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Hyperbolic Paraboloid

Hyperbolic Paraboloid
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2015-09-13 22:41
FunctionSolid GeometryCalculus
This example demonstrates the geometric shape of a hyperbolic paraboloid, a type of quadratic surface with unique concave and convex properties. Using GeoGebra's CurveCartesian and Surface commands, you can dynamically adjust parameters a, b, and c to observe changes in the hyperbolic paraboloid. Suitable for high school mathematics education and learning about surface theory in calculus.

GeoGebra Commands & Parameters

  1. CurveCartesian((a * t) + ox, oy, t^(2) + oz, t, -2.449489742783178, 2.449489742783178) → j
  2. Surface(((a * sqrt(w)) * cosh(v)) + x(O), ((b * sqrt(w)) * sinh(v)) + y(O), w + z(O), v, 0, 6.28319, w, 0, 6) → d
  3. Surface((((-a) * sqrt(w)) * cosh(v)) + x(O), ((b * sqrt(w)) * sinh(v)) + y(O), w + z(O), v, 0, 6.28319, w, 0, 6) → e
  4. Surface(((a * sqrt(w)) * cosh(v)) + x(O), (((-b) * sqrt(w)) * sinh(v)) + y(O), w + z(O), v, 0, 6.28319, w, 0, 6) → f
  5. Surface((((-a) * sqrt(w)) * cosh(v)) + x(O), (((-b) * sqrt(w)) * sinh(v)) + y(O), w + z(O), v, 0, 6.28319, w, 0, 6) → g
  6. Surface((((-a) * sqrt(w)) * sinh(v)) + x(O), ((b * sqrt(w)) * cosh(v)) + y(O), (-w) + z(O), v, 0, 6.28319, w, 0, 6) → m
  7. Surface((((-a) * sqrt(w)) * sinh(v)) + x(O), (((-b) * sqrt(w)) * cosh(v)) + y(O), (-w) + z(O), v, 0, 6.28319, w, 0, 6) → n
  8. Surface(((a * sqrt(w)) * sinh(v)) + x(O), ((b * sqrt(w)) * cosh(v)) + y(O), (-w) + z(O), v, 0, 6.28319, w, 0, 6) → o
  9. Surface(((a * sqrt(w)) * sinh(v)) + x(O), (((-b) * sqrt(w)) * cosh(v)) + y(O), (-w) + z(O), v, 0, 6.28319, w, 0, 6) → l
  10. CurveCartesian(ox, (b * t) + oy, (-t^(2)) + oz, t, -2.44949, 2.44949) → i
  11. CurveCartesian((a * cosh(t)) + ox, (b * sinh(t)) + oy, 1 + oz, t, 0, 6.28319) → h
  12. CurveCartesian(((-a) * cosh(t)) + ox, (b * sinh(t)) + oy, 1 + oz, t, 0, 6.28319) → p
  13. CurveCartesian((a * cosh(t)) + ox, ((-b) * sinh(t)) + oy, 1 + oz, t, 0, 6.28319) → q
  14. CurveCartesian(((-a) * cosh(t)) + ox, ((-b) * sinh(t)) + oy, 1 + oz, t, 0, 6.28319) → r
  15. CurveCartesian((a * sinh(t)) + ox, (b * cosh(t)) + oy, -1 + oz, t, 0, 6.28319) → s
  16. CurveCartesian(((-a) * sinh(t)) + ox, (b * cosh(t)) + oy, -1 + oz, t, 0, 6.28319) → t
  17. CurveCartesian((a * sinh(t)) + ox, ((-b) * cosh(t)) + oy, -1 + oz, t, 0, 6.28319) → u
  18. CurveCartesian(((-a) * sinh(t)) + ox, ((-b) * cosh(t)) + oy, -1 + oz, t, 0, 6.28319) → v