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Rotating Unit Cube

Rotating Unit Cube
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2020-01-08 16:16
TrigonometryCoordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the dynamic rotation of a unit cube in 3D space. It involves core mathematical concepts such as solid geometry, rotation, coordinate geometry, and vectors. Construction highlights include commands like Segment, Polygon, Midpoint, Line, Ray, Intersect, CurveCartesian, Mirror, and Circle from GeoGebra. Suitable for high school and above students studying solid geometry, spatial visualization, and dynamic geometric transformations.

GeoGebra Commands & Parameters

  1. Segment(C_3, C') → n
  2. Segment(Q, C_3) → s
  3. Polygon(B, C_3, O) → poly1, o, b, c_1
  4. Midpoint(B, C_3) → M_1
  5. Midpoint(C_3, O) → M_2
  6. Midpoint(Q, C_3) → M_3
  7. Segment(C_3, O) → t_5
  8. Line(B, O) → i
  9. Ray(O, B) → p
  10. Segment(O, B) → a_1
  11. Midpoint(a_1) → A
  12. Segment(H, E) → b_1
  13. Segment(E, O) → d_1
  14. Segment(H, G) → e_1
  15. Segment(G, O) → f_1
  16. Intersect(d_1, f_1) → I
  17. Polygon(D, G, I, F) → poly1_1, d_2, g_1, i_1, f_2
  18. Polygon(J, E, I, F) → poly3, j_1, e_2, i_2, f_3
  19. Polygon(J, B, H, E) → poly4, j_2, b_2, h_1, e_3
  20. Intersect(b_2, j_2) → K
  21. Polygon(K, D, F, J) → poly5, k_1, d_3, f_4, j_3
  22. Polygon(K, D, G, H) → poly6, k_2, d_4, g_2, h_2
  23. Intersect(b_2, j_2) → L
  24. Segment(L, I) → l_1
  25. Polygon(B, E, O) → poly7, o_1, b_3, e_4
  26. Segment(E, O) → m_1
  27. Midpoint(b_3) → M
  28. Midpoint(E, B) → N
  29. CurveCartesian(x(O + (((R * sqrt(2 / 3)) * cos(t + π / 2)) * u) + (((R * sqrt(2 / 3)) * sin(t + π / 2)) * v)), y(O + (((R * sqrt(2 / 3)) * cos(t + π / 2)) * u) + (((R * sqrt(2 / 3)) * sin(t + π / 2)) * v)), t, 0, 6.283185307179586) → n_1
  30. Mirror(C'', O) → C'''
  31. Circle(C'', C''', P) → c
  32. Circle(C''', C'', P) → d