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Intersection of a Sphere and a Cube

Intersection of a Sphere and a Cube
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2017-04-12 13:40
VectorSolid GeometryGeometric Construction
This example demonstrates the intersection of a sphere and a cube. It involves core mathematical concepts such as intersection, solid geometry, and spatial geometric relationships. The construction uses GeoGebra commands/objects like Point, Cube, Sphere, OrthogonalLine, PointIn, Plane, IntersectPath, Circle, Intersect, and Locus as detailed in the construction summary. It is suitable for high school students and math enthusiasts studying solid geometry and intersection calculations.

GeoGebra Commands & Parameters

  1. Point(Circle[D, Distance[C, D], Segment[C, D]]) → E
  2. Cube(C, D, E) → b, F, caraEFJI, caraGHIJ, arestaCF, arestaCD, arestaDE, arestaEF, arestaCG, arestaFJ, arestaGJ, arestaGH, G, arestaDH, arestaHI, arestaEI, arestaIJ, H, I, J, caraCDEF, caraCFJG, caraCDHG, caraDEIH
  3. Sphere(A, Radi) → a
  4. OrthogonalLine(A, xOyPlane) → f
  5. PointIn(a) → B
  6. Plane(B, f) → c
  7. IntersectPath(c, a) → d
  8. Circle(f, B) → e
  9. Point(e) → K
  10. Plane(K, f) → g
  11. IntersectPath(g, a) → h
  12. IntersectPath(g, caraCDEF) → i1
  13. IntersectPath(g, caraCDHG) → i2
  14. IntersectPath(g, caraCFJG) → i3
  15. IntersectPath(g, caraEFJI) → i4
  16. IntersectPath(g, caraDEIH) → i5
  17. IntersectPath(g, caraGHIJ) → i6
  18. Intersect(i1, h) → p1,
  19. Intersect(i2, h) → p2,
  20. Intersect(i3, h) → p3,
  21. Intersect(i4, h) → p4,
  22. Intersect(i5, h) → p5,
  23. Intersect(i6, h) → p6,
  24. Locus(p1, K) → LG1
  25. Locus(p2, K) → LG2
  26. Locus(p3, K) → LG3
  27. Locus(p4, K) → LG4
  28. Locus(p5, K) → LG5
  29. Locus(p6, K) → LG6

AI Drawing Prompt Reference

Draw a cube and a sphere to show their intersection. Start by creating a circle and a line to determine a point, then construct a cube using this point. Next, draw a sphere with the point as the center and find its intersection with the coordinate plane. Then, determine a plane using the sphere's center and the intersection line, and find the intersections of this plane with the sphere and each face of the cube. Finally, find the intersections of these lines and the sphere's intersection with the plane, and draw the loci of these intersection points as the sphere's center moves, showing the changing shape of the intersection.
The prompt above was compiled from the original drawing commands and is for reference only.