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BDG Pool Table Geometric Construction

BDG Pool Table Geometric Construction
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2017-07-06 01:44
PolygonAngleTrigonometryCoordinate GeometryGeometric Construction
In collections Rate & Accumulation Yr 4 Much&Fast
This example demonstrates the geometric construction and angle relationships of pool tables of different sizes (3X3, 3X4, 3X5, 3X6). It involves core mathematical concepts such as angles, fractions, derivatives, secant lines, expected value, and ratios. The construction uses GeoGebra commands like Intersect, Point, OrthogonalLine, Polygon, Rotate, Angle, Line, Segment, and Ray. It is suitable for high school mathematics teaching, aiding in the understanding of geometric constructions and related concepts.

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

Draw a rectangle with four points, then from one vertex, draw a line at a 45-degree angle and rotate that vertex by 45 degrees to get another point, connecting these two points. From the other endpoint, draw another 45-degree line and rotate the other vertices of the rectangle, creating multiple intersections and line segments to form a complex geometric pattern showing angle relationships and constructions.
The prompt above was compiled from the original drawing commands and is for reference only.