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Intersections of Parametric Surfaces with Planes

Intersections of Parametric Surfaces with Planes
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2016-10-14 17:12
Coordinate GeometryParametric EquationGeometric ConstructionSlider Animation
In collections intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve
This example demonstrates the intersections of parametric surfaces with planes. Key mathematical concepts include parametric equations, intersections of surfaces and planes. Using GeoGebra commands like Surface, Element, Textfield, etc., the parametric surface can be constructed, and the intersection points can be observed by adjusting parameters with sliders. Suitable for high school mathematics education and learning parametric equations and solid geometry.

GeoGebra Commands & Parameters

  1. Textfield(u0_{min}) → Textfeld3
  2. Textfield(u0_{max}) → Textfeld4
  3. Textfield(v0_{min}) → Textfeld5
  4. Textfield(v0_{max}) → Textfeld6
  5. Textfield(f0x) → inputBox1
  6. Textfield(f0y) → inputBox2
  7. Textfield(f0z) → inputBox3
  8. Element(lfy, Funktion) → fy
  9. Element(lfx, Funktion) → fx
  10. Element(lfz, Funktion) → fz
  11. Textfield(Funktion) → inputBox4
  12. Surface(fx(u, v), fy(u, v), fz(u, v), u, u_{min}, u_{max}, v, v_{min}, v_{max}) → f3
  13. Textfield(Nn) → inputBox5