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Intersection of Cylinder and Sphere by Patrick Clément

Intersection of Cylinder and Sphere by Patrick Clément
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2015-07-19 17:55
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
This example demonstrates the intersection of a cylinder and a sphere. Key mathematical concepts include the intersection lines of a cylinder and a sphere in solid geometry. Using GeoGebra commands such as CurveCartesian, Point, Mirror, and Surface, the intersection lines can be constructed. Suitable for high school students learning solid geometry.

GeoGebra Commands & Parameters

  1. CurveCartesian((b * cos(t)), sqrt(a^(2) - b^(2) - c^(2) - (((2 * b) * c) * sin(t))), c + (b * sin(t)), t, 0, 6.283185307179586) → cou
  2. Point(Segment[(0, -4, c), (0, (-a), c)]) → A
  3. Mirror(A, (0, 0, c)) → A'
  4. CurveCartesian((b * cos(t)), (-sqrt(a^(2) - b^(2) - c^(2) - (((2 * b) * c) * sin(t)))), c + (b * sin(t)), t, 0, 6.28319) → cou'
  5. Surface((b * cos(u)) + p, (sqrt(a^(2) - b^(2) - c^(2) - (((2 * b) * c) * sin(u))) * (1 - v)) + (v * y(A')), c + (b * sin(u)), u, 0, 6.283185307179586, v, 0, 1) → rc1
  6. Surface((b * cos(u)) + p, ((-sqrt(a^(2) - b^(2) - c^(2) - (((2 * b) * c) * sin(u)))) * (1 - v)) + (v * y(A)), c + (b * sin(u)), u, 0, 6.283185307179586, v, 0, 1) → rc2
  7. Surface((v * cos(u)), sqrt(a^(2) - v^(2) - c^(2) - (((2 * v) * c) * sin(u))), c + (v * sin(u)), u, 0, 6.283185307179586, v, b, a + c) → rs1
  8. Surface((v * cos(u)), (-sqrt(a^(2) - v^(2) - c^(2) - (((2 * v) * c) * sin(u)))), c + (v * sin(u)), u, 0, 6.283185307179586, v, b, a + c) → rs2
  9. Surface((b * cos(u)) + p, v, c + (b * sin(u)), u, angl, π - angl, v, y(A), y(A')) → rc3
  10. Surface((b * cos(u)) + (p * q), (p * (1 - q)) + (v * sqrt(a^(2) - b^(2) - c^(2) - (((2 * b) * c) * sin(u)))), c + (b * sin(u)), u, 0, 6.28319, v, -1, 1) → sc
  11. Surface((v * cos(u)), (p * (1 - q)) + sqrt(a^(2) - v^(2) - c^(2) - (((2 * v) * c) * sin(u))), c + (v * sin(u)), u, -0.02, 6.3, v, 0, b) → ss1
  12. Surface((v * cos(u)), (p * (1 - q)) - sqrt(a^(2) - v^(2) - c^(2) - (((2 * v) * c) * sin(u))), c + (v * sin(u)), u, -0.02, 6.3, v, 0, b) → ss2
  13. Cylinder(A + (p, 0, 0), A' + (p, 0, 0), b) → d, e, f, g
  14. Sphere((0, 0, 0), a) → i

AI Drawing Prompt Reference

Draw the intersection of a cylinder and a sphere. First, draw a sphere centered at the origin with radius a. Then, draw a cylinder with its base center on the z-axis, radius b, and height 2c. Finally, draw the intersection lines, which consist of two curves and two surfaces.
The prompt above was compiled from the original drawing commands and is for reference only.