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Cube and Inscribed Sphere

Cube and Inscribed Sphere
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2019-04-12 18:25
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the comparison between a cube and its inscribed sphere. Key mathematical concepts include solid geometry and coordinate geometry. Using GeoGebra commands such as Surface, Rotate, Sphere, Translate, Line, Polygon, CurveCartesian, Mirror, and Plane, the construction of the cube and its inscribed sphere is achieved. Suitable for middle school and above students or teachers.

GeoGebra Commands & Parameters

  1. Surface((t, (s * (1 - sin(acosd(t)))), 0), t, 0, 1, s, 0, 1) → sup
  2. Rotate(sup, (-(90°)), yAxis) → sup2
  3. Sphere((0, 1, 0), 1) → esf
  4. Translate(Rotate[sup, (-(90°)), xAxis], Vector[(0, 1, 1)]) → sup3
  5. Line(PCentro, PCentro + (0, 0, 1)) → r
  6. Polygon({(1, 0, 0), (0, 0, 0), (0, 0, 1), (1, 0, 1)}) → Cara1
  7. CurveCartesian(PCentro + (0, (-cos(t)), sin(t)), t, 0, π / 2) → c2
  8. Polygon({(1, 0, 0), (1, 1, 0), (1, 1, 1), (1, 0, 1)}) → Cara2
  9. Surface(c2, 90°, r) → s
  10. Mirror(capa1, PCentro) → capa2
  11. Polygon((1, 0, 1), (1, 1, 1), (1, 1, 1), (1, 0, 1)) → Cara3, f, g, h, i
  12. Mirror({Cara1, Cara2, Cara3}, PCentro) → capa2b
  13. Plane(x = 0) → Plano1
  14. Plane(z = 0) → Plano2
  15. Mirror(capa2b, Plano1) → capa2c
  16. Plane(y = 1) → Plano3
  17. Mirror(capa2b, Plano2) → capa2d
  18. Mirror(capa2b, Plano3) → capa2e
  19. CurveCartesian(PCentro + (cos(t), 0, sin(t)), t, 0, π / 2) → c21
  20. CurveCartesian(PCentro + (cos(t), (-sin(t)), 0), t, 0, π / 2) → c22