MathPlotAI Logo MathPlotAI

Leonard's Cubes

Leonard's Cubes
Loading the math board and drawing, please wait…
2020-01-24 23:02
VectorTrigonometrySolid GeometryCalculusGeometric Construction
This example demonstrates the dynamic construction of cubes to illustrate geometric properties and transformations. Core math concepts include solid geometry, vector operations, trigonometric function applications, and analytical geometry. Construction highlights GeoGebra commands like Vector, OrthogonalLine, Translate, Mirror, and Polygon. Suitable for high school and above students studying solid geometry, calculus (e.g., upper and lower sums/Riemann sums), and geometric transformations.

GeoGebra Commands & Parameters

  1. Vector(C, X) → u
  2. Vector(C, Z) → w
  3. OrthogonalLine(Rotation, yAxis) → a
  4. OrthogonalLine(Rotation, xAxis) → b
  5. Vector(C, Y) → v
  6. Translate(O, Vector[(g * u)]) → A_1
  7. Translate(O, Vector[(g * v)]) → B_2
  8. Mirror(B_2, O) → D_1
  9. Mirror(A_1, O) → E_1
  10. Translate(A_1, v) → G_1
  11. Translate(D_1, u) → H_1
  12. Mirror(G_1, B_2) → I
  13. Mirror(H_1, D_1) → J
  14. Translate(J, w) → C_1
  15. Translate(I, w) → D
  16. Translate(G_1, w) → A
  17. Translate(H_1, w) → B
  18. Mirror(C_1, O) → E
  19. Mirror(D, O) → F
  20. Mirror(A, O) → G
  21. Mirror(B, O) → H
  22. Polygon(Rotation, AA, BB, CC) → poly1, vues, aa, bb, cc
  23. Translate(L, Vector[(g * u)]) → L'
  24. Translate(L, Vector[(g * v)]) → L'_1
  25. Mirror(L'_1, L) → M
  26. Mirror(L', L) → L''
  27. Translate(L', Vector[w / sqrt(2)]) → L''_1
  28. Translate(L'_1, Vector[w / sqrt(2)]) → N
  29. Translate(L'', Vector[w / sqrt(2)]) → L'''
  30. Translate(M, Vector[w / sqrt(2)]) → M'
  31. Mirror(L''_1, L) → P
  32. Mirror(N, L) → N'
  33. Mirror(Rotation, M') → Vues'
  34. Mirror(AA, M') → AA'
  35. Mirror(BB, M') → BB'
  36. Mirror(CC, M') → CC'
  37. Polygon(L''', M', L''_1, N) → poly2, l''', m', l''_1, n
  38. Mirror(N, L'_1) → N'_1
  39. Mirror(L''_1, L') → Q
  40. Polygon(N'_1, P, N', Q) → poly3, n'_1, p, n', q
  41. Polygon(N'_1, Q, L''_1, N) → poly4, n'_2, q_1, l''_2, n_1
  42. Polygon(R, S, T, U) → poly5, r, s, t_1, u_1
  43. Translate(V, Vector[(g * u / 2) + ((sqrt(2) / 4 * g) * w)]) → V'
  44. Translate(V, Vector[(g * v / 2) + ((sqrt(2) / 4 * g) * w)]) → V'_1
  45. Mirror(V'_1, V) → W
  46. Mirror(V', V) → V''
  47. Translate(V, Vector[((-g) * u / 2) + ((sqrt(2) / 4 * g) * w)]) → V'_2
  48. Translate(V, Vector[((-g) * v / 2) + ((sqrt(2) / 4 * g) * w)]) → V'_3
  49. Mirror(Rotation, V'_2) → Vues'_1
  50. Mirror(AA, V'_2) → AA'_1
  51. Mirror(BB, V'_2) → BB'_1
  52. Mirror(CC, V'_2) → CC'_1
  53. Mirror(V'_2, V) → B_1
  54. Mirror(V'_3, V) → F_1

AI Drawing Prompt Reference

Draw a dynamically constructed cube to illustrate its geometric properties and transformations. Start by creating three perpendicular vectors, then use these vectors to generate the vertices and edges of the cube. Construct each face of the cube using translation and reflection operations, and finally combine them to form the complete cube. The process should highlight the application of vectors, trigonometric calculations, and spatial geometric transformations.
The prompt above was compiled from the original drawing commands and is for reference only.