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Rotation of Cube Inscribed in Sphere

Rotation of Cube Inscribed in Sphere
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2020-08-17 02:07
Solid Geometry
This example demonstrates the rotation of a cube inscribed in a sphere. Key mathematical concepts include solid geometry, cube, sphere, and rotation. Using GeoGebra commands such as Cube, PointIn, DynamicCoordinates, Line, Sphere, and Rotate, the example dynamically shows the rotation of the cube and its relative position to the sphere. Suitable for high school and above students or teachers for teaching and learning solid geometry, rotation, and spatial imagination.

GeoGebra Commands & Parameters

  1. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  2. PointIn(faceABFE) → K
  3. DynamicCoordinates(K, round((x(K) * 10)) / 10, round((y(K) * 10)) / 10, round((z(K) * 10)) / 10) → I
  4. Line(I, J) → l
  5. Sphere((0, 0, 0), sqrt(12)) → b
  6. Rotate(a, α, l) → a'
  7. Distance(E, H) → EH
  8. Midpoint(A, B) → AB
  9. Midpoint(B, C) → BC
  10. Midpoint(C, D) → CD
  11. Midpoint(D, A) → DA
  12. Midpoint(E, F) → EF
  13. Midpoint(F, G) → FG
  14. Midpoint(G, H) → GH
  15. Midpoint(H, E) → HE
  16. Midpoint(A, E) → AE
  17. Midpoint(B, F) → BF
  18. Midpoint(C, G) → CG
  19. Midpoint(D, H) → DH
  20. Intersect(l, b, 1) → P1
  21. Intersect(l, b, 2) → P2

AI Drawing Prompt Reference

Draw a cube inscribed in a sphere. The cube rotates around the sphere's center. The vertices of the cube lie on the sphere's surface, and the sphere's radius is half the cube's diagonal. Show the cube's position during rotation to help understand spatial geometry and rotation.
The prompt above was compiled from the original drawing commands and is for reference only.