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From Cube to Sphere

From Cube to Sphere
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2018-09-12 02:45
Coordinate GeometrySolid GeometryTransformation
This example demonstrates the transformation of a cube into a sphere through geometric transformations. It involves coordinate transformations, rotations, and the drawing of plane curves. Using commands like Mirror, CurveCartesian, Rotate, and Surface, the dynamic changes in geometric shapes can be observed. Suitable for high school mathematics education and learning about solid geometry transformations.

GeoGebra Commands & Parameters

  1. Mirror(B, xOyPlane) → B_1
  2. CurveCartesian((a * (1 - v + (v * r / sqrt(s^(2) + a^(2) + a^(2))))), (s * (1 - v + (v * r / sqrt(s^(2) + a^(2) + a^(2))))), (a * (1 - v + (v * r / sqrt(s^(2) + a^(2) + a^(2))))), s, (-a), a) → c_a
  3. Rotate(c_a, π / 2, xAxis) → c_{a1}
  4. Rotate(c_a, π, xAxis) → c_{a2}
  5. Rotate(c_a, (3 * π / 2), xAxis) → c_{a3}
  6. Rotate(c_a, π / 2, zAxis) → c_{a4}
  7. Rotate(c_a, π, zAxis) → c_{a5}
  8. Rotate(c_a, (3 * π / 2), zAxis) → c_{a6}
  9. Rotate(c_{a1}, π, zAxis) → c_{a7}
  10. Rotate(c_{a1}, (3 * π / 2), zAxis) → c_{a8}
  11. Rotate(c_{a2}, π / 2, zAxis) → c_{a10}
  12. Rotate(c_{a2}, π, zAxis) → c_{a11}
  13. Rotate(c_{a2}, (3 * π / 2), zAxis) → c_{a12}
  14. Surface((a * (1 - v + (v * r / sqrt(s^(2) + t^(2) + a^(2))))), (s * (1 - v + (v * r / sqrt(s^(2) + t^(2) + a^(2))))), (t * (1 - v + (v * r / sqrt(s^(2) + t^(2) + a^(2))))), s, (-a), a, t, (-a), a) → f
  15. Rotate(f, π / 2, zAxis) → f_1
  16. Rotate(f, π, zAxis) → f_2
  17. Rotate(f, (3 * π / 2), zAxis) → f_3
  18. Rotate(f, π / 2, yAxis) → f_4
  19. Rotate(f, (3 * π / 2), yAxis) → f_5
  20. Mirror(A, xOyPlane) → A_1
  21. Mirror(A, (0, 0, 0)) → A_2
  22. Mirror(B_1, (0, 0, 0)) → B_3
  23. Mirror(A_1, (0, 0, 0)) → A_3
  24. Mirror(B, (0, 0, 0)) → B_2