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Oloide

Oloide
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2019-01-07 01:52
Solid GeometryTransformationGeometric Construction
This example demonstrates the Oloide, a unique geometric shape formed by two ellipsoids sharing a common spherical surface. Key mathematical concepts include ellipsoids, spheres, and geometric transformations. Using GeoGebra commands such as Intersect, CurveCartesian, Surface, and Mirror, the construction process of the Oloide is dynamically shown. Suitable for high school and above students or teachers.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → C
  2. CurveCartesian((r * cos(t + pi / 3)) - r / 2, (r * sin(t + pi / 3)), 0, t, 0, (2 * pi / 3)) → a
  3. CurveCartesian((r * cos(t)) + r / 2, 0, (r * sin(t)), t, 0, (2 * pi / 3)) → b
  4. Surface((a(t) * k) + (b(t) * (1 - k)), k, 0, 1, t, 0, (2 * pi / 3)) → c
  5. Mirror(c, Plane[y = 0]) → c1
  6. Mirror(c, Plane[z = 0]) → c3
  7. Mirror(c1, Plane[z = 0]) → c2
  8. Mirror(a, Plane[y = 0]) → a'
  9. Mirror(b, Plane[z = 0]) → b'