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复数同伦映射图

复数同伦映射图
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2017-03-12 02:21
函数复数变换
所属专题 Mapping Diagrams to Visualize Complex Analysis
该范例演示了复数同伦映射图，涉及复数函数的概念。通过使用GeoGebra命令，如Sequence、Zip、CurveCartesian等，构建了复数幂函数的映射图。该范例适合高中数学教学，特别是复数与函数章节的教学。

GeoGebra 命令及参数

  1. Sequence(t, t, t_0, t_2, dt) → t_*
  2. Zip((r * ℯ^((B * ί))), B, t_*) → z_*
  3. Zip((x(B), y(B), height_{image}), B, fz_*) → fpoint_*
  4. CurveCartesian((r * cos(t)), (r * sin(t)), height_{image}, t, 0, 6.283185307179586) → d
  5. Textfield(fz_*) → inputBox1
  6. Vector(z_#, f_{(z#).}) → w
  7. Textfield(f_{(z#)}) → inputBox2
  8. CurveCartesian(t, 0, height_{image}, t, -5, 5) → Xh
  9. CurveCartesian(0, t, height_{image}, t, -5, 5) → Yh
  10. Textfield(z_*) → inputBox3
  11. Sphere((0, 0, 4), 1) → RS
  12. Zip(Segment[A, (0, 0, 5)], A, fpoint_*) → RS_v
  13. Zip(Intersect[A, RS], A, RS_v) → RSpt_v
  14. Intersect(zAxis, RS, 2) → A
  15. Segment(A, f_{(z#).}) → f
  16. Intersect(f, RS) → P_∞, C
  17. Zip(Vector[A, B], A, z_*, B, fpoint_*) → fvec_*
  18. Sequence(t, t, t_0 + dt, t_2 + dt, dt) → t_1
  19. Zip((r * ℯ^((B * ί))), B, t_1) → z_1
  20. Element(Euler_S, n + 1) → IntEst
  21. Zip((real(Z), imaginary(Z), height_{image}), Z, Euler_S) → ESum
  22. Sequence(Element[ESum, k], k, 1, n + 1) → ESum_n
  23. Zip(Vector[A, B], A, z_*, B, ESum_n) → ESumV_n
  24. Sequence(Element[dz_*, k], k, 1, n) → dz_n
  25. Zip(Line[A, B], A, z_*, B, fpoint_*) → list1
  26. Zip(Intersect[h, Line[A, B]], A, z_*, B, fpoint_*) → list2