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Hyperboloid of Two Sheets by Ku, Yin Bon (Albert)

Hyperboloid of Two Sheets by Ku, Yin Bon (Albert)
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2015-09-14 00:18
Coordinate GeometrySolid GeometryParametric Equation
This example demonstrates the geometric shape and equation of the elliptic hyperboloid of two sheets, a type of quadratic surface. Key math concepts include parametric equations, spatial coordinate geometry, and surface transformations. The construction utilizes GeoGebra commands like Surface and CurveCartesian, along with parameters a, b, c, and coordinate points O, ox, oy, oz. Suitable for high school students and university-level mathematics education focusing on solid geometry and surface equations.

GeoGebra Commands & Parameters

  1. Surface(((a * sinh(w)) * cos(v)) + ox, ((b * sinh(w)) * sin(v)) + oy, ((-c) * cosh(w)) + oz, v, 0, 6.28319, w, 0, 6) → d
  2. Surface(((a * sinh(w)) * cos(v)) + ox, ((b * sinh(w)) * sin(v)) + oy, (c * cosh(w)) + oz, v, 0, 6.28319, w, 0, 6) → m
  3. CurveCartesian((a * cos(t)) + ox, (b * sin(t)) + oy, oz + (c * sqrt(2)), t, 0, 6.28319) → h
  4. CurveCartesian((a * cos(t)) + ox, (b * sin(t)) + oy, oz - (c * sqrt(2)), t, 0, 6.28319) → f
  5. CurveCartesian(ox, (b * sinh(w)) + oy, (c * cosh(w)) + oz, w, -6, 6) → e
  6. CurveCartesian(ox, (b * sinh(w)) + oy, ((-c) * cosh(w)) + oz, w, -6, 6) → i
  7. CurveCartesian((a * sinh(w)) + ox, oy, (c * cosh(w)) + oz, w, -6, 6) → j
  8. CurveCartesian((a * sinh(w)) + ox, oy, ((-c) * cosh(w)) + oz, w, -6, 6) → l