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From Sphere to Cube

From Sphere to Cube
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2015-04-22 18:28
Solid GeometryGeometric Construction
In collections surface 3D surface 3D
This example demonstrates the transformation process from a sphere to a cube. It involves the geometric properties of spheres and cubes, and how one shape can be transformed into another. It uses commands like Surface, CurveCartesian, Sequence, Segment, and Point in GeoGebra, suitable for high school or university students and teachers.

GeoGebra Commands & Parameters

  1. Surface((cos(u)^(1 / n) * cos(v)^(1 / n)), (sin(u)^(1 / n) * cos(v)^(1 / n)), sin(v)^(1 / n), u, 0, U, v, -1.5708, V) → a_1
  2. CurveCartesian((cos(u)^(1 / n) * cos(π / 4)^(1 / n)), (sin(u)^(1 / n) * cos(π / 4)^(1 / n)), sin(π / 4)^(1 / n), u, 0, U) → b
  3. CurveCartesian((cos(u)^(1 / n) * cos(((-π)) / 4)^(1 / n)), (sin(u)^(1 / n) * cos(((-π)) / 4)^(1 / n)), sin(((-π)) / 4)^(1 / n), u, 0, U) → c
  4. Sequence(CurveCartesian[(cos((i * π / 4))^(1 / n) * cos(v)^(1 / n)), (sin((i * π / 4))^(1 / n) * cos(v)^(1 / n)), sin(v)^(1 / n), v, -1.5708, V], i, 1, 7, 2) → liste1
  5. Sequence(CurveCartesian[(cos((i * π / 4))^(1 / n) * cos(v)^(1 / n)), (sin((i * π / 4))^(1 / n) * cos(v)^(1 / n)), sin(v)^(1 / n), v, -1.5708, V], i, 0, 6, 2) → liste2
  6. CurveCartesian(cos(u)^(1 / n), sin(u)^(1 / n), 0, u, 0, U) → d
  7. Segment((1, 0, ((-n)) / 30), (1, 0, n / 30)) → e
  8. Segment((-1, 0, ((-n)) / 30), (-1, 0, n / 30)) → f
  9. Segment((0, 1, ((-n)) / 30), (0, 1, n / 30)) → g
  10. Segment((0, -1, ((-n)) / 30), (0, -1, n / 30)) → h
  11. Segment((m, m, ((-n)) / 30), (m, m, n / 30)) → i
  12. Segment((m, (-m), ((-n)) / 30), (m, (-m), n / 30)) → j
  13. Segment(((-m), m, ((-n)) / 30), ((-m), m, n / 30)) → k
  14. Segment(((-m), (-m), ((-n)) / 30), ((-m), (-m), n / 30)) → l
  15. Point(Circle[(1, -1, -1), Distance[(-1, -1, -1), (1, -1, -1)], Segment[(-1, -1, -1), (1, -1, -1)]]) → A
  16. Cube((-1, -1, -1), (1, -1, -1), A) → cub, B, faceABFE, faceCDEF, arête2, arête1, arête4, arêteAB, arête3, arêteBF, arêteCF, arêteCD, C, arête5, arêteDE, arêteAE, arêteEF, D, E, F, face1, face3, face2, face4