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Oloide by Patrick Clément

Oloide by Patrick Clément
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2016-07-05 21:22
Coordinate GeometrySolid GeometryGeometric Construction
In collections intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve surface 3D surface 3D
This example demonstrates the Oloide, a geometric shape. It involves solid geometry and geometric construction. Using the Surface and CurveCartesian commands, the surface and curves of the Oloide are constructed. Suitable for high school students and math enthusiasts.

GeoGebra Commands & Parameters

  1. Surface(((d + (cos(u) * (1 - v)) + (v * ((-d) + 1 / (d + 1 / cos(u))))) * cos(a)) - ((sin(a) * v) * sqrt(1 - (1 / (d + 1 / cos(u)))^(2))), (sin(u) * (1 - v)), ((d + (cos(u) * (1 - v)) + (v * ((-d) + 1 / (d + 1 / cos(u))))) * sin(a)) + ((cos(a) * v) * sqrt(1 - (1 / (d + 1 / cos(u)))^(2))), u, (-π), π, v, 0, 1) → b
  2. Surface(d + (cos(u) * (1 - v)) + (v * ((-d) + 1 / (d + 1 / cos(u)))), (sin(u) * (1 - v)), ((-v) * sqrt(1 - (1 / (d + 1 / cos(u)))^(2))), u, (-π), π, v, 0, 1) → j
  3. CurveCartesian(d + cos(t), sin(t), 0, t, 0, (2 * π)) → c
  4. CurveCartesian(cos(t), 0, sin(t), t, 0, (2 * π)) → e