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Net of a Pyramid by Sudeep Gokarakonda

Net of a Pyramid by Sudeep Gokarakonda
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2019-02-13 16:54
PolygonSolid GeometryGeometric Construction
This example demonstrates the net of a pyramid, showing how the surfaces of a pyramid unfold into a 2D plane. Key math concepts include polygons, solid geometry, geometric construction, rotation, and translation. It is constructed using GeoGebra commands such as Point, Segment, Line, Circle, Intersect, Rotate, Polygon, OrthogonalLine, Midpoint, Vector, Translate, LineBisector, CircleArc, Ray, and If. Suitable for high school solid geometry education, helping students understand the relationship between 3D shapes and their 2D nets, and developing spatial reasoning skills.

GeoGebra Commands & Parameters

  1. Point(Circle[A, l]) → B
  2. Segment(A, B) → a
  3. Line(A, B) → b_2
  4. Circle(B, (3 * l / 4.5)) → c
  5. Intersect(c, b_2, 2) → C
  6. Rotate(C, 30°, B) → C'
  7. Line(C', b_2) → d
  8. Segment(B, C') → e
  9. Line(A, e) → f
  10. Intersect(d, f) → D
  11. Polygon(A, B, C', D) → poly1, a_1, b_1, c', d_1
  12. Segment(A, C') → g
  13. Segment(D, B) → h_1
  14. Intersect(g, h_1) → E
  15. OrthogonalLine(E, a_1) → i
  16. Circle(E, h) → k
  17. Intersect(k, i, 2) → F
  18. Segment(B, F) → j
  19. Segment(C', F) → l_5
  20. Segment(F, D) → m
  21. Segment(F, A) → n
  22. Segment(A, D) → q
  23. Midpoint(b_1) → G
  24. Segment(G, F) → r
  25. Line(E, G) → c_1
  26. Circle(G, F) → f_1
  27. Intersect(f_1, c_1, 2) → H
  28. Intersect(c_1, d_1) → I
  29. Circle(I, F) → g_1
  30. Intersect(g_1, c_1, 1) → J
  31. Vector(F, J) → u
  32. Point(c') → L
  33. Circle(L, F) → q_1
  34. Vector(F, H) → w
  35. Midpoint(A, B) → K
  36. Line(K, E) → e_1
  37. Circle(K, h) → p_1
  38. Intersect(e_1, c') → M
  39. Circle(M, h) → r_1
  40. Intersect(r_1, e_1, 2) → N
  41. Intersect(p_1, e_1, 1) → O
  42. Vector(F, N) → v
  43. Vector(F, O) → z
  44. Translate(F, Vector[(z * o)]) → F'_1
  45. Translate(F, Vector[(u * (o - 1))]) → F'_2
  46. Translate(F, Vector[(v * (o - 2))]) → F'_3
  47. Translate(F, Vector[(w * (o - 3))]) → F'
  48. Segment(F, N) → s
  49. LineBisector(s) → a_2
  50. Intersect(a_2, c') → P
  51. CircleArc(P, N, F) → c_2
  52. Ray(P, F'_3) → d_2
  53. Intersect(c_2, d_2, 1) → Q
  54. Segment(F, O) → e_2
  55. LineBisector(e_2) → f_2
  56. Intersect(f_2, a_1) → R
  57. CircleArc(R, F, O) → g_2
  58. Ray(R, F'_1) → h_2
  59. Intersect(g_2, h_2, 1) → S
  60. CircleArc(I, F, J) → k_2
  61. CircleArc(G, H, F) → p_2
  62. Ray(I, F'_2) → i_2
  63. Intersect(k_2, i_2, 1) → T
  64. Ray(G, F') → j_2
  65. Intersect(p_2, j_2, 1) → U
  66. Circle(I, E) → s_1
  67. OrthogonalLine(I, a_1) → i_1
  68. Intersect(s_1, i_1, 2) → V
  69. Intersect(s_1, i_1, 1) → W
  70. OrthogonalLine(V, i_1) → j_1
  71. OrthogonalLine(W, i_1) → k_1
  72. OrthogonalLine(G, k_1) → l_1
  73. Intersect(j_1, l_1) → Z
  74. Intersect(k_1, l_1) → A_1
  75. Midpoint(V, Z) → B_1
  76. Midpoint(A_1, W) → C_1
  77. Circle(B_1, r) → t_1
  78. Circle(C_1, r) → q_2
  79. OrthogonalLine(B_1, k_1) → m_1
  80. Intersect(t_1, m_1, 1) → D_1
  81. Intersect(q_2, m_1, 2) → E_1
  82. Vector(C', Z) → u_1
  83. Vector(B, A_1) → v_1
  84. Vector(N, D_1) → w_1
  85. Vector(O, E_1) → z_1
  86. Translate(N, Vector[(w_1 * (o - 4))]) → N'
  87. Translate(O, Vector[(z_1 * (o - 4))]) → O'
  88. Translate(B, Vector[(v_1 * (o - 4))]) → B'
  89. Translate(A, Vector[(v_1 * (o - 4))]) → A'
  90. Translate(C', Vector[(u_1 * (o - 4))]) → C''
  91. Translate(D, Vector[(u_1 * (o - 4))]) → D'
  92. If(o < 1, S, If[o < 4, O, If[o < 5, O', E_1]]) → F_1
  93. If(o < 1, F, If[o < 2, T, J]) → G_1
  94. If(o < 3, F, If[o < 4, U, H]) → H_1
  95. If(o < 2, F, If[o < 3, Q, If[o < 4, N, If[o < 5, N', D_1]]]) → I_1
  96. If(o < 4, A, If[o < 5, A', W]) → J_1
  97. If(o < 4, B, If[o < 5, B', A_1]) → K_1
  98. If(o < 4, C', If[o < 5, C'', Z]) → L_1
  99. If(o < 4, D, If[o < 5, D', V]) → M_1
  100. Polygon(F_1, J_1, K_1) → poly2, k_3, f_3, j_3
  101. Polygon(L_1, H_1, K_1) → poly3, k_4, l_2, h_3
  102. Polygon(L_1, I_1, M_1) → poly4, m_2, l_3, i_3
  103. Polygon(M_1, G_1, J_1) → poly5, j_4, m_3, g_3
  104. Intersect(m, j_3) → N_1
  105. Segment(I_1, N_1) → n_1
  106. Intersect(j_3, i_3) → O_1
  107. Intersect(c', i_3) → Q_1
  108. Intersect(c', i_3) → R_1
  109. Intersect(c', i_3) → S_1
  110. Intersect(c', i_3) → U_1
  111. Intersect(c', i_3) → A_2
  112. Intersect(l_2, i_3) → B_2
  113. Segment(B_2, O_1) → n_2
  114. Segment(B_2, M_1) → r_2
  115. Midpoint(M_1, L_1) → C_2
  116. Midpoint(L_1, K_1) → D_2
  117. Midpoint(K_1, J_1) → E_2
  118. Midpoint(J_1, M_1) → F_2
  119. Polygon(J_1, M_1, L_1, K_1) → poly6, j_5, m_4, l_4, k_5
  120. Intersect(j_3, d_1) → P_1
  121. Segment(P_1, M_1) → c_3
  122. Midpoint(r) → T_1
  123. Point(a_2) → G_2

AI Drawing Prompt Reference

Draw a net of a square pyramid. Start by creating a circle with center A and selecting a point B on it. Connect A and B, then create a line b2 parallel to AB. With B as the center, create a circle c that intersects b2 at point C. Rotate C around B by 30 degrees to get C', then connect B and C'. Create a line d parallel to BC'. The intersection of d and AB is point D. Use A, B, C', and D as vertices to form a polygon. Continue constructing other lines and auxiliary lines to complete the net of the square pyramid.
The prompt above was compiled from the original drawing commands and is for reference only.