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Dynamic Logarithmic Properties Demonstration

Dynamic Logarithmic Properties Demonstration
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2017-04-28 10:31
VectorFunctionCalculus
In collections Exponential & Logarithmic Functions Exponential & Logarithmic Functions
This example dynamically illustrates the reciprocal property of logarithmic functions through interactive geometry, showcasing the geometric characteristics of logarithmic functions. It involves core mathematical concepts such as logarithmic functions, vectors, sequences, and limits in differential calculus. The construction utilizes GeoGebra commands and objects like Textfield, Intersect, Dilate, Segment, Vector, Translate, Rotate, and Distance for dynamic interaction and precise calculations. Suitable for high school and above mathematics learners to understand the properties and geometric applications of logarithmic functions.

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

AI Drawing Prompt Reference

Draw a dynamic demonstration of logarithmic functions, including function f and its inverse f_1. Use translation, rotation, and scaling operations to illustrate the geometric properties of logarithmic functions. First, input the function expression, then create the graph of the function and its inverse through translation and rotation. Next, use scaling and rotation to demonstrate the properties of logarithmic functions. Finally, use distance calculations to verify certain geometric relationships.
The prompt above was compiled from the original drawing commands and is for reference only.