) → poly6, s, r_1, t
  31. OrthogonalLine(T, t) → i_1
  32. Intersect(i_1, t) → U
  33. Segment(U, T) → q_1
  34. Polygon(N, O, 4) → poly5, q, n_1, p_1, s_1, P, Q
  35. Polygon(Z, B_1, A_1) → poly7, a_2, z_1, b_1
  36. Segment(B_1, C_1) → f_2
  37. Textfield(u) → InputBox1
  38. Segment(A_1, D) → i_2
  39. Segment(B_1, C_1) → GeometricMean_1
  40. Midpoint(F, G) → E_1
  41. Segment(D_1, H) → GeometricMean
  42. Segment(E_1, H) → Mean
  43. OrthogonalLine(H, n) → l_2
  44. Intersect(n, h_1) → F_1
  45. Intersect(l_2, n) → G_1
  46. Midpoint(n) → H_1
  47. Segment(F, G_1) → m_2
  48. Segment(G_1, G) → n_2
  49. Segment(U, R) → j_2
  50. Segment(U, S) → k_2
  51. Rotate(R, 90°, U) → R'
  52. OrthogonalLine(R', i_1) → j_1
  53. OrthogonalLine(S, j_1) → k_1
  54. Intersect(j_1, k_1) → J
  55. Polygon(U, R', J, S) → ab, u_1, r', j_3, s_2
  56. CircleArc(U, R, R') → c_2
  57. Segment(R, U) → l_1
  58. Midpoint(F, G) → K
  59. Segment(K, H) → m_1
  60. Segment(F, K) → p_2
  61. Segment(K, G) → q_2