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Conformal Mapping Demonstration

Conformal Mapping Demonstration
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2020-09-30 08:07
FunctionComplex NumberTransformation
In collections MATH3401 - Lectures
This example visually demonstrates the geometric properties of conformal mapping through dynamic graphics, illustrating how complex functions preserve angles and shapes. It involves core math concepts like complex numbers, function mapping, and transformation characteristics. GeoGebra commands and objects used include Spline, Point, Segment, Vector, Length, and Angle for construction. Suitable for high school and above learners to understand the visual representation and geometric meaning of complex functions.

GeoGebra Commands & Parameters

  1. Spline({A, B, C}, 3) → a
  2. Point(a) → G
  3. Spline({D, E, F}, 3) → b
  4. Point(b) → H
  5. Point(a) → I
  6. Point(a) → J
  7. Point(b) → K
  8. Point(b) → L
  9. Segment(K, L) → g
  10. Segment(I, J) → j
  11. Point(a) → M
  12. Vector(M, N) → u
  13. Vector(M, O) → v
  14. Length(u) → o1
  15. Length(v) → o2
  16. Angle(u, v) → α
  17. Vector(P, (Q * t) + (N * (1 - t))) → w
  18. Vector(P, (R * t) + (O * (1 - t))) → c
  19. Length(c) → o3
  20. Length(w) → o4
  21. Angle(w, c) → β
  22. Spline({(S * t) + (A * (1 - t)), (T * t) + (B * (1 - t)), (U * t) + (C * (1 - t))}, 3) → d
  23. Spline({(V * t) + (D * (1 - t)), (W * t) + (E * (1 - t)), (Z * t) + (F * (1 - t))}, 3) → e
  24. Point(d) → A_1
  25. Point(d) → B_1
  26. Point(e) → C_1
  27. Point(e) → D_1
  28. Segment(A_1, B_1) → h
  29. Segment(C_1, D_1) → i

AI Drawing Prompt Reference

Draw a conformal mapping demonstration consisting of two smooth spline curves representing the domain and its image. Take points on each curve and draw segments connecting them to show corresponding relationships. Construct several vectors emanating from points on the curves to represent directions. Label the lengths of these vectors and the angles between them to visually demonstrate that conformal mapping preserves angles.
The prompt above was compiled from the original drawing commands and is for reference only.