MathPlotAI Logo MathPlotAI

Dice Roll Simulation

Dice Roll Simulation
Loading the math board and drawing, please wait…
2018-10-23 04:23
Solid GeometryProbability & StatisticsGeometric Construction
This example demonstrates the rolling process of a six-sided die and its probability distribution. It involves core mathematical concepts such as Probability & Statistics, Geometry Transformation, and Solid Geometry. The construction uses GeoGebra commands and objects like Point, Cube, Circle, Line, and Rotate. Suitable for high school students learning probability statistics and solid geometry, or for mathematical modeling education.

GeoGebra Commands & Parameters

  1. Point(Circle[(0, 0, 1), Distance[(0, 0, 0), (0, 0, 1)], Segment[(0, 0, 0), (0, 0, 1)]]) → A
  2. Cube((0, 0, 0), (0, 0, 1), A) → a, B, faceABFE, faceCDEF, edge2, edge1, edge4, edgeAB, edge3, edgeBF, edgeCF, edgeCD, C, edge5, edgeDE, edgeAE, edgeEF, D, E, F, face1, face3, face2, face4
  3. Circle((0.5, -0.01, 0.5), p, yAxis) → c
  4. Circle((1.01, 0.5 + s, 0.5 - s), p, xAxis) → c_1
  5. Circle((1.01, 0.5 - s, 0.5 - s), p, xAxis) → d_1
  6. Circle((d, 1.01, 3 / 6), p, yAxis) → e
  7. Circle((1.01, 0.5 - s, 0.5 + s), p, xAxis) → e_1
  8. Circle((d, 1.01, 0.5 - s), p, yAxis) → f
  9. Circle((-0.01, 0.5 - s, 0.5 + s), p, xAxis) → f_1
  10. Circle((d, 1.01, 0.5 + s), p, yAxis) → g
  11. Circle((-0.01, 0.5 + s, 0.5 - s), p, xAxis) → g_1
  12. Circle((1 - d, 1.01, 0.5), p, yAxis) → h
  13. Circle((1 - d, 1.01, 0.5 + s), p, yAxis) → k
  14. Circle((0.5 + s, 0.5 + s, -0.01), p, zAxis) → k_1
  15. Circle((0.5 - s, 0.5 - s, -0.01), p, zAxis) → p_1
  16. Circle((1 - d, 1.01, 0.5 - s), p, yAxis) → q
  17. Circle((0.5 - s, 0.5 - s, 1.01), p, zAxis) → q_1
  18. Circle((1.01, 0.5, 0.5), p, xAxis) → r
  19. Circle((0.5 - s, 0.5 + s, 1.01), p, zAxis) → r_1
  20. Circle((0.5 + s, 0.5 + s, 1.01), p, zAxis) → s_1
  21. Circle((1.01, 0.5 + s, 0.5 + s), p, xAxis) → t
  22. Circle((0.5 + s, 0.5 - s, 1.01), p, zAxis) → t_1
  23. Circle((0.5, 0.5, -0.01), p, zAxis) → h_1
  24. Line(M, yAxis) → i
  25. Line(M, xAxis) → j
  26. Line(M, zAxis) → l
  27. Rotate(Rotate[Rotate[a, α, i], β, j], γ, l) → b
  28. Rotate(Rotate[Rotate[c, α, i], β, j], γ, l) → c_2
  29. Rotate(Rotate[Rotate[c_1, α, i], β, j], γ, l) → d_2
  30. Rotate(Rotate[Rotate[d_1, α, i], β, j], γ, l) → e_2
  31. Rotate(Rotate[Rotate[e, α, i], β, j], γ, l) → f_2
  32. Rotate(Rotate[Rotate[e_1, α, i], β, j], γ, l) → g_2
  33. Rotate(Rotate[Rotate[f, α, i], β, j], γ, l) → h_2
  34. Rotate(Rotate[Rotate[f_1, α, i], β, j], γ, l) → k_2
  35. Rotate(Rotate[Rotate[g, α, i], β, j], γ, l) → p_2
  36. Rotate(Rotate[Rotate[g_1, α, i], β, j], γ, l) → q_2
  37. Rotate(Rotate[Rotate[h, α, i], β, j], γ, l) → r_2
  38. Rotate(Rotate[Rotate[h_1, α, i], β, j], γ, l) → s_2
  39. Rotate(Rotate[Rotate[k, α, i], β, j], γ, l) → t_2
  40. Rotate(Rotate[Rotate[k_1, α, i], β, j], γ, l) → c_3
  41. Rotate(Rotate[Rotate[p_1, α, i], β, j], γ, l) → d_3
  42. Rotate(Rotate[Rotate[q, α, i], β, j], γ, l) → e_3
  43. Rotate(Rotate[Rotate[q_1, α, i], β, j], γ, l) → f_3
  44. Rotate(Rotate[Rotate[r, α, i], β, j], γ, l) → g_3
  45. Rotate(Rotate[Rotate[r_1, α, i], β, j], γ, l) → h_3
  46. Rotate(Rotate[Rotate[s_1, α, i], β, j], γ, l) → k_3
  47. Rotate(Rotate[Rotate[t, α, i], β, j], γ, l) → p_3
  48. Rotate(Rotate[Rotate[t_1, α, i], β, j], γ, l) → q_3