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Sphere Geometry Construction Demo

Sphere Geometry Construction Demo
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2020-05-23 16:24
CirclePolygonSolid GeometryGeometric Construction
This example demonstrates the construction and interaction of spherical and related geometric elements. Core math concepts include circles, polygons, solid geometry, and geometric transformations. GeoGebra commands used are Circle, Polygon, Rotate, Mirror, Segment, etc. Suitable for high school solid geometry teaching and geometric construction practice.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 4) → c
  3. Intersect(c, xAxis, 2) → B
  4. Rotate(B, 90°) → C
  5. Mirror(C, A) → D
  6. Segment(A, C) → f
  7. Circle(A, 1) → d
  8. Intersect(d, f, 1) → E
  9. Circle(A, 2) → e
  10. Intersect(e, f, 1) → F
  11. Circle(A, 3) → g
  12. Intersect(g, f, 1) → G
  13. Circle(A, 3.5) → h
  14. Intersect(h, f, 1) → H
  15. Circle(A, 3.85) → k
  16. Intersect(k, f, 1) → I
  17. Mirror(K, zAxis) → K'
  18. Mirror(L, zAxis) → L'
  19. Mirror(M, zAxis) → M'
  20. Mirror(N, zAxis) → N'
  21. Mirror(O, zAxis) → O'
  22. Segment(J, K) → i
  23. Segment(K, L) → j
  24. Segment(L, M) → l
  25. Segment(M, N) → m
  26. Segment(N, O) → n
  27. Segment(O, C) → p
  28. Segment(J, K') → q
  29. Segment(K', L') → r
  30. Segment(L', M') → s
  31. Segment(M', N') → t
  32. Segment(N', O') → a
  33. Segment(O', D) → b
  34. Line(C, zAxis) → as
  35. Rotate(O, 45°, as) → O'_1
  36. Rotate(N, 45°, as) → N'_1
  37. Rotate(M, 45°, as) → M'_1
  38. Rotate(L, 45°, as) → L'_1
  39. Rotate(K, 45°, as) → K'_1
  40. Rotate(J, 45°, as) → J'
  41. Rotate(K', 45°, as) → K''
  42. Rotate(L', 45°, as) → L''
  43. Rotate(M', 45°, as) → M''
  44. Rotate(N', 45°, as) → N''
  45. Rotate(O', 45°, as) → O''
  46. Rotate(D, 45°, as) → D'
  47. Segment(O'', D') → f_1
  48. Segment(O'', N'') → g_1
  49. Segment(N'', M'') → h_1
  50. Segment(M'', L'') → i_1
  51. Segment(L'', K'') → j_1
  52. Segment(K'', J') → k_1
  53. Segment(J', K'_1) → l_1
  54. Segment(K'_1, L'_1) → m_1
  55. Segment(L'_1, M'_1) → n_1
  56. Segment(M'_1, N'_1) → p_1
  57. Segment(N'_1, O'_1) → q_1
  58. Segment(C, O'_1) → r_1
  59. LineBisector(C, D', xOyPlane) → s_1
  60. LineBisector(C, D) → t_1
  61. Intersect(s_1, t_1) → P
  62. Line(P, zAxis) → rotas
  63. Sequence(Rotate[l1, (nn * 90°), rotas], nn, 1, 7) → l2
  64. Sequence(Rotate[l3, (nn * 90°), rotas], nn, 1, 7) → l4
  65. Rotate(J, (360°) / 8, rotas) → J'_1
  66. Polygon(J, J'_1, 8, xOyPlane) → veelhoek1, a_1, R, S, T, U, V, b_1, c_1, d_1, e_1, f_2, g_2, h_2, Q
  67. Point(rotas) → W
  68. Rotate(C, (360°) / 8, rotas) → C'
  69. Midpoint(C, C') → Z
  70. Plane(Z, P, P + (0, 0, 1)) → spieg
  71. Mirror(L, spieg) → L'_2
  72. Mirror(M, spieg) → M'_2
  73. Mirror(N, spieg) → N'_2
  74. Mirror(O, spieg) → O'_2
  75. Intersect(j, spieg) → C_1
  76. Midpoint(L'_1, L) → A_1
  77. Midpoint(M'_1, M) → B_1
  78. Midpoint(N'_1, N) → D_1
  79. Plane(A_1, B_1, D_1) → p_2
  80. Midpoint(K'_1, K) → E_1
  81. Rotate(spieg, (360°) / 16, rotas) → spieg'
  82. Intersect(spieg', i) → F_1
  83. Mirror(K, spieg) → K'_2
  84. Mirror(F_1, spieg) → G_1
  85. Segment(P, C') → s_2
  86. Segment(P, C) → t_2
  87. OrthogonalLine(C, t_2, xOyPlane) → a_2
  88. OrthogonalLine(C', s_2, xOyPlane) → b_2
  89. Intersect(a_2, b_2) → H_1
  90. Line(O, a_2) → c_2
  91. Line(O'_2, b_2) → f_3
  92. Line(N, a_2) → g_3
  93. Line(N'_2, b_2) → h_3
  94. Line(M, a_2) → i_3
  95. Line(M'_2, b_2) → l_3
  96. Line(L, a_2) → m_3
  97. Line(L'_2, b_2) → n_3
  98. Intersect(c_2, f_3) → I_1
  99. Intersect(g_3, h_3) → J_1
  100. Intersect(i_3, l_3) → K_1
  101. Intersect(m_3, n_3) → L_1
  102. Polygon(C_1, L, L_1) → driehoek1, i_2, j_2, l_2
  103. Polygon(L, M, K_1, L_1) → vierhoek1, l_4, m_2, k_2, n_2
  104. Polygon(M, N, J_1, K_1) → vierhoek2, m_4, n_4, q_2, d_2
  105. Polygon(N, O, I_1, J_1) → vierhoek3, n_5, o, e_2, j_3
  106. Polygon(O, C, H_1, I_1) → vierhoek4, o_1, c_3, k_3, p_3
  107. Polygon(H_1, C', O'_2, I_1) → vierhoek5, q_3, c', o'_2, r_3
  108. Polygon(I_1, O'_2, N'_2, J_1) → vierhoek6, s_3, t_3, n'_2, a_3
  109. Polygon(J_1, N'_2, M'_2, K_1) → vierhoek7, b_3, d_3, m'_2, e_3
  110. Polygon(K_1, M'_2, L'_2, L_1) → vierhoek8, f_4, g_4, l'_2, h_4
  111. Polygon(L_1, L'_2, C_1) → driehoek2, i_4, j_4, k_4
  112. Segment(W, F_1) → q_4
  113. Segment(W, V) → r_4
  114. Segment(V, C_1) → s_4
  115. Rotate(b_2, (360°) / 8, zAxis) → t_4
  116. Mirror(L'_2, spieg') → M_1
  117. Mirror(M'_2, spieg') → N_1
  118. Mirror(N'_2, spieg') → O_1
  119. Mirror(O'_2, spieg') → P_1
  120. Mirror(C_1, spieg') → Q_1
  121. Line(C', rotas) → a_4
  122. Rotate(b_2, (360°) / 32, a_4) → b_4
  123. Polygon(F_1, C_1, Q_1) → driehoek3, c_4, d_4, e_4
  124. Polygon(C_1, L_1, M_1, Q_1) → vierhoek9, f_5, g_5, h_5, i_5
  125. Polygon(L'_2, M'_2, N_1, M_1) → vierhoek10, j_5, k_5, l_5, m_5
  126. Polygon(M'_2, N'_2, O_1, N_1) → vierhoek11, p_5, q_5, r_5, s_5
  127. Line(K'_2, a_2) → t_5
  128. Line(K, b_2) → a_5
  129. Intersect(t_5, a_5) → S_1
  130. Polygon(K'_2, C_1, S_1) → driehoek4, b_5, k'_2, c_5
  131. Polygon(G_1, K'_2, S_1, V) → vierhoek12, d_5, e_5, f_6, v
  132. Polygon(V, S_1, K, F_1) → vierhoek13, v_1, g_6, k_6, h_6
  133. Polygon(S_1, C_1, K) → driehoek5, k_7, i_6, j_6
  134. Segment(C', C) → l_6
  135. Line(H_1, l_6) → m_6
  136. Rotate(M, (360°) / 8, rotas) → M'_3
  137. Rotate(K_1, (360°) / 8, rotas) → R_1
  138. Segment(M'_3, R_1) → n_6
  139. Rotate(m_6, (360°) / 8, rotas) → p_6
  140. Line(C_1, m_6) → q_6
  141. Line(Q_1, p_6) → r_6
  142. Intersect(r_6, q_6) → T_1
  143. Line(L'_2, m_6) → s_6
  144. Line(M'_2, m_6) → t_6
  145. Line(N'_2, m_6) → a_6
  146. Line(O'_2, m_6) → b_6
  147. Plane(W, F_1, C') → p_7
  148. Intersect(s_6, p_7) → U_1
  149. Intersect(t_6, p_7) → V_1
  150. Intersect(a_6, p_7) → W_1
  151. Intersect(b_6, p_7) → Z_1
  152. Segment(F_1, T_1) → c_6
  153. Segment(T_1, U_1) → d_6
  154. Segment(U_1, V_1) → e_6
  155. Segment(V_1, W_1) → f_7
  156. Segment(O'_2, Z_1) → g_7
  157. Segment(Z_1, W_1) → h_7
  158. Segment(Z_1, C') → i_7
  159. Polygon(F_1, C_1, T_1) → driehoek6, j_7, l_7, m_7
  160. Polygon(C_1, L'_2, U_1, T_1) → vierhoek14, n_7, q_7, u_1, r_7
  161. Polygon(L'_2, M'_2, V_1, U_1) → vierhoek15, s_7, t_7, a_7, b_7
  162. Polygon(M'_2, N'_2, W_1, V_1) → vierhoek16, c_7, d_7, w_1, e_7
  163. Polygon(N'_2, O'_2, Z_1, W_1) → vierhoek17, f_8, g_8, z_1, h_8
  164. Polygon(Z_1, O'_2, C') → driehoek7, i_8, j_8, k_8
  165. Segment(B_2, C_2) → p_4
  166. Sequence(Rotate[l5, (nn * (360°) / 8), rotas], nn, 1, 7) → l6
  167. Mirror(l7, spieg') → l7'
  168. Sequence(Rotate[l7, (nn * (360°) / 8), rotas], nn, 1, 7) → l8
  169. Sequence(Rotate[l7', (nn * (360°) / 8), rotas], nn, 1, 7) → l9
  170. Sequence(Rotate[l10, (nn * (360°) / 8), rotas], nn, 1, 7) → l11
  171. Polygon(V, J, 8, xOyPlane) → veelhoek2, l_8, E_2, F_2, G_2, H_2, I_2, m_8, n_8, p_8, q_8, r_8, s_8, t_8, D_2
  172. Polygon(C_2, B_2, 8, xOyPlane) → veelhoek3, a_8, K_2, L_2, M_2, N_2, O_2, b_8, c_8, d_8, e_8, f_9, g_9, h_9, J_2
  173. Polygon(G_1, V, C_2) → driehoek8, i_9, j_9, v_2
  174. Polygon(V, F_1, B_2) → driehoek9, k_9, v_3, l_9
  175. Sequence(Rotate[driehoek8, (nn * (360°) / 8), rotas], nn, 1, 7) → l12
  176. Sequence(Rotate[driehoek9, (nn * (360°) / 8), rotas], nn, 1, 7) → l13
  177. Polygon(W, O_2, C_2) → driehoek10, m_9, w, o_2
  178. Sequence(Rotate[driehoek10, (nn * (360°) / 8), rotas], nn, 1, 7) → l14
  179. Rotate(H_1, (360°) / 8, P) → P_2
  180. Polygon(H_1, P_2, 8, xOyPlane) → veelhoek4, n_9, R_2, S_2, T_2, U_2, V_2, p_9, q_9, r_9, s_9, t_9, a_9, b_9, Q_2
  181. Segment(C, D) → c_9
  182. Sequence(Segment[Rotate[C, (nn * (360°) / 8), P], Rotate[D, (nn * (360°) / 8), P]], nn, 1, 7) → l15
  183. Sequence(Segment[Rotate[P, (nn * (360°) / 8), P], Rotate[C, (nn * (360°) / 8), P]], nn, 1, 7) → l16
  184. Segment(H_1, P) → d_9
  185. Sequence(Segment[Rotate[H_1, (nn * (360°) / 8), P], Rotate[P, (nn * (360°) / 8), P]], nn, 1, 7) → l17
  186. PointIn(spieg) → W_2
  187. PointIn(spieg) → Z_2
  188. PointIn(spieg) → A_3
  189. Segment(V, A_3) → e_9
  190. Segment(A_3, Z_2) → f_{10}
  191. Segment(Z_2, W_2) → g_{10}
  192. Segment(W_2, W) → h_{10}
  193. Rotate(l18, (360°) / 8, rotas) → l18'
  194. Plane(F_1, W, W + (0, 0, 1)) → p_{10}
  195. Segment(W, F_1) → i_{10}
  196. Line(A_3, p_4) → j_{10}
  197. Line(Z_2, p_4) → k_{10}
  198. Line(W_2, p_4) → l_{10}
  199. Intersect(j_{10}, p_{10}) → B_3
  200. Intersect(k_{10}, p_{10}) → C_3
  201. Intersect(l_{10}, p_{10}) → D_3
  202. Polygon(W, W_2, D_3) → driehoek11, m_{10}, w_2, n_{10}
  203. Polygon(W_2, Z_2, C_3, D_3) → vierhoek18, q_{10}, z_2, r_{10}, s_{10}
  204. Polygon(Z_2, A_3, B_3, C_3) → vierhoek19, t_{10}, a_{10}, b_{10}, c_{10}
  205. Intersect(p_4, p_{10}) → E_3
  206. Polygon(V, E_3, B_3, A_3) → vierhoek20, v_4, d_{10}, e_{10}, f_{11}
  207. Mirror(l19, p_{10}) → l19'
  208. Sequence(Rotate[l19, (nn * (360°) / 8), rotas], nn, 1, 7) → l20
  209. Sequence(Rotate[l19', (nn * (360°) / 8), rotas], nn, 1, 7) → l21

AI Drawing Prompt Reference

Draw a sphere centered at the origin with radius 4. Its equator intersects the horizontal axis at a point. Rotate this point 90 degrees around the center to get a top point, then reflect it through the center to get a bottom point, and connect them to form a vertical diameter. Along this diameter, mark points at distances 1, 2, 3, 3.5, and 3.85 from the center, and draw concentric circles with these radii. Mirror these points across the vertical axis to the opposite side, then connect adjacent points to form horizontal segments, creating a grid of meridians on the sphere. Finally, rotate the entire grid 45 degrees around the vertical axis to produce a symmetric set of meridians, completing the sphere's latitude-longitude structure.
The prompt above was compiled from the original drawing commands and is for reference only.