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基本几何作图范例

基本几何作图范例
几何画板及绘图内容加载中，请稍等……
2015-09-25 00:45
圆多边形角几何作图
①本范例演示了使用 GeoGebra 进行基本几何图形的构造过程；②涉及的核心数学概念包括几何作图、角度测量、图形变换等；③作图要点——从下方『构造摘要』提炼用到了 Segment（线段）、Rotate（旋转）、Angle（角度）、Point（点）、Circle（圆）、Intersect（交点）、AttachCopyToView（视图附着）、Ellipse（椭圆）等 GeoGebra 命令/对象；④适合初中及以上学生学习和理解几何作图的基本方法，可用于课堂教学或课后练习。

GeoGebra 命令及参数

  1. Segment(A_1, B_1) → a
  2. Segment(X_1, Y_1) → b
  3. Rotate(C_1, 32*°, B_2) → A_2
  4. Angle(C_1, B_2, A_2) → α
  5. Segment(B_2, A_2) → c
  6. Segment(B_2, C_1) → d
  7. Rotate(C, 45*°, B_3) → A_3
  8. Angle(C, B_3, A_3) → β
  9. Segment(B_3, A_3) → e
  10. Segment(B_3, C) → f
  11. Segment(A_4, B) → g
  12. Rotate(D, 60*°, A) → D'
  13. Angle(D, A, D') → γ
  14. Segment(A, D') → h
  15. Segment(A, D) → i
  16. Rotate(Z, 120*°, Y) → X
  17. Angle(Z, Y, X) → δ
  18. Segment(X, Y) → j
  19. Segment(Y, Z) → k
  20. Point(g) → E
  21. Circle(A_4, Segment[E, A_4]) → p
  22. Circle(B, Segment[A_4, E]) → q
  23. Intersect(p, q, 1) → F
  24. Intersect(p, q, 2) → G
  25. Segment(F, G) → l
  26. Angle(g, l) → ε
  27. AttachCopyToView(PolyLine[(14.266727717871698, -29.20442136434609), (15.212743824201402, -29.393624585612024), (16.300662346480564, -29.630128612194447), (16.44256476243002, -29.67742941751093), (17.577784090025666, -29.819331833460385), (20.841539656863144, -30.43424230257468), (22.307864621674188, -30.954551161056006), (22.544368648256615, -31.09645357700546), (22.5916694535731, -31.42755921422085), (22.638970258889586, -33.41419303751319), (22.638970258889586, -35.211623639539596), (22.40246623230716, -35.4954284714385), (21.97675898445879, -35.826534108653895), (21.551051736610425, -36.06303813523631), (21.125344488762057, -36.1103389405528), (19.375214692052104, -36.25224135650225), (16.773670399645415, -35.96843652460335), (15.63845107204977, -35.40082686080553), (15.591150266733285, -35.25892444485608), (15.685751877366256, -35.44812766612202), (15.874955098632196, -35.87383491397038), (16.91557281559487, -38.19157437447811), (17.199377647493783, -38.617281622326466), (17.81428811660809, -38.75918403827592), (18.476499391038885, -38.80648484359241), (19.044109054836706, -38.71188323295944), (19.375214692052104, -38.617281622326466), (19.89552355053344, -38.19157437447811), (20.557734824964236, -36.867151825616546), (20.88884046217963, -35.92113571928686), (20.841539656863144, -35.59003008207147), (20.79423885154666, -35.30622525017257), (20.60503563028072, -35.02242041827366), (20.51043401964775, -34.83321719700772), (20.368531603698294, -34.69131478105827), (19.848222745216955, -34.31290833852639), (19.186011470786163, -33.83990028536155), (19.044109054836706, -33.6979978694121), (18.80760502825428, -33.50879464814616), (18.23999536445646, -33.17768901093077), (18.00349133787403, -33.03578659498132), (17.766987311291604, -32.799282568398894), (17.34128006344324, -32.51547773649999), (16.773670399645415, -32.08977048865163), (16.300662346480564, -31.711364046119755), (15.969556709265166, -31.52216082485382), (15.780353487999225, -31.380258408904368), (15.118142213568433, -30.812648745106554), (14.64513416040358, -30.386941497258196), (14.45593093913764, -30.197738275992258), (14.361329328504668, -30.00853505472632), (14.219426912555212, -29.7720310281439), (14.124825301922243, -29.488226196244995), (14.030223691289272, -29.299022974979056), (NaN, NaN), (12.75310194774417, -40.9350210828342), (12.516597921161745, -40.887720277517715), (12.138191478629862, -40.887720277517715), (11.901687452047437, -40.9350210828342), (11.712484230781495, -40.982321888150686), (11.523281009515555, -41.07692349878365), (11.334077788249614, -41.26612672004959), (11.192175372300158, -41.50263074663201), (11.097573761667187, -41.69183396789795), (11.097573761667187, -41.881037189163884), (11.097573761667187, -42.070240410429825), (11.144874566983672, -42.25944363169576), (11.286776982933128, -42.448646852961694), (11.428679398882585, -42.59054926891115), (11.617882620148524, -42.7324516848606), (11.901687452047437, -42.92165490612654), (12.090890673313377, -42.96895571144302), (12.232793089262833, -43.01625651675951), (12.374695505212289, -43.063557322075994), (12.516597921161745, -43.01625651675951), (12.6585003371112, -42.96895571144302), (12.800402753060656, -42.87435410081006), (12.989605974326597, -42.7324516848606), (13.131508390276052, -42.59054926891115), (13.178809195592537, -42.40134604764521), (13.226110000909022, -42.022939605113336), (13.226110000909022, -41.69183396789795), (13.226110000909022, -41.408029135999044), (13.178809195592537, -41.2188259147331), (13.131508390276052, -41.07692349878365), (13.036906779643083, -40.9350210828342), (12.895004363693626, -40.84041947220123), (NaN, NaN), (17.53048328470918, -42.022939605113336), (17.152076842177298, -42.11754121574631), (16.91557281559487, -42.25944363169576), (16.72636959432893, -42.40134604764521), (16.537166373062988, -42.59054926891115), (16.44256476243002, -42.7324516848606), (16.34796315179705, -42.87435410081006), (16.34796315179705, -43.110858127392476), (16.34796315179705, -43.30006134865842), (16.44256476243002, -43.678467791190286), (16.63176798369596, -43.9622726230892), (16.8209712049619, -44.198776649671615), (17.104776036860812, -44.48258148157052), (17.293979258126754, -44.62448389751997), (17.483182479392696, -44.71908550815294), (17.672385700658634, -44.71908550815294), (17.861588921924575, -44.67178470283646), (18.050792143190517, -44.52988228688701), (18.23999536445646, -44.293378260304586), (18.381897780405914, -44.05687423372216), (18.52380019635537, -43.77306940182326), (18.61840180698834, -43.44196376460787), (18.61840180698834, -43.25276054334193), (18.571101001671856, -43.01625651675951), (18.476499391038885, -42.82705329549357), (18.4291985857224, -42.68515087954412), (18.287296169772944, -42.59054926891115), (18.192694559139973, -42.40134604764521), (18.050792143190517, -42.21214282637928), (17.90888972724106, -42.11754121574631), (17.766987311291604, -42.070240410429825), (17.625084895342148, -42.11754121574631), (NaN, NaN), (12.611199531794714, -42.21214282637928), (12.421996310528774, -42.11754121574631), (12.280093894579318, -42.022939605113336), (12.421996310528774, -41.881037189163884), (12.56389872647823, -41.73913477321443), (12.705801142427685, -41.69183396789795), (12.895004363693626, -41.8337363838474), (12.989605974326597, -42.022939605113336), (12.942305169010112, -42.16484202106279), (12.895004363693626, -42.30674443701224), (12.705801142427685, -42.40134604764521), (12.516597921161745, -42.40134604764521), (12.421996310528774, -42.21214282637928), (12.374695505212289, -42.070240410429825), (NaN, NaN), (17.01017442622784, -43.3473621539749), (16.91557281559487, -43.48926456992435), (16.868272010278385, -43.678467791190286), (16.91557281559487, -43.86767101245623), (17.057475231544327, -44.05687423372216), (17.199377647493783, -44.246077454988104), (17.293979258126754, -44.387979870937556), (17.43588167407621, -44.293378260304586), (17.53048328470918, -44.10417503903865), (17.672385700658634, -43.86767101245623), (17.766987311291604, -43.678467791190286), (17.71968650597512, -43.53656537524083), (17.625084895342148, -43.39466295929138), (17.483182479392696, -43.30006134865842), (17.34128006344324, -43.3473621539749), (17.199377647493783, -43.44196376460787), (17.152076842177298, -43.58386618055732), (17.199377647493783, -43.77306940182326), (17.24667845281027, -43.91497181777271), true], 1, (-23.95232297784837, -52.9967264385377), (40.660577084470454, -24.42704002738117), (0, 604), (1366, 0)) → stroke1
  28. Segment(I, J) → m
  29. Point(m) → K
  30. Circle(I, Segment[I, K]) → r
  31. Circle(J, Segment[I, K]) → s
  32. Intersect(r, s, 1) → L
  33. Intersect(r, s, 2) → M
  34. Segment(L, M) → n
  35. Angle(m, n) → ζ
  36. Ellipse(N, O, P) → t
  37. Ellipse(Q, R, S) → c_1
  38. Circle(T, U) → d_1
  39. Ellipse(V, W, D_1) → e_1
  40. Ellipse(E_1, F_1, G_1) → f_1
  41. Intersect(m, n) → H_1
  42. Point(m) → I_1
  43. Circle(H_1, Segment[H_1, I_1]) → g_1
  44. Circle(J, Segment[H_1, I_1]) → h_1
  45. Intersect(g_1, h_1, 1) → J_1
  46. Intersect(g_1, h_1, 2) → K_1
  47. Segment(J_1, K_1) → a_1
  48. Intersect(m, a_1) → L_1
  49. Point(i) → M_1
  50. Circle(A, Segment[A, M_1]) → k_1
  51. Intersect(k_1, h, 1) → N_1
  52. Circle(N_1, Segment[N_1, M_1]) → p_1
  53. Circle(M_1, Segment[M_1, N_1]) → q_1
  54. Intersect(p_1, q_1, 1) → O_1
  55. Point(k) → P_1
  56. Circle(Y, Segment[Y, P_1]) → r_1
  57. Intersect(r_1, j, 1) → Q_1
  58. Circle(P_1, Segment[Q_1, P_1]) → s_1
  59. Circle(Q_1, Segment[Q_1, P_1]) → t_1
  60. Intersect(s_1, t_1, 2) → R_1
  61. Segment(Y, R_1) → b_1
  62. Circle(T_1, Segment[S_1, T_1]) → c_2
  63. Point(c_2) → U_1
  64. Circle(U_1, Segment[T_1, U_1]) → d_2
  65. Point(d_2) → V_1
  66. Circle(V_1, Segment[U_1, V_1]) → e_2
  67. Point(e_2) → W_1
  68. Circle(W_1, Segment[V_1, W_1]) → f_2
  69. Intersect(c_2, d_2, 2) → Z_1
  70. Intersect(d_2, e_2, 2) → C_2
  71. Intersect(e_2, f_2, 2) → D_2
  72. Intersect(e_2, f_2, 1) → E_2
  73. Intersect(d_2, e_2, 1) → F_2
  74. Intersect(c_2, d_2, 1) → G_2
  75. Circle(E_2, Segment[E_2, F_2]) → g_2
  76. Circle(F_2, Segment[E_2, F_2]) → h_2
  77. Circle(G_2, Segment[F_2, G_2]) → k_2
  78. Circle(C_2, Segment[Z_1, C_2]) → p_2
  79. Circle(Z_1, Segment[C_2, Z_1]) → q_2
  80. Circle(D_2, Segment[C_2, D_2]) → r_2
  81. Intersect(h_2, k_2, 2) → H_2
  82. Intersect(g_2, h_2, 2) → I_2
  83. Intersect(p_2, r_2, 2) → J_2
  84. Circle(H_2, Segment[I_2, H_2]) → s_2
  85. Circle(I_2, Segment[I_2, H_2]) → t_2
  86. Intersect(p_2, q_2, 1) → K_2
  87. Circle(J_2, Segment[K_2, J_2]) → c_3
  88. Circle(K_2, Segment[J_2, K_2]) → d_3
  89. Intersect(s_2, t_2, 1) → L_2
  90. Intersect(k_2, s_2, 1) → M_2
  91. Intersect(c_2, k_2, 1) → N_2
  92. Intersect(c_2, q_2, 2) → O_2
  93. Intersect(q_2, d_3, 2) → P_2
  94. Intersect(c_3, d_3, 1) → Q_2
  95. Intersect(r_2, c_3, 1) → R_2
  96. Intersect(f_2, r_2, 1) → S_2
  97. Intersect(f_2, g_2, 2) → T_2
  98. Intersect(g_2, t_2, 2) → U_2
  99. Circle(M_2, Segment[L_2, H_2]) → e_3
  100. Circle(N_2, Segment[G_2, N_2]) → f_3
  101. Circle(L_2, Segment[U_1, T_1]) → g_3
  102. Circle(U_2, Segment[I_2, U_2]) → h_3
  103. Circle(T_2, Segment[E_2, T_2]) → k_3
  104. Circle(S_2, Segment[W_1, S_2]) → p_3
  105. Circle(R_2, Segment[D_2, R_2]) → q_3
  106. Circle(Q_2, Segment[J_2, Q_2]) → r_3
  107. Circle(P_2, Segment[K_2, P_2]) → s_3
  108. Circle(O_2, Segment[Z_1, O_2]) → t_3
  109. Circle(S_1, Segment[T_1, S_1]) → c_4
  110. Intersect(f_2, k_3, 2) → V_2
  111. Circle(V_2, Segment[U_2, T_2]) → d_4
  112. Intersect(s_2, e_3, 2) → W_2
  113. Intersect(t_2, g_3, 2) → Z_2
  114. Intersect(d_3, r_3, 2) → C_3
  115. Intersect(c_3, q_3, 2) → D_3
  116. Circle(W_2, Segment[W_2, L_2]) → e_4
  117. Circle(Z_2, Segment[L_2, Z_2]) → f_4
  118. Circle(D_3, Segment[R_2, D_3]) → g_4
  119. Circle(C_3, Segment[C_3, Q_2]) → h_4