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Dynamic Logarithmic Properties Demo

Dynamic Logarithmic Properties Demo
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2017-04-28 01:20
FunctionGeometric Construction
In collections Exponential & Logarithmic Functions Exponential & Logarithmic Functions
This example demonstrates the dynamic and modifiable properties of logarithmic functions through interactive exploration. It involves core math concepts like logarithmic functions, geometric transformations, and vector operations. Constructed using GeoGebra commands such as Textfield, Intersect, Dilate, Segment, Vector, Translate, Rotate, and Distance. Ideal for high school and advanced mathematics education and exploratory learning.

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. Translate(A'_2, v) → K
  25. Rotate(K, If[3 < d ≤ 4, ((-(d - 3)) * π / 2), ((-π)) / 2], F) → K'
  26. Intersect(f, p, 1) → N
  27. Rotate(F, If[5 < d ≤ 6, ((d - 5) * π / 2), π / 2], F) → F'_1
  28. Rotate(F', If[5 < d ≤ 6, ((d - 5) * π / 2), π / 2], F) → F''
  29. Dilate(F, If[6 < d ≤ 7, 7 - d, 0], M) → F'_2
  30. Vector(F, F'_2) → w
  31. Translate(F'_1, w) → P
  32. Translate(F'', w) → F'''
  33. Distance(A, C) → distanceAC
  34. Vector(A, A'_2) → i
  35. Dilate(Q, If[3 < d ≤ 4, 4 - d, 0], V) → Q'
  36. Vector(Q, Q') → v_1
  37. Distance(Q, V) → distanceQV
  38. Vector(A, C') → b_1
  39. Translate(i, b_1) → i'
  40. Translate(C, b_1) → C'_1
  41. Vector(K, C'_1) → e
  42. Distance(K, C'_1) → distanceKC'1
  43. Dilate(Q, If[4 < d ≤ 5, 5 - d, 0], C'_1) → Q'_1
  44. Vector(Q, Q'_1) → q
  45. Translate(V, q) → V'
  46. Vector(Q'_1, V') → u_1
  47. Distance(Q'_1, V') → distanceQ'1V'
  48. Dilate(W, If[6 < d ≤ 7, 7 - d, 0], L) → W'
  49. Vector(W, W') → w_1
  50. Distance(W, L) → distanceWL