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Intersection of a Plane and a Sphere

Intersection of a Plane and a Sphere
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2015-02-07 19:38
TrigonometrySolid GeometryGeometric Construction
This example demonstrates the geometric shape formed by the intersection of a plane and a sphere. Key mathematical concepts include spherical geometry and trigonometry. Using GeoGebra commands such as Polygon, PointIn, and Surface, the intersection of a plane and a sphere can be constructed. Suitable for high school mathematics education and students learning solid geometry.

GeoGebra Commands & Parameters

  1. Polygon((0, -3.14159 + π / c, -1.5708 + π / c), (0, π - π / c, -1.5708 + π / c), (0, π - π / c, 1.5708 - π / c), (0, -3.14159 + π / c, 1.5708 - π / c)) → poly1, d, e, f, g
  2. PointIn(poly1) → A
  3. Surface((cos(u) * cos(v)) - 1, ((π / a * sin(u)) * cos(v)), (π / ((2 * b)) * sin(v)), u, (-a), a, v, (-b), b) → s
  4. Surface(((1.01 * cos(u)) * cos(v)) - 1, (((1.01 * π / a) * sin(u)) * cos(v)), ((1.01 * π / ((2 * b))) * sin(v)), u, ((-a)) / c + (y(A) * a / π), (y(A) * a / π) + a / c, v, ((-b) * 2 / c) + ((z(A) * 2) * b / π), ((z(A) * 2) * b / π) + (b * 2 / c)) → sc