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Logarithmic Property Dynamic Demonstration

Logarithmic Property Dynamic Demonstration
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2019-09-17 02:58
Function
This example dynamically demonstrates the reciprocal property of logarithms through interactive graphics, showcasing the characteristics of logarithmic functions. Core mathematical concepts include logarithmic functions, geometric transformations, and vector operations. It utilizes commands and objects like Textfield, Intersect, Dilate, Segment, Vector, Translate, Rotate, Distance in GeoGebra. Suitable for high school mathematics education to enhance understanding of logarithmic properties and geometric transformations.

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. Translate(i, b_1) → i'
  35. Dilate(W, If[6 < d ≤ 7, 7 - d, 0], L) → W'
  36. Vector(W, W') → w_1
  37. Distance(W, L) → distanceWL
  38. Dilate(T, If[2 < d ≤ 3, 3 - d, 0], U) → T'
  39. Vector(T, T') → e
  40. Distance(T, U) → distanceTU
  41. Rotate(C, If[3 < d ≤ 4, ((-(d - 3)) * π), (-π)], A) → C'_1
  42. Vector(A, C'_1) → q
  43. Dilate(A, If[4 < d ≤ 5, 5 - d, 0], T) → A'_3
  44. Vector(A, A'_3) → u_1
  45. Translate(C'_1, u_1) → Q
  46. Vector(A'_3, Q) → v_1