对数性质动态演示 by Tim Brzezinski

对数性质动态演示 by Tim Brzezinski
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2019-09-17 02:58
①本范例动态演示对数的倒数性质,通过交互式图形展示对数函数的特性;②涉及核心数学概念包括对数函数、几何变换、向量运算;③作图要点运用了Textfield, Intersect, Dilate, Segment, Vector, Translate, Rotate, Distance等GeoGebra命令与对象;④适合高中数学教学,用于加深学生对对数性质及几何变换的理解。

GeoGebra 命令及参数

  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