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Intersection of Cylinder and Sphere in 3D Space

Intersection of Cylinder and Sphere in 3D Space
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2014-04-24 20:34
Coordinate GeometrySolid GeometryGeometric Construction
In collections intersection: surface-surface, curve-curve
This example demonstrates the intersection of a cylinder along the x, y, and z axes, and a sphere centered at the origin. Key mathematical concepts include solid geometry, specifically cylinders and spheres. The Surface command is used to construct the surfaces of the cylinder and sphere, as well as their intersection. Suitable for high school and above students studying solid geometry.

GeoGebra Commands & Parameters

  1. Surface(4 + cos(b), 3 + sin(b), 2 + (5 * sin(a)), a, 0, 3.141592653589793, b, 0, 3.141592653589793) → cil2_z
  2. Surface(4 + (2 * cos(b)), 5 + (2 * sin(b)), 2 + (5 * sin(a)), a, 0, 3.141592653589793, b, 0, 6.28319) → cil_z
  3. Surface(((7 * sin(a)) * cos(a)), sin(b), cos(b), a, 0, 6.28319, b, 0, 6.28319) → cil_x
  4. Surface(sin(a), (7 * cos(b)), cos(a), a, 0, 6.28319, b, 0, 6.28319) → cil_y
  5. Surface(((2.5 * cos(u)) * cos(v)), ((2.5 * sin(u)) * cos(v)), (2.5 * sin(v)), u, 0, 6.28319, v, 0, 6.28319) → sfera_{0,0,0}
  6. Surface((7 * sin(a)), sin(b), cos(b), a, 0, 6.283185307179586, b, 0, 6.283185307179586) → cil'_x
  7. Surface(10 + (sin(a) * sin(b)), 10 + (sin(b) * cos(a)), 10 + cos(b), a, 0, 3.141592653589793, b, 0, 3.141592653589793) → sfera_{xyz}
  8. Surface((1.5 * cos(a)), (5 * sin(b)), (1.5 * sin(a)), a, 0, 6.28319, b, 0, 6.28319) → cil'_y