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Stereoscopic Lawson Klein Bottle

Stereoscopic Lawson Klein Bottle
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2017-11-09 04:40
Solid GeometryCalculusIntegralGeometric ConstructionGraphing
This example demonstrates the stereoscopic 3D visualization of the Lawson Klein Bottle. It involves core mathematical concepts like Geometric Distribution, Probability, Calculus, Indefinite Integral, and Kite. The construction uses commands such as Surface, CurveCartesian, and Translate in GeoGebra. Suitable for university mathematics students or enthusiasts interested in advanced geometry.

GeoGebra Commands & Parameters

  1. Surface(X(u, v), Y(u, v), Z(u, v), v, 0, (2 * π), u, 0, (2 * π)) → Bottle
  2. CurveCartesian(X((n * v), ((n - 1) * v)), Y((n * v), ((n - 1) * v)), Z((n * v), ((n - 1) * v)), v, 0, (4 * π)) → Bcurve
  3. Translate(Rotate[Rotate[Bcurve, β, xAxis], γ - 3°, zAxis], Vector[(0, 3, 0)]) → Lcurve
  4. Translate(Rotate[Rotate[Bottle, β, xAxis], γ - 3°, zAxis], Vector[(0, 3, 0)]) → Lbottle
  5. Translate(Rotate[Rotate[Bcurve, β, xAxis], γ + 3°, zAxis], Vector[(0, -3, 0)]) → Rcurve
  6. Translate(Rotate[Rotate[Bottle, β, xAxis], γ + 3°, zAxis], Vector[(0, -3, 0)]) → Rbottle