Mapping Squares with Complex Functions

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2015-10-21 19:26

This example demonstrates the mapping of squares using complex functions, illustrating the application of complex functions in geometric transformations. Key mathematical concepts include complex numbers, function transformations, and geometric mappings. The construction uses GeoGebra commands such as OrthogonalLine, Point, Sequence, and Element. Suitable for high school mathematics education and students learning about complex function transformations.

GeoGebra Commands & Parameters

OrthogonalLine(a, yAxis) → c
Point(c) → A
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
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
Sequence(CurveCartesian[x((a + (r * t) + ((ί * r) * k))^(p)), y((a + (r * t) + ((ί * r) * k))^(p)), t, -1, 1], k, -1, 1, 1 / n) → liste5
Sequence(CurveCartesian[x((a - (r * k) + ((ί * r) * t))^(p)), y((a - (r * k) + ((ί * r) * t))^(p)), t, -1, 1], k, -1, 1, 1 / n) → liste6
Element(liste6, 1) → e
Point({liste3, liste4}) → M