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Riemann Sphere in GeoGebra

Riemann Sphere in GeoGebra
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2015-02-16 19:14
Solid GeometryComplex NumberGeometric Construction
In collections GeoGebra, Complex Maps and Riemann Sphere
This example demonstrates the correspondence between points in the Argand plane and their spherical representations. Key mathematical concepts include complex numbers, spherical geometry, and spatial transformations. Construction involves GeoGebra commands such as Intersect, Sphere, SpRs, and Segment. Suitable for high school students or college freshmen to understand the integration of complex number geometry and solid geometry.

GeoGebra Commands & Parameters

  1. Intersect(Line[Pn, P], Sphere[(x(Pn), y(Pn), z(Pn) - r), r], 2) → SpRsP
  2. Sphere((x(Pn), y(Pn), z(Pn) - r), r) → a
  3. SpRs(Pn, r, Q) → SpRsQ
  4. Segment(Pn, Q) → c
  5. Segment(Pn, P) → b

AI Drawing Prompt Reference

Draw a point P on the complex plane. Draw a sphere with center P and radius r. Find the intersection point Q between the complex plane and the sphere. Draw line segment c from P to Q, and line segment b from P to Q. Describe the relationships and construction order of these figures.
The prompt above was compiled from the original drawing commands and is for reference only.