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Plane & Sphere Intersections

Plane & Sphere Intersections
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2021-11-21 20:49
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the intersection of a plane and a sphere, visually showing how the intersection forms a circle. It involves core mathematical concepts like solid geometry, spatial geometric relationships, and intersection operations. The construction uses GeoGebra commands and objects such as Sphere, Point, OrthogonalPlane, and IntersectPath. Suitable for high school students and geometry enthusiasts.

GeoGebra Commands & Parameters

  1. Sphere((0, 0), 1) → a
  2. Point(Segment[(1.25, 0, 0), (-1.25, 0, 0)]) → A
  3. OrthogonalPlane(A, xAxis) → p
  4. IntersectPath(p, a) → c

AI Drawing Prompt Reference

Draw a sphere with radius 1, then take two points A and -A on the x-axis, construct a plane orthogonal to the x-axis passing through point A, and find the intersection circle between this plane and the sphere.
The prompt above was compiled from the original drawing commands and is for reference only.