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Mapping Squares with 1/z

Mapping Squares with 1/z
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2015-10-22 19:34
FunctionComplex NumberTransformation
This example demonstrates how the transformation 1/z maps squares. Key mathematical concepts include complex numbers and functions. Using GeoGebra commands such as OrthogonalLine, Point, and Sequence, the transformation process is dynamically illustrated. Suitable for high school mathematics education, particularly in teaching complex number and function transformations.

GeoGebra Commands & Parameters

  1. OrthogonalLine(a, yAxis) → c
  2. Point(c) → A
  3. Sequence(CurveCartesian[x(a + (r * t) + ((ί * r) * k)), y(a + (r * t) + ((ί * r) * k)), t, -1, 1], k, -1, 1, 1 / n) → liste3
  4. Sequence(CurveCartesian[x(a - (r * k) + ((ί * r) * t)), y(a - (r * k) + ((ί * r) * t)), t, -1, 1], k, -1, 1, 1 / n) → liste4
  5. Sequence(CurveCartesian[x(1 / (a - (r * k) + ((ί * r) * t))), y(1 / (a - (r * k) + ((ί * r) * t))), t, -1, 1], k, -1, 1, 1 / n) → liste6
  6. Element(liste6, 1) → e
  7. Point({liste3, liste4}) → M
  8. Sequence(CurveCartesian[x(1 / (a + (r * t) + ((ί * r) * k))), y(1 / (a + (r * t) + ((ί * r) * k))), t, -1, 1], k, -1, 1, 1 / n) → liste5