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Dynamic Logarithmic Action Demonstration

Dynamic Logarithmic Action Demonstration
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2017-04-28 20:44
FunctionGeometric Construction
In collections Exponential & Logarithmic Functions
This example dynamically demonstrates the power property of logarithms, visually integrating logarithmic functions with geometric elements like polygons and vectors. Key math concepts include logarithmic functions, power operations, geometric transformations, and vector mathematics. It leverages GeoGebra commands such as Textfield, Intersect, Dilate, Segment, Vector, Translate, Rotate, Distance, Midpoint, Line, and Circle for dynamic graph generation and manipulation. Suitable for high school and above mathematics education to understand logarithmic properties and geometric applications.

GeoGebra Commands & Parameters

  1. Textfield(a) → InputBox1
  2. Textfield(f_1) → InputBox2
  3. Textfield(f) → InputBox3
  4. Intersect(f, h, 1) → E
  5. Dilate(F, If[0 < d ≤ 1, 1 - d, 0], A) → F'
  6. Dilate(A, If[1 < d ≤ 2, 2 - d, 0], B) → A'
  7. Segment(A, A') → j
  8. Dilate(B, If[2 < d ≤ 3, 3 - d, 0], G) → B'
  9. Vector(B, B') → u
  10. Translate(A, u) → A'_1
  11. Translate(A', u) → A''
  12. Segment(A'_1, A'') → j'
  13. Rotate(A'_1, If[3 < d ≤ 4, ((-(d - 3)) * π / 2), ((-π)) / 2], F) → H
  14. Rotate(A'', If[3 < d ≤ 4, ((-(d - 3)) * π / 2), ((-π)) / 2], F) → A'''
  15. Segment(H, A''') → j''
  16. Rotate(A'_1, If[3 < d ≤ 4, ((d - 3) * π / 2), π / 2], F) → I
  17. Rotate(A'', If[3 < d ≤ 4, ((d - 3) * π / 2), π / 2], F) → A'''_1
  18. Dilate(D, If[4 < d ≤ 5, 5 - d, 0], E) → D'
  19. Segment(D, D') → l
  20. Dilate(A, If[1 < d ≤ 2, 2 - d, 0], C) → A'_2
  21. Segment(A, A'_2) → m
  22. Dilate(A, If[2 < d ≤ 3, 3 - d, 0], R) → C'
  23. Vector(C, C') → v
  24. Intersect(f, p, 1) → N
  25. Rotate(F, If[5 < d ≤ 6, ((d - 5) * π / 2), π / 2], F) → F'_1
  26. Rotate(F', If[5 < d ≤ 6, ((d - 5) * π / 2), π / 2], F) → F''
  27. Dilate(F, If[6 < d ≤ 7, 7 - d, 0], M) → F'_2
  28. Vector(F, F'_2) → w
  29. Translate(F'_1, w) → P
  30. Translate(F'', w) → F'''
  31. Distance(A, C) → distanceAC
  32. Vector(A, A'_2) → i
  33. Vector(A, C') → b_1
  34. Midpoint(Z, A_1) → Q
  35. Line(B_1, C_1) → e
  36. Segment(B_1, C_1) → g_1
  37. Circle(B_1, g_1 / 3) → c_1
  38. Intersect(c_1, e, 2) → T
  39. Circle(T, g_1 / 3) → d_1
  40. Intersect(d_1, e, 2) → U
  41. Dilate(Z, If[2 < d ≤ 3, 3 - d, 0], Q) → Z'
  42. Segment(Z, Z') → q
  43. Dilate(Q, If[3 < d ≤ 4, 4 - d, 0], A_1) → Q'
  44. Segment(Q, Q') → h_1
  45. Dilate(B_1, If[4 < d ≤ 5, 5 - d, 0], T) → D_1
  46. Segment(B_1, D_1) → i_1
  47. Dilate(T, If[5 < d ≤ 6, 6 - d, 0], U) → T'
  48. Segment(T, T') → j_1
  49. Dilate(U, If[6 < d ≤ 7, 7 - d, 0], C_1) → U'
  50. Segment(U, U') → k_1
  51. Segment(A, A'_2) → l_1
  52. Distance(Z, A_1) → distanceZA1
  53. Distance(B_1, C_1) → distanceB1C1
  54. Dilate(A, If[7 < d ≤ 8, 8 - d, 0], Z) → A'_3
  55. Vector(A, A'_3) → u_1
  56. Dilate(A, If[7 < d ≤ 8, 8 - d, 0], B_1) → A'_4
  57. Vector(A, A'_4) → v_1
  58. Translate(A, u_1) → A'_5
  59. Translate(A'_2, u_1) → L
  60. Segment(A'_5, L) → m_1
  61. Translate(A, v_1) → A'_6
  62. Translate(A'_2, v_1) → W
  63. Segment(A'_6, W) → n_1
  64. Rotate(A'_5, If[8 < d ≤ 9, ((d - 8) * π), π], Q) → E_1
  65. Rotate(L, If[8 < d ≤ 9, ((d - 8) * π), π], Q) → L'
  66. Segment(E_1, L') → p_1
  67. Rotate(A'_6, If[8 < d ≤ 9, ((d - 8) * π), π], T) → F_1
  68. Rotate(W, If[8 < d ≤ 9, ((d - 8) * π), π], T) → W'
  69. Segment(F_1, W') → q_1
  70. Rotate(F_1, If[9 < d ≤ 10, ((d - 9) * π), π], U) → G_1
  71. Rotate(W', If[9 < d ≤ 10, ((d - 9) * π), π], U) → W''
  72. Segment(G_1, W'') → r_1