MathPlotAI Logo MathPlotAI

Kuen Surface

Kuen Surface
Loading the math board and drawing, please wait…
2015-02-04 22:11
FunctionCoordinate GeometryParametric Equation
This example demonstrates the Kuen surface, a special surface in hyperbolic geometry. It involves concepts of hyperbolic geometry and piecewise functions. Using GeoGebra commands like Surface and Sequence, the construction process of the surface can be dynamically shown. Suitable for university-level calculus and geometry courses.

GeoGebra Commands & Parameters

  1. Surface((((2 * (cos(u) + (u * sin(u)))) * sin(v))) / (1 + (u^(2) * sin(v)^(2))), (((2 * (sin(u) - (u * cos(u)))) * sin(v))) / (1 + (u^(2) * sin(v)^(2))), (log(tan((1 / 2 * v))) + ((2 * cos(v))) / (1 + (u^(2) * sin(v)^(2)))) / c, u, 0, b, v, 0.02, 3.13) → a
  2. Sequence(CurveCartesian[(((2 * (cos(u) + (u * sin(u)))) * sin(v))) / (1 + (u^(2) * sin(v)^(2))), (((2 * (sin(u) - (u * cos(u)))) * sin(v))) / (1 + (u^(2) * sin(v)^(2))), (log(tan((1 / 2 * v))) + ((2 * cos(v))) / (1 + (u^(2) * sin(v)^(2)))) / c, u, 0, b], v, 0.02, 3.13, 3.11 / n) → liste1
  3. Sequence(CurveCartesian[(((2 * (cos(u) + (u * sin(u)))) * sin(v))) / (1 + (u^(2) * sin(v)^(2))), (((2 * (sin(u) - (u * cos(u)))) * sin(v))) / (1 + (u^(2) * sin(v)^(2))), (log(tan((1 / 2 * v))) + ((2 * cos(v))) / (1 + (u^(2) * sin(v)^(2)))) / c, v, 0.02, 3.13], u, 0, b, b / n) → liste2
  4. Surface((((2 * (cos(u) + (u * sin(u)))) * sin(v))) / (1 + (u^(2) * sin(v)^(2))), ((-(((2 * (sin(u) - (u * cos(u)))) * sin(v))))) / (1 + (u^(2) * sin(v)^(2))), (log(tan((1 / 2 * v))) + ((2 * cos(v))) / (1 + (u^(2) * sin(v)^(2)))) / c, u, 0, b, v, 0.02, 3.13) → d