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Double Heart Surface Geometric Construction Inside a Sphere

Double Heart Surface Geometric Construction Inside a Sphere
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2016-07-02 00:47
Solid GeometryParametric EquationGeometric Construction
This example demonstrates the geometric construction of a double heart-shaped surface within a sphere. Core concepts include solid geometry and parametric equations. Construction utilizes GeoGebra's Sphere and Surface commands with variables a, b, amax to control shape. Suitable for high school and college students exploring spatial graphics, parametric modeling, and mathematical visualization.

GeoGebra Commands & Parameters

  1. Sphere((0, 0, 0), 1) → b
  2. Surface((sin((v * (1 - u))) * sin((u * π))), (-cos((v * (1 - u)))), (sin((v * (1 - u))) * cos((u * π))), u, 0, uu, v, a, amax) → o
  3. Surface(((-sin((v * (1 - u)))) * sin((u * π))), (-cos((v * (1 - u)))), (sin((v * (1 - u))) * cos((u * π))), u, 0, uu, v, a, amax) → p
  4. Surface(((-sin((v * (1 - u)))) * sin((u * π))), cos((v * (1 - u))), ((-sin((v * (1 - u)))) * cos((u * π))), u, 0, uu, v, a, amax) → h
  5. Surface((sin((v * (1 - u))) * sin((u * π))), cos((v * (1 - u))), ((-sin((v * (1 - u)))) * cos((u * π))), u, 0, uu, v, a, amax) → i