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Conformal Mapping Demo

Conformal Mapping Demo
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2013-12-28 22:59
FunctionComplex NumberTransformationGeometric ConstructionGraphing
In collections complex-numbers
This example demonstrates the conformal mapping of one orthogonal grid to another through a complex function, showcasing the geometric properties of complex functions and the concept of conformal mapping. It involves core math concepts like complex functions, conformal mapping, and orthogonality. Constructed using GeoGebra commands such as Sequence, Point, and Locus, it is suitable for high school and above students to explore the applications and properties of complex functions in geometry.

GeoGebra Commands & Parameters

  1. Sequence(Segment[(x(C), k), (x(C) + 0.5, k)], k, y(C), y(C) + 0.5, 0.1) → orizzontali
  2. Sequence(Segment[(k, y(C)), (k, y(C) + 0.5)], k, x(C), x(C) + 0.5, 0.1) → verticali
  3. Point(orizzontali) → A
  4. Point(verticali) → B
  5. Locus(AA, A) → luogo1
  6. Locus(BB, B) → luogo2

AI Drawing Prompt Reference

Draw an orthogonal grid and map it to another orthogonal grid through a complex function to demonstrate the geometric properties of complex functions and the concept of conformal mapping. First, create a grid with horizontal and vertical line segments, then trace the images of these segments under the complex function to form two new loci, finally showing the comparison between the original and mapped grids.
The prompt above was compiled from the original drawing commands and is for reference only.