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Sections of Spheres by Anthony OR 柯志明

Sections of Spheres by Anthony OR 柯志明
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2014-11-04 01:08
Coordinate GeometrySolid GeometryGeometric Construction
In collections Area, Surface Area, Volume, Cross Section, 3D 3D Geometry & Cross Sections Sections of 3D Shapes Cross sections Spheres & Cross Sections Cross Sections
This example demonstrates the various cross-sections formed by intersecting a sphere with different planes, showcasing geometric principles of spheres and cross-sections. It involves core concepts like sphere geometry, section geometry, and analytical geometry. Constructed using GeoGebra commands such as Polygon, PointIn, Translate, Rotate, Plane, OrthogonalLine, Sphere, and IntersectPath. Suitable for high school geometry instruction and exploratory learning.

GeoGebra Commands & Parameters

  1. Polygon(B + (-2, -2), B + (2, -2), B + (2, 2), B + (-2, 2)) → poly3, e, f, g, i
  2. PointIn(poly3) → C
  3. Translate((0, 0, 0), Vector[B, C]) → A
  4. Polygon(A + (-4, -4), A + (4, -4), A + (4, 4), A + (-4, 4)) → poly1, a, b, c, d
  5. Rotate(Rotate[Translate[poly1, Vector[A, A + (0, 0, h)]], (90° * s), A + (0, 0, h), yAxis], (90° * t), A, zAxis) → poly2
  6. PointIn(poly2) → G
  7. PointIn(poly2) → H
  8. PointIn(poly2) → I
  9. Plane(G, I, H) → n
  10. OrthogonalLine(A, n) → d_1
  11. Sphere((0, 0, 2), 2) → j
  12. IntersectPath(n, j) → k

AI Drawing Prompt Reference

Draw a sphere with a radius of 2 centered 2 units above the origin. Then draw a square horizontally, with its vertices 2 units below the sphere's center. Rotate this square around the sphere's center to form a plane. On this plane, choose three points to define another plane. Then draw a vertical line through the sphere's center on this plane. Finally, find the intersection of this vertical line with the sphere to form a circular cross-section.
The prompt above was compiled from the original drawing commands and is for reference only.