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Square Pyramid with Open and Close Function

Square Pyramid with Open and Close Function
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2018-05-28 14:34
Solid GeometryGeometric ConstructionSlider Animation
This example uses a slider to demonstrate the unfolding and folding of a square pyramid, illustrating its 3D structure and net. Key mathematical concepts include solid geometry, transformations such as rotation and translation. Using GeoGebra commands like Point, Segment, Polygon, Rotate, Translate, etc., the dynamic process of unfolding and folding the pyramid can be observed. Suitable for middle school and above students to learn solid geometry.

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(E, F) → p
  23. Segment(A, D) → q
  24. Midpoint(b_1) → G
  25. Segment(G, F) → r
  26. Segment(E, G) → t
  27. Line(E, G) → c_1
  28. Circle(G, F) → f_1
  29. Intersect(f_1, c_1, 2) → H
  30. Intersect(c_1, d_1) → I
  31. Circle(I, F) → g_1
  32. Intersect(g_1, c_1, 1) → J
  33. Vector(F, J) → u
  34. Point(c') → L
  35. Circle(L, F) → q_1
  36. Vector(F, H) → w
  37. Midpoint(A, B) → K
  38. Line(K, E) → e_1
  39. Circle(K, h) → p_1
  40. Intersect(e_1, c') → M
  41. Circle(M, h) → r_1
  42. Intersect(r_1, e_1, 2) → N
  43. Intersect(p_1, e_1, 1) → O
  44. Vector(F, N) → v
  45. Vector(F, O) → z
  46. Translate(F, Vector[(z * o)]) → F'_1
  47. Translate(F, Vector[(u * (o - 1))]) → F'_2
  48. Translate(F, Vector[(v * (o - 2))]) → F'_3
  49. Translate(F, Vector[(w * (o - 3))]) → F'
  50. Segment(F, N) → s
  51. LineBisector(s) → a_2
  52. Intersect(a_2, c') → P
  53. CircleArc(P, N, F) → c_2
  54. Ray(P, F'_3) → d_2
  55. Intersect(c_2, d_2, 1) → Q
  56. Segment(F, O) → e_2
  57. LineBisector(e_2) → f_2
  58. Intersect(f_2, a_1) → R
  59. CircleArc(R, F, O) → g_2
  60. Ray(R, F'_1) → h_2
  61. Intersect(g_2, h_2, 1) → S
  62. CircleArc(I, F, J) → k_2
  63. CircleArc(G, H, F) → p_2
  64. Ray(I, F'_2) → i_2
  65. Intersect(k_2, i_2, 1) → T
  66. Ray(G, F') → j_2
  67. Intersect(p_2, j_2, 1) → U
  68. Circle(I, E) → s_1
  69. OrthogonalLine(I, a_1) → i_1
  70. Intersect(s_1, i_1, 2) → V
  71. Intersect(s_1, i_1, 1) → W
  72. OrthogonalLine(V, i_1) → j_1
  73. OrthogonalLine(W, i_1) → k_1
  74. OrthogonalLine(G, k_1) → l_1
  75. Intersect(j_1, l_1) → Z
  76. Intersect(k_1, l_1) → A_1
  77. Midpoint(V, Z) → B_1
  78. Midpoint(A_1, W) → C_1
  79. Circle(B_1, r) → t_1
  80. Circle(C_1, r) → q_2
  81. OrthogonalLine(B_1, k_1) → m_1
  82. Intersect(t_1, m_1, 1) → D_1
  83. Intersect(q_2, m_1, 2) → E_1
  84. Vector(C', Z) → u_1
  85. Vector(B, A_1) → v_1
  86. Vector(N, D_1) → w_1
  87. Vector(O, E_1) → z_1
  88. Translate(N, Vector[(w_1 * (o - 4))]) → N'
  89. Translate(O, Vector[(z_1 * (o - 4))]) → O'
  90. Translate(B, Vector[(v_1 * (o - 4))]) → B'
  91. Translate(A, Vector[(v_1 * (o - 4))]) → A'
  92. Translate(C', Vector[(u_1 * (o - 4))]) → C''
  93. Translate(D, Vector[(u_1 * (o - 4))]) → D'
  94. If(o < 1, S, If[o < 4, O, If[o < 5, O', E_1]]) → F_1
  95. If(o < 1, F, If[o < 2, T, J]) → G_1
  96. If(o < 3, F, If[o < 4, U, H]) → H_1
  97. If(o < 2, F, If[o < 3, Q, If[o < 4, N, If[o < 5, N', D_1]]]) → I_1
  98. If(o < 4, A, If[o < 5, A', W]) → J_1
  99. If(o < 4, B, If[o < 5, B', A_1]) → K_1
  100. If(o < 4, C', If[o < 5, C'', Z]) → L_1
  101. If(o < 4, D, If[o < 5, D', V]) → M_1
  102. Polygon(F_1, J_1, K_1) → poly2, k_3, f_3, j_3
  103. Polygon(L_1, H_1, K_1) → poly3, k_4, l_2, h_3
  104. Polygon(L_1, I_1, M_1) → poly4, m_2, l_3, i_3
  105. Polygon(M_1, G_1, J_1) → poly5, j_4, m_3, g_3
  106. Intersect(m, j_3) → N_1
  107. Segment(I_1, N_1) → n_1
  108. Intersect(j_3, i_3) → O_1
  109. Intersect(c', i_3) → Q_1
  110. Intersect(c', i_3) → R_1
  111. Intersect(c', i_3) → S_1
  112. Intersect(c', i_3) → U_1
  113. Intersect(c', i_3) → A_2
  114. Intersect(l_2, i_3) → B_2
  115. Segment(B_2, O_1) → n_2
  116. Segment(B_2, M_1) → r_2
  117. Midpoint(M_1, L_1) → C_2
  118. Midpoint(L_1, K_1) → D_2
  119. Midpoint(K_1, J_1) → E_2
  120. Midpoint(J_1, M_1) → F_2
  121. Segment(G_1, F_2) → s_2
  122. Segment(C_2, I_1) → t_2
  123. Segment(D_2, H_1) → a_3
  124. Segment(E_2, F_1) → b_3
  125. Polygon(J_1, M_1, L_1, K_1) → poly6, j_5, m_4, l_4, k_5
  126. Intersect(j_3, d_1) → P_1
  127. Segment(P_1, M_1) → c_3
  128. Midpoint(p) → V_1
  129. OrthogonalLine(V_1, p) → d_3
  130. Point(d_3) → W_1
  131. Midpoint(r) → T_1
  132. Midpoint(a_3) → Z_1
  133. Point(a_2) → G_2
  134. Point(Circle[H_2, l]) → I_2
  135. Segment(H_2, I_2) → e_3
  136. Line(H_2, I_2) → b
  137. Circle(I_2, (3 * l / 4.5)) → p_3
  138. Intersect(p_3, b, 2) → J_2
  139. Rotate(J_2, 30°, I_2) → K_2
  140. Segment(I_2, K_2) → n_3
  141. Line(K_2, b) → q_3
  142. Line(H_2, n_3) → r_3
  143. Intersect(q_3, r_3) → L_2
  144. Segment(H_2, K_2) → s_3
  145. Segment(I_2, L_2) → t_3
  146. Intersect(s_3, t_3) → M_2
  147. Circle(M_2, h) → c_4
  148. OrthogonalLine(M_2, b) → a_4
  149. Intersect(c_4, a_4, 2) → N_2
  150. Polygon(I_2, N_2, K_2) → poly8, k_6, i_5, n_5
  151. Polygon(H_2, L_2, K_2, I_2) → poly9, h_5, l_6, k_7, i_6
  152. Polygon(H_2, N_2, L_2) → poly10, l_7, h_6, n_6
  153. Polygon(L_2, N_2, K_2) → poly11, k_8, l_8, n_7
  154. Midpoint(k_7) → O_2
  155. Segment(M_2, O_2) → b_4
  156. Segment(M_2, N_2) → d_4
  157. Segment(N_2, O_2) → e_4
  158. Angle(O_2, M_2, N_2) → β
  159. Midpoint(N_2, M_2) → P_2
  160. Midpoint(O_2, N_2) → Q_2
  161. Line(P_2, Q_2) → f_4
  162. Circle(P_2, l) → g_4
  163. Intersect(g_4, f_4, 1) → R_2
  164. Intersect(g_4, f_4, 2) → S_2
  165. Midpoint(b_3) → V_2