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Complex Mapping Diagram with Homotopy

Complex Mapping Diagram with Homotopy
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2017-03-12 02:21
FunctionComplex NumberTransformation
This example demonstrates a complex mapping diagram with homotopy, involving complex functions. Using GeoGebra commands such as Sequence, Zip, and CurveCartesian, the power function mapping is constructed. Suitable for high school mathematics education, particularly in complex numbers and functions.

GeoGebra Commands & Parameters

  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