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Stereographic Projection

Stereographic Projection
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2018-05-21 04:57
Coordinate GeometrySolid GeometryGeometric Construction
This example illustrates the concept of stereographic projection. It involves key mathematical concepts in solid geometry, such as spheres, planes, and projection lines. Using GeoGebra commands like Circle, Line, Sphere, and Intersect, users can intuitively understand the principles of stereographic projection. Suitable for high school or university solid geometry courses.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, B) → c
  3. Point(c) → C
  4. Point(c) → D
  5. Line(C, D) → f
  6. Point(c) → E
  7. Line(E, A) → g
  8. Point(zAxis) → F
  9. Sphere(A, F) → a
  10. OrthogonalLine(F, xOyPlane) → h
  11. Circle(G, H, I) → d
  12. Circle(J, K, L) → e
  13. Intersect(e, d) → M, N, ,
  14. Point(e) → O
  15. Line(O, F) → i
  16. Intersect(i, a, 1) → P
  17. Line(J, F) → j
  18. Line(K, F) → k
  19. Line(L, F) → l
  20. Intersect(l, a) → T, U
  21. Intersect(k, a) → V, W
  22. Intersect(j, a) → Z, A_1
  23. Plane(V, Z, T) → b
  24. IntersectPath(b, a) → p
  25. Line(H, F) → m
  26. Line(G, F) → n
  27. Line(I, F) → q
  28. Intersect(n, a) → Q, R
  29. Intersect(q, a) → S, B_1
  30. Intersect(m, a) → C_1, D_1
  31. Plane(S, Q, C_1) → o
  32. IntersectPath(o, a) → r
  33. Line(N, F) → t
  34. Intersect(r, p, 2) → E_1
  35. Line(F, M) → f_1
  36. Intersect(r, p, 1) → F_1
  37. IntersectPath(o, b) → g_1
  38. Mirror(G_1, d) → H_1
  39. Mirror(H_1, e) → I_1
  40. Mirror(G_1, e) → J_1
  41. Circle(I_1, J_1, G_1) → c_1
  42. Mirror(K_1, d) → L_1
  43. Mirror(L_1, e) → M_1
  44. Mirror(K_1, e) → N_1
  45. Circle(K_1, L_1, M_1) → d_1
  46. Line(L_1, F) → h_1
  47. Line(M_1, F) → i_1
  48. Line(N_1, F) → j_1
  49. Line(H_1, F) → k_1
  50. Line(I_1, F) → l_1
  51. Line(J_1, F) → m_1
  52. Intersect(h_1, a, 1) → O_1
  53. Intersect(k_1, a, 1) → P_1
  54. Intersect(l_1, a, 1) → Q_1
  55. Intersect(m_1, a, 1) → R_1
  56. Plane(R_1, Q_1, P_1) → w_1
  57. IntersectPath(w_1, a) → e_1
  58. Intersect(i_1, a, 1) → S_1
  59. Intersect(j_1, a, 1) → T_1
  60. Plane(O_1, S_1, C_1) → a_1
  61. Plane(T_1, S_1, O_1) → b_1
  62. IntersectPath(b_1, a) → p_1
  63. Intersect(c_1, d_1) → U_1, V_1, ,
  64. Intersect(e_1, p_1) → W_1, Z_1, ,
  65. Line(W_1, Z_1) → n_1
  66. IntersectPath(b, o) → q_1
  67. LaTeX(V_1, true, true) → Text1
  68. Circle(O, V_1, U_1) → s_1
  69. Tangent(O, e) → f_2,
  70. Mirror(O, d) → O'
  71. LineBisector(O, O') → g_2
  72. Intersect(f_2, g_2) → B_2
  73. Circle(B_2, O) → c_2
  74. Mirror(O', e) → O''
  75. Line(F, O'') → h_2
  76. Line(F, O') → i_2
  77. Intersect(i_2, a, 2) → C_2
  78. Intersect(h_2, a, 2) → D_2
  79. Plane(P, D_2, C_2) → o_1
  80. IntersectPath(o_1, a) → r_1
  81. IntersectPath(b_1, o_1) → j_2
  82. IntersectPath(o_1, b_1) → k_2
  83. IntersectPath(b_1, o_1) → l_2
  84. IntersectPath(o_1, b_1) → m_2
  85. IntersectPath(o_1, b_1) → n_2
  86. IntersectPath(o_1, b_1) → p_2
  87. IntersectPath(o_1, a_1) → q_2
  88. Plane(Q_1, R_1, Q) → u_1
  89. IntersectPath(o_1, u_1) → r_2
  90. Line(F, K_1) → s_2
  91. Intersect(s_2, p_1, 1) → A_2
  92. Plane(T_1, A_2, O_1) → v_1
  93. IntersectPath(o_1, v_1) → t_2