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复对数函数的几何演示

复对数函数的几何演示
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2016-04-09 06:00
函数复数变换几何作图轨迹
①本范例通过几何图形演示复对数函数的性质；②涉及核心数学概念包括复数、对数、旋转、单位圆；③作图要点：使用Line, Point, Circle, Polygon, Vector, OrthogonalLine, Translate, Intersect, Locus等GeoGebra命令和对象构建图形；④适合高中及以上数学学习者，用于理解复对数函数的几何意义和变换特性。

GeoGebra 命令及参数

  1. Line(Q, R) → j
  2. Point(j) → S
  3. Circle(D, E) → d_1
  4. Point(d_1) → J
  5. Polygon(A, B, C) → poly1, c_1, a_1, b_1
  6. Vector(F, G) → u
  7. OrthogonalLine(F, u) → e_1
  8. Point(e_1) → H
  9. Translate(G, u) → G'_1
  10. Translate(H, u) → H'_1
  11. Polygon(F, H, H'_1, G) → poly2, f, h, h', g
  12. Vector(F, G'_1) → v
  13. Translate(F, v) → F'
  14. Translate(H, v) → H'
  15. Translate(H'_1, v) → I
  16. Translate(G, v) → G'
  17. Polygon(F', H', I, G') → poly2', f', h'_1, i, g'
  18. Translate(F', v) → F''
  19. Translate(H', v) → H''
  20. Translate(I, v) → I'
  21. Translate(G', v) → G''
  22. Polygon(F'', H'', I', G'') → poly2'', f'', h'', i', g''
  23. Point(poly1) → L
  24. Point(poly2) → M
  25. Point(poly2') → N
  26. Point(poly2'') → O
  27. Intersect(xAxis, yAxis) → P_1
  28. Circle(P_1, 1) → k
  29. Polygon(K, T, 5) → poly3, k_1, t, p, q, r, U, V, W
  30. Polygon(K, V, T, W, U) → poly4, k_2, v_1, t_1, w, u_1
  31. Point(poly4) → Z
  32. Locus(S', S) → loc6
  33. Locus(J', J) → loc1
  34. Locus(L', L) → loc2
  35. Locus(M', M) → loc3
  36. Locus(N', N) → loc4
  37. Locus(O', O) → loc5
  38. Locus(Z', Z) → loc7