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Thom's Lemma

Thom's Lemma
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2023-03-20 05:35
Coordinate GeometryComplex NumberGeometric Construction
In collections geometriadinamica.es
This example illustrates Thom's Lemma, involving complex numbers and geometric construction. Using GeoGebra commands such as Point, Circle, CircleArc, etc., it constructs points and circles on the complex plane. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Point(yAxis) → B
  2. Point(yAxis) → A
  3. If(y(B) ≟ 0, Intersect[f, xAxis, 1], Intersect[f, xAxis, 2]) → R_1
  4. If(y(A) ≟ 0, Intersect[g, xAxis, 1], Intersect[g, xAxis, 2]) → R_2
  5. Circle(O, R_1) → c
  6. CircleArc(O, R_1, Q1) → e
  7. OrthogonalLine(Q1, yAxis) → r
  8. OrthogonalLine(R_2, xAxis) → s
  9. Intersect(r, s) → Q2
  10. Circle(R_2, Q2) → k
  11. CircleArc(R_2, R4, Q2) → p

AI Drawing Prompt Reference

Draw a graph involving complex numbers and geometric construction, illustrating Thom's Lemma. The graph includes points and circles on the complex plane, a circular arc, two orthogonal lines, and a circle. Request the AI drawing tool to construct these objects based on the given coordinates and conditions, ensuring their positions and relationships are accurate.
The prompt above was compiled from the original drawing commands and is for reference only.