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Mapping Squares

Mapping Squares
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2015-10-22 20:08
FunctionCoordinate GeometryComplex NumberLocus
This example demonstrates the mapping of squares under the complex function f(z)=z+1/z, showcasing geometric transformations, function graphs, and conic sections. It involves key math concepts like complex mappings, coordinate geometry, and locus. Constructed using GeoGebra commands like OrthogonalLine, Point, Sequence, and Element, it is suitable for high school and advanced learners exploring complex functions and their visual representations.

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(a - (r * k) + ((ί * r) * t) + 1 / (a - (r * k) + ((ί * r) * t))), y(a - (r * k) + ((ί * r) * t) + 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(a + (r * t) + ((ί * r) * k) + 1 / (a + (r * t) + ((ί * r) * k))), y(a + (r * t) + ((ί * r) * k) + 1 / (a + (r * t) + ((ί * r) * k))), t, -1, 1], k, -1, 1, 1 / n) → liste5

AI Drawing Prompt Reference

Draw the mapping of squares under the complex function f(z)=z+1/z, showcasing geometric transformations, function graphs, and conic sections. Key objects include a vertical line, a marked point, curves, and a combined point. Construction order: first draw the vertical line, then mark the point, then draw the curves, finally combine the points.
The prompt above was compiled from the original drawing commands and is for reference only.