6X6 to 10 Pool Table Geometric Construction

6X6 to 10 Pool Table Geometric Construction
Loading the math board and drawing, please wait…
2017-07-06 01:17
This example demonstrates the geometric construction of pool tables ranging from 6X6 to 10. Core mathematical concepts include polygons and geometric construction. Using GeoGebra commands such as Intersect, Point, and OrthogonalLine, the geometric shape of the pool table can be constructed. Suitable for students at the junior high school level and above to learn about polygon-related knowledge and geometric construction.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Point(yAxis) → C
  4. OrthogonalLine(C, yAxis) → f
  5. OrthogonalLine(B, xAxis) → g
  6. Intersect(g, f) → D
  7. Polygon(A, B, D, C) → poly1, a, b, d, c
  8. Rotate(B, 45°, A) → B'
  9. Angle(B, A, B') → α
  10. Line(A, B') → h
  11. Intersect(h, d) → E
  12. Segment(A, E) → i
  13. Rotate(A, 45°, E) → A'
  14. Rotate(D, (-(45°)), E) → D'
  15. Angle(D', E, D) → β
  16. Line(E, D') → j
  17. Intersect(j, b) → F
  18. Segment(E, F) → k
  19. Rotate(B, (-(45°)), F) → B'_1
  20. Angle(B'_1, F, B) → γ
  21. Line(F, B'_1) → l
  22. Intersect(l, a) → G
  23. Segment(F, G) → m
  24. Rotate(A, (-(45°)), G) → A'_1
  25. Angle(A'_1, G, A) → δ
  26. Line(G, A'_1) → n
  27. Intersect(n, d) → H
  28. Segment(G, H) → p
  29. Rotate(C, 45°, H) → C'
  30. Angle(C, H, C') → ε
  31. Line(H, C') → q
  32. Intersect(q, c) → I
  33. Segment(H, I) → r
  34. Rotate(A, 45°, I) → A'_2
  35. Angle(A, I, A'_2) → ζ
  36. Line(I, A'_2) → s
  37. Intersect(s, a) → J
  38. Segment(I, J) → t
  39. Rotate(B, 45°, J) → B'_2
  40. Angle(B, J, B'_2) → η
  41. Line(J, B'_2) → e
  42. Ray(G, A'_1) → g_1
  43. Intersect(g_1, c) → K
  44. Segment(G, K) → h_1
  45. Rotate(C, (-(45°)), K) → C'_1
  46. Angle(C'_1, K, C) → θ
  47. Ray(K, C'_1) → i_1
  48. Intersect(d, i_1) → L
  49. Segment(K, L) → j_1
  50. Rotate(E, (-(45°)), L) → E'
  51. Angle(E', L, E) → ι
  52. Ray(L, E') → k_1
  53. Intersect(b, k_1) → M
  54. Segment(L, M) → l_1
  55. Rotate(B, (-(45°)), M) → B'_3
  56. Angle(B'_3, M, B) → κ
  57. Ray(M, B'_3) → m_1
  58. Intersect(m_1, a) → N
  59. Segment(M, N) → n_1
  60. Rotate(A, (-(45°)), N) → A'_3
  61. Angle(A'_3, N, A) → λ
  62. Ray(N, A'_3) → p_1
  63. Intersect(c, p_1) → O
  64. Segment(N, O) → q_1
  65. Rotate(C, (-(45°)), O) → C'_2
  66. Angle(C'_2, O, C) → μ
  67. Ray(O, C'_2) → r_1
  68. Intersect(d, r_1) → P
  69. Segment(O, P) → s_1
  70. Rotate(D, (-(45°)), P) → D'_1
  71. Angle(D'_1, P, D) → ν
  72. Ray(P, D'_1) → f_1
  73. Intersect(b, f_1) → Q
  74. Segment(P, Q) → t_1
  75. Ray(J, B'_2) → b_1
  76. Ray(J, B'_2) → a_1
  77. Intersect(b, a_1) → R
  78. Segment(J, R) → c_1
  79. Rotate(B, (-(45°)), Q) → B'_4
  80. Angle(B'_4, Q, B) → ξ
  81. Ray(Q, B'_4) → d_1
  82. Intersect(d_1, a) → S
  83. Segment(Q, S) → e_1
  84. Rotate(A, (-(45°)), S) → A'_4
  85. Angle(A'_4, S, A) → ο
  86. Ray(S, A'_4) → f_2
  87. Intersect(c, f_2) → T
  88. Segment(S, T) → g_2

AI Drawing Prompt Reference

Construct a pool table ranging from 6x6 to 10. Start by defining four vertices A, B, C, and D on the coordinate axes, then use rotations and intersections to create a series of lines and angles, ultimately forming a regular polygon. Pay attention to the angles and line intersections to ensure each step is accurate.
The prompt above was compiled from the original drawing commands and is for reference only.