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四棱锥及其性质

四棱锥及其性质
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2020-05-14 00:37
解析几何立体几何几何作图
这个范例演示了一个四棱锥的构造及其性质。它涉及立体几何中的核心概念，如棱锥的定义、棱面、棱线等。通过使用GeoGebra命令如Point、Polygon、Intersect等，可以直观地展示棱锥的各个组成部分。适合高中阶段的学生学习立体几何。

GeoGebra 命令及参数

  1. Point(yAxis) → F
  2. Polygon(D, A, B, C) → vierhoek1, d, a, b, c
  3. Intersect(a, xAxis) → E
  4. Polygon(F, A, E) → driehoek1, e_1, f_1, a_1
  5. Prism(driehoek1, 1) → g, G, RibbeEI, RibbeGH, RibbeHI, RibbeGI, H, I, zijvlakAFGH, zijvlakAEIH, zijvlakEFGI, zijvlakGHI, RibbeFG, RibbeAH
  6. Plane(A, E, H) → vlak1
  7. PointIn(zijvlakEFGI) → M
  8. Midpoint(M, Mirror[M, vlak1]) → N_1
  9. PointIn(zijvlakEFGI) → L
  10. Midpoint(L, Mirror[L, vlak1]) → K_1
  11. Surface(l, (0.9 * cos(t)), (0.9 * sin(t)), l, -1, 1, t, 0°, 180°) → e
  12. Surface((0.9 * cos(t)), l, (0.9 * sin(t)), l, -1, 1, t, 0°, 180°) → f
  13. PointIn(zijvlakEFGI) → J
  14. PointIn(zijvlakEFGI) → K
  15. PointIn(zijvlakEFGI) → N
  16. Point(RibbeFG) → P
  17. PointIn(zijvlakEFGI) → Q
  18. PointIn(zijvlakEFGI) → R
  19. PointIn(zijvlakEFGI) → S
  20. Point(RibbeEI) → T
  21. CurveCartesian((0.9 * cos(t)), (0.9 * cos(t)), (0.9 * sin(t)), t, 0°, 180°) → i
  22. CurveCartesian((0.9 * cos(t)), -1, (0.9 * sin(t)), t, 0°, 90°) → j
  23. CurveCartesian((-0.9 * cos(t)), (0.9 * cos(t)), (0.9 * sin(t)), t, 0°, 180°) → h
  24. CurveCartesian(1, (0.9 * cos(t)), (0.9 * sin(t)), t, 90°, 180°) → l
  25. Segment(L, K) → n
  26. Segment(K, J) → p
  27. Segment(J, T) → q
  28. Segment(M, S) → r
  29. Segment(S, N) → s
  30. Segment(N, R) → t
  31. Segment(R, Q) → g_1
  32. Segment(Q, P) → h_1
  33. Polygon(I, T, P, G, J, K, L, M, S, N, R, Q) → veelhoek1, i_1, q_1, p_1, g_2, t_1, j_1, k_1, l_1, m_1, s_1, n_1, r_1
  34. Segment(F, A) → b_1
  35. Segment(A, E) → c_1
  36. Segment(F, E) → d_1
  37. Point(l) → A_1
  38. Point(l) → B_1
  39. Point(l) → C_1
  40. Point(l) → D_1
  41. Point(l) → E_1
  42. Line(A_1, RibbeHI) → f_2
  43. Line(B_1, RibbeHI) → h_2
  44. Line(C_1, RibbeHI) → i_2
  45. Line(D_1, RibbeHI) → j_2
  46. Line(E_1, RibbeHI) → k_2
  47. Intersect(RibbeAH, f_2) → F_1
  48. Intersect(RibbeAH, h_2) → G_1
  49. Intersect(RibbeAH, i_2) → H_1
  50. Intersect(RibbeAH, j_2) → I_1
  51. Intersect(RibbeAH, k_2) → J_1
  52. Polygon(Z, T, I, H) → vierhoek2, z_1, t_2, i_3, h_3
  53. Polygon(F_1, A_1, T, Z) → vierhoek3, l_2, m_2, t_3, z_2
  54. Polygon(G_1, B_1, A_1, F_1) → vierhoek4, n_2, p_2, q_2, r_2
  55. Polygon(H_1, C_1, B_1, G_1) → vierhoek5, s_2, a_2, b_2, c_2
  56. Polygon(I_1, D_1, C_1, H_1) → vierhoek6, d_2, e_2, f_3, g_3
  57. Polygon(J_1, E_1, D_1, I_1) → vierhoek7, j_3, k_3, l_3, m_3
  58. Polygon(A, V, E_1, J_1) → vierhoek8, a_3, v, n_3, p_3
  59. Line(A, H) → as
  60. Rotate(vierhoek2, 90°, as) → vierhoek2'
  61. Rotate(vierhoek3, 90°, as) → vierhoek3'
  62. Rotate(vierhoek4, 90°, as) → vierhoek4'
  63. Rotate(vierhoek5, 90°, as) → vierhoek5'
  64. Rotate(vierhoek6, 90°, as) → vierhoek6'
  65. Rotate(vierhoek7, 90°, as) → vierhoek7'
  66. Rotate(vierhoek8, 90°, as) → vierhoek8'
  67. CircleArc(E, T, V) → c_3
  68. Midpoint(J, Mirror[J, vlak1]) → L_1
  69. Midpoint(K, Mirror[K, vlak1]) → M_1
  70. Polygon(L_1, J, K, M_1) → vierhoek9, q_3, j_4, k_4, r_3
  71. Polygon(T, J, L_1) → driehoek2, s_3, t_4, j_5
  72. Plane(A, H, O) → sym
  73. Mirror(driehoek2, sym) → driehoek2'
  74. Mirror(vierhoek9, sym) → vierhoek9'
  75. Polygon(K, L, K_1, M_1) → vierhoek10, k_5, l_4, b_3, d_3
  76. Polygon(M, L, K_1, N_1) → vierhoek11, e_3, f_4, m_4, l_5
  77. Mirror(vierhoek10, sym) → vierhoek10'
  78. Mirror(vierhoek11, sym) → vierhoek11'
  79. CircleArc(F, W, P) → c_4
  80. CurveCartesian((-0.9 * cos(t)), (0.9 * cos(t)), (0.9 * sin(t)), t, 124°, 180°) → k
  81. Point(k) → O_1
  82. Point(k) → P_1
  83. Point(k) → Q_1
  84. Point(k) → R_1
  85. Point(k) → S_1
  86. Midpoint(O_1, Mirror[O_1, vlak1]) → T_1
  87. Polygon(M, O_1, T_1, N_1) → vierhoek12, m_5, o_1, g_4, h_4
  88. Midpoint(P_1, Mirror[P_1, vlak1]) → U_1
  89. Polygon(O_1, P_1, U_1, T_1) → vierhoek13, i_4, n_4, u_1, p_4
  90. Midpoint(Q_1, Mirror[Q_1, vlak1]) → V_1
  91. Polygon(P_1, Q_1, V_1, U_1) → vierhoek14, q_4, r_4, v_1, s_4
  92. Midpoint(R_1, Mirror[R_1, vlak1]) → W_1
  93. Polygon(Q_1, R_1, W_1, V_1) → vierhoek15, a_4, b_4, w_1, d_4
  94. Midpoint(S_1, Mirror[S_1, vlak1]) → Z_1
  95. Polygon(R_1, S_1, Z_1, W_1) → vierhoek16, e_4, f_5, g_5, h_5
  96. Polygon(U, V, Z_1, S_1) → vierhoek17, u, v_2, i_5, n_5
  97. Mirror(vierhoek12, sym) → vierhoek12'
  98. Mirror(vierhoek13, sym) → vierhoek13'
  99. Mirror(vierhoek14, sym) → vierhoek14'
  100. Mirror(vierhoek15, sym) → vierhoek15'
  101. Mirror(vierhoek16, sym) → vierhoek16'
  102. Mirror(vierhoek17, sym) → vierhoek17'
  103. Segment(A_2, L) → m
  104. Segment(H, A) → p_5
  105. Polygon(A, B_2, C_2, V) → vierhoek18, a_5, q_5, r_5, v_3
  106. Polygon(W, D_2, B_2, A) → vierhoek19, w, s_5, t_5, a_6
  107. Polygon(V, C_2, E_2, U) → vierhoek20, v_4, b_5, c_5, u_2
  108. Polygon(E_2, D_2, W, U) → vierhoek21, d_5, e_5, w_2, u_3
  109. CurveCartesian((-0.9 * cos(t)), (0.9 * cos(t)), (0.9 * sin(t)), t, 0°, 180°) → o_2
  110. Rotate(o_2, 90°, zAxis) → o_3