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Logarithmic Action Dynamic Discovery

Logarithmic Action Dynamic Discovery
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2019-06-27 00:20
TrigonometryCoordinate GeometryTransformationGeometric Construction
In collections Exploring Exponential & Logarithmic Functions Exploring Exponential & Logarithmic Functions
This example demonstrates the dynamic and modifiable properties of logarithms in a geometric context, involving concepts like logarithmic operations, rotation, square, orthocenter, and fractal geometry. It utilizes GeoGebra commands and objects such as Textfield, Intersect, Dilate, Segment, Vector, Translate, Rotate, and Distance as outlined in the construction summary. Suitable for high school and above, it serves as an educational tool for exploring the relationship between logarithmic functions 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. 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

AI Drawing Prompt Reference

Draw a geometric figure demonstrating logarithmic transformations, including logarithmic operations, rotations, squares, orthocenters, and fractal geometry. Start by creating input fields for the logarithmic function and parameter d, then perform a series of transformations such as rotations, translations, and dilations based on the value of d, generating a series of segments and points to illustrate the relationship between logarithmic functions and geometric transformations.
The prompt above was compiled from the original drawing commands and is for reference only.