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Cube in a Sphere Construction

Cube in a Sphere Construction
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2017-05-05 23:14
Solid GeometryGeometric Construction
This example demonstrates the geometric construction of a cube inside a sphere. Key mathematical concepts include solid geometry and geometric construction. Using commands like Intersect, Point, Cube, Segment, and Sphere, the intersection of the cube and sphere is constructed. Suitable for high school or university solid geometry courses.

GeoGebra Commands & Parameters

  1. Intersect(yAxis, xAxis) → A
  2. Point(xAxis) → B
  3. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  4. 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
  5. Segment(E, C) → f
  6. Segment(H, B) → g
  7. Intersect(f, g) → I
  8. Sphere(I, H) → b
  9. Segment(I, E) → h
  10. Segment(I, F) → i
  11. Midpoint(edgeEF) → J
  12. Intersect(edgeEF, h) → K
  13. Segment(E, B) → j
  14. Segment(F, A) → k
  15. Intersect(k, j) → L
  16. Polygon(E, C, A) → DiameterTriangle, a_1, e, c
  17. Polygon(J, I, L) → MidTriangle, l_1, j_1, i_1
  18. Segment(I, J) → l
  19. Polygon(I, E, F) → RadiTriangle, f_1, i_2, e_1

AI Drawing Prompt Reference

Draw a cube inside a sphere, showing their intersection through geometric construction. Start by plotting the intersection of coordinate axes and a circle, then construct three vertices of the cube. Form the cube using these points. Next, find an intersection point between the cube and sphere, use it as the center to draw the sphere, and connect it with the cube's vertices with helper lines. Complete the geometric construction of the intersection between the cube and sphere.
The prompt above was compiled from the original drawing commands and is for reference only.