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Meusnier Surface

Meusnier Surface
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2016-11-14 01:34
VectorSolid GeometryTransformationParametric EquationGeometric Construction
In collections surface 3D /3D-Oberflächen 1 surface 3D /3D-Oberflächen 1
This example demonstrates the Meusnier surface, a ruled surface generated by a family of curves (e.g., circles or ellipses) intersecting a fixed line. It involves core mathematical concepts like surface generation, vector operations, geometric transformations, and parametric equations. Key GeoGebra commands used include Intersect, Segment, Vector, Rotate, Translate, and Surface. Suitable for high school students and math enthusiasts studying surface geometry and transformations.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Segment(A, B) → a
  3. Vector((0, 0, 0), (0, 0, 1)) → u
  4. Rotate(A, b, zAxis) → A'
  5. Rotate(B, (-b), zAxis) → B'
  6. Segment(A', B') → a'
  7. Translate(A', Vector[(b * u)]) → A''
  8. Translate(B', Vector[(b * u)]) → B''
  9. Segment(Translate[A', Vector[((0.1 * u) * b)]], Translate[B', Vector[((0.1 * u) * b)]]) → a''
  10. Surface((v * sin(u)), (v * cos(u)), (d * u), u, (-12 * π), (12 * π), v, 0, 1) → c