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Geometric Mean

Geometric Mean
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2018-02-16 21:12
CircleAngleGeometric Construction
This example demonstrates the construction of geometric mean using the concept of geometric mean. It involves key mathematical concepts such as geometric mean, circle, and angle. Using GeoGebra commands like Segment, Semicircle, Point, etc., the construction of geometric mean-related figures is achieved. Suitable for high school mathematics education and learning.

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. Segment(D_1, H) → GeometricMean
  41. Segment(E_1, H) → Mean
  42. OrthogonalLine(H, n) → l_2
  43. Intersect(n, h_1) → F_1
  44. Intersect(l_2, n) → G_1
  45. Midpoint(n) → H_1
  46. Segment(F, G_1) → m_2
  47. Segment(G_1, G) → n_2
  48. Segment(U, R) → j_2
  49. Segment(U, S) → k_2
  50. Rotate(R, 90°, U) → R'
  51. OrthogonalLine(R', i_1) → j_1
  52. OrthogonalLine(S, j_1) → k_1
  53. Intersect(j_1, k_1) → J
  54. Polygon(U, R', J, S) → ab, u_1, r', j_3, s_2
  55. CircleArc(U, R, R') → c_2
  56. Segment(R, U) → l_1
  57. Line(F, G) → m_1
  58. OrthogonalLine(H, m_1) → p_2
  59. Intersect(m_1, p_2) → K
  60. Segment(F, K) → q_2
  61. Segment(K, G) → r_2
  62. Segment(H, K) → t_2

AI Drawing Prompt Reference

Draw a geometric mean diagram, including a line segment and its semicircle, find the midpoint of the line segment, draw a perpendicular line, intersect it with the semicircle to get a point, connect this point to the ends of the line segment to form two triangles. Rotate a perpendicular line from the midpoint to get another point, connect it to one end of the line segment to form another triangle. Finally, label the geometric mean-related segments and angles to demonstrate the concept of geometric mean.
The prompt above was compiled from the original drawing commands and is for reference only.