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Geometric Mean Demonstration by chlafrance02

Geometric Mean Demonstration by chlafrance02
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2018-02-17 01:40
CircleFunctionTrigonometryGeometric Construction
This example dynamically demonstrates the relationship between a semicircle and line segments, visually illustrating the geometric mean. It involves core concepts like geometric mean, tangent function, geometric transformations, expected value, incircle, and power functions. Construction uses commands such as Segment, Semicircle, Point, OrthogonalLine, Intersect, Line, Rotate, Angle, Polygon, TableText, Midpoint, Textfield, CircleArc. Suitable for high school mathematics teaching to understand the calculation and properties of the geometric mean.

GeoGebra Commands & Parameters

  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