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Stereometric projection on Riemann sphere

Stereometric projection on Riemann sphere
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2015-08-03 00:18
TrigonometrySolid GeometryComplex NumberGeometric Construction
In collections On Sphere
This example demonstrates stereometric projection on the Riemann sphere. It involves core mathematical concepts such as spherical geometry, projection transformations, and properties of the Riemann sphere. The construction uses GeoGebra commands and objects like Circle, Intersect, Point, Sphere, Locus, and Line. Suitable for high school and above students to understand the connection between complex numbers and geometry, as well as applications of spherical projections.

GeoGebra Commands & Parameters

  1. Circle(U, W) → d
  2. Intersect(zAxis, xAxis) → A
  3. Point(zAxis) → B
  4. Sphere(A, B) → a
  5. Point(d) → C
  6. Point(yAxis) → F
  7. Point(yAxis) → O
  8. Locus(D, C) → loc1
  9. Line(R, S) → c
  10. Point(c) → V
  11. Locus(T, V) → loc2

AI Drawing Prompt Reference

Draw a stereometric projection onto a Riemann sphere. First, draw a circle d. Then, find the intersection point A of the z-axis and x-axis. Take a point B on the z-axis, and draw a sphere a with A and B as its diameter. Next, take a point C on circle d, and points F and O on the y-axis. Draw an arc trajectory loc1 starting from C. Then, draw a line c, and an arc trajectory loc2 starting from a point V on the y-axis. Finally, take a point V on line c.
The prompt above was compiled from the original drawing commands and is for reference only.