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直圆柱!

直圆柱!
几何画板及绘图内容加载中，请稍等……
2020-08-16 23:23
圆立体几何几何作图
这个范例演示了直圆柱的几何构造。涉及的核心数学概念包括圆、立体几何和几何作图。通过使用GeoGebra命令如Point、Circle、Intersect等，可以构建直圆柱的各个组成部分。适合初中及以上学生或教师使用。

GeoGebra 命令及参数

  1. Point(xAxis) → A
  2. Circle(A, r) → c
  3. Intersect(c, xAxis) → B, C
  4. Ellipse(E, D, C) → e
  5. Intersect(xAxis, yAxis) → F
  6. Vector(F, G) → u
  7. Translate(B, Vector[(u * h)]) → B'_1
  8. Translate(C, Vector[(u * h)]) → C'_1
  9. Translate(A, Vector[(u * h)]) → A'
  10. Translate(e, Vector[(u * h)]) → e'_1
  11. Polygon(B'_1, B, C, C'_1) → poly1, b', b, c_1, c'
  12. Arc(e'_1, C'_1, B'_1) → f
  13. Arc(e, B, C) → g
  14. Arc(e, C, B) → k
  15. Arc(e'_1, C'_1, B'_1) → p_5
  16. Arc(e'_1, B'_1, C'_1) → q
  17. Arc(e, B, C) → s
  18. Segment(A', A) → h_6
  19. Segment(A', C'_1) → p
  20. Angle(A, A', C'_1) → α
  21. Line(A, A') → j
  22. Intersect(e'_1, j) → H, I
  23. Intersect(k, j) → J,
  24. Circle(I, r) → t
  25. Intersect(t, j, 2) → K
  26. Circle(K, I) → d_1
  27. Circle(J, r) → e_1
  28. Intersect(e_1, j, 1) → L
  29. Circle(L, J) → f_1
  30. Intersect(f_1, j, 2) → M
  31. Intersect(d_1, j, 2) → N
  32. Intersect(s, j) → O,
  33. Vector(H, N) → v
  34. Vector(O, M) → w
  35. Translate(H, Vector[(v * n)]) → H'_1
  36. Translate(D, Vector[(u * h)]) → D'
  37. Translate(E, Vector[(u * h)]) → E'
  38. Line(B, B'_1) → l
  39. Line(C, C'_1) → m
  40. Intersect(d_1, l, 1) → P
  41. Intersect(d_1, m, 1) → Q
  42. Vector(B'_1, P) → z
  43. Vector(C'_1, Q) → u_1
  44. Translate(B'_1, Vector[(z * n)]) → B''
  45. Translate(C'_1, Vector[(u_1 * n)]) → C''
  46. Midpoint(B'_1, A') → R
  47. Midpoint(B, A) → S
  48. Line(R, S) → a_1
  49. Intersect(q, a_1) → T,
  50. Intersect(d_1, a_1, 1) → U
  51. Vector(T, U) → v_1
  52. Translate(T, Vector[(v_1 * n)]) → T'
  53. Intersect(f_1, l, 1) → V
  54. Intersect(f_1, m, 1) → W
  55. Intersect(f_1, a_1, 2) → Z
  56. Intersect(s, a_1) → A_1,
  57. Vector(B, V) → w_1
  58. Vector(A_1, Z) → z_1
  59. Vector(C, W) → b_1
  60. Translate(B, Vector[(w_1 * (n - 1))]) → B'
  61. Translate(A_1, Vector[(z_1 * (n - 1))]) → C_1
  62. Translate(O, Vector[(w * (n - 1))]) → O'
  63. Translate(C, Vector[(b_1 * (n - 1))]) → C'
  64. If(n ≟ 0.02, B'_1, If[n < 1, B'', P]) → B_1
  65. If(n ≟ 0.02, T, If[n < 1, T', U]) → D_1
  66. If(n ≟ 0.02, H, If[n < 1, H'_1, N]) → E_1
  67. If(n ≟ 0.02, C'_1, If[n < 1, C'', Q]) → F_1
  68. Conic(B_1, D_1, E_1, F_1, I) → g_1
  69. Conic(I, B_1, D_1, E_1, F_1) → h_1
  70. If(n < 1, B, If[n < 2, B', V]) → G_1
  71. If(n < 1, A_1, If[n < 2, C_1, Z]) → H_1
  72. If(n < 1, O, If[n < 2, O', M]) → I_1
  73. If(n < 1, C, If[n < 2, C', W]) → J_1
  74. Conic(G_1, H_1, I_1, J_1, J) → k_1
  75. Vector(H, O) → i_1
  76. Translate(H, Vector[(i_1 * (n - 2))]) → H'
  77. If(n < 2, H, If[n < 3, H', O]) → K_1
  78. Segment(H, K_1) → j_1
  79. Arc(e, B, C) → q_1
  80. Intersect(g, k_1) → M_1, N_1, R_1, S_1
  81. Arc(k_1, M_1, N_1) → r_1
  82. Arc(k_1, N_1, M_1) → p_1
  83. Arc(e, C, B) → s_1
  84. OrthogonalLine(I, j) → l_1
  85. OrthogonalLine(J, l) → m_1
  86. Circle(I, w_2) → t_1
  87. Intersect(t_1, l_1, 1) → L_1
  88. Intersect(t_1, l_1, 2) → O_1
  89. OrthogonalLine(O_1, l_1) → n_1
  90. OrthogonalLine(L_1, m_1) → a_2
  91. Intersect(m_1, n_1) → P_1
  92. Intersect(m_1, a_2) → Q_1
  93. Circle(H, r) → c_2
  94. Intersect(c_2, j, 2) → T_1
  95. Circle(T_1, H) → d_2
  96. OrthogonalLine(H, j) → b_2
  97. Intersect(d_2, l_1, 1) → U_1
  98. OrthogonalLine(T_1, j) → e_2
  99. Intersect(d_2, e_2, 1) → V_1
  100. Angle(U_1, T_1, V_1) → β
  101. Circle(L_1, r) → f_2
  102. Intersect(f_2, l_1, 2) → W_1
  103. Vector(I, W_1) → u_2
  104. Translate(d_2, Vector[(u_2 * (n - 3))]) → g_2
  105. Center(g_2) → Z_1
  106. Intersect(g_2, b_2) → A_2, B_3
  107. Rotate(A_2, w_3, Z_1) → B_2
  108. If(n < 3, H, If[n < 4, B_2, L_1]) → C_2
  109. Mirror(C_2, j) → D_2
  110. Mirror(E_2, j) → F_2
  111. Midpoint(I, L_1) → G_2
  112. Intersect(m, l_1) → H_2
  113. Midpoint(H_2, C'_1) → I_2
  114. Vector(H_2, G_2) → v_2
  115. OrthogonalLine(C'_1, m) → i_2
  116. Polygon(D_2, F_2, E_2, C_2) → poly2, d_3, f_3, e_3, c_3
  117. Vector(C'_1, W_1) → z_2
  118. Translate(C'_1, Vector[(z_2 * (n - 3))]) → J_2
  119. If(n < 3, C'_1, If[n < 4, J_2, W_1]) → K_2
  120. Mirror(K_2, j) → L_2
  121. Conic(D_2, L_2, I, K_2, C_2) → h_2
  122. Arc(h_2, B_2, D_2) → k_2
  123. Arc(h_2, B_2, D_2) → p_2
  124. Conic(F_2, N_2, J, M_2, E_2) → q_2
  125. Intersect(q_2, k_1) → O_2, P_2, Q_2, R_2
  126. Center(h_2) → S_2
  127. Center(q_2) → T_2
  128. OrthogonalLine(T_2, j) → j_2
  129. OrthogonalLine(S_2, j) → m_2
  130. Intersect(h_2, m_2) → U_2, V_2
  131. Intersect(q_2, j_2) → W_2, Z_2
  132. Polygon(U_2, D_2, F_2, W_2) → poly3, u_3, d_4, f_4, w_5
  133. Polygon(V_2, C_2, E_2, Z_2) → poly4, v_3, c_4, e_4, z_3
  134. Intersect(q_2, d_3, 2) → A_3
  135. Intersect(q_2, e_3, 2) → C_3
  136. Polygon(F_2, A_3, C_3, E_2) → poly5, f_5, a_3, c_5, e_5
  137. Arc(q_2, C_3, A_3) → s_2
  138. Arc(q_2, E_2, F_2) → t_2
  139. Arc(q_2, E_2, F_2) → g_3
  140. Segment(A_3, C_3) → l_2
  141. Intersect(k_1, l_2) → D_3, E_3
  142. Segment(E_3, A_3) → n_2
  143. Segment(D_3, C_3) → b_3
  144. Segment(F_2, E_2) → h_3
  145. Arc(k_1, D_3, E_3) → k_3
  146. Segment(E_3, D_3) → i_3
  147. Segment(D_2, C_2) → j_3
  148. Segment(L_2, K_2) → l_3
  149. Arc(q_2, W_2, F_2) → p_3
  150. Arc(q_2, E_2, Z_2) → q_3
  151. Arc(q_2, E_2, Z_2) → r_3
  152. Arc(q_2, W_2, F_2) → s_3
  153. Intersect(k_1, d_3) → F_3, J_3
  154. Intersect(k_1, e_3) → G_3, K_3
  155. Arc(k_1, G_3, F_3) → t_3
  156. Arc(k_1, F_3, R_2) → g_4
  157. Arc(k_1, O_2, G_3) → h_4
  158. Segment(F_2, E_2) → r_2
  159. Intersect(k_1, r_2) → H_3, I_3
  160. Segment(F_2, I_3) → m_3
  161. Segment(E_2, H_3) → n_3
  162. Arc(q_2, E_2, F_2) → k_4
  163. Arc(k_1, H_3, I_3) → p_4
  164. Segment(I_3, H_3) → a_4
  165. Segment(F_2, E_2) → b_4
  166. Segment(E_2, Z_2) → i_4
  167. Segment(D_2, F_2) → j_4
  168. Segment(C_2, E_2) → l_4
  169. Arc(k_1, N_1, M_1) → q_4
  170. Arc(k_1, N_1, M_1) → r_4
  171. Midpoint(j_4) → L_3
  172. Translate(e, Vector[(u * h)]) → e'
  173. Arc(k_1, M_1, N_1) → s_4
  174. Arc(k_1, R_2, N_1) → t_4
  175. Arc(k_1, R_2, O_2) → d_5
  176. Arc(k_1, P_2, Q_2) → g_5
  177. Center(h_1) → M_3
  178. Segment(M_3, F_1) → a
  179. Midpoint(c_1) → N_3
  180. Point(xAxis) → O_3
  181. Circle(O_3, r) → h_5
  182. Intersect(h_5, xAxis) → P_3, Q_3
  183. Ellipse(R_3, S_3, Q_3) → k_5
  184. OrthogonalLine(S_3, i_2) → i
  185. OrthogonalLine(Q_3, i_2) → m_4
  186. OrthogonalLine(P_3, i_2) → n_4
  187. OrthogonalLine(R_3, i_2) → a_5
  188. Intersect(i_2, a_5) → T_3
  189. Intersect(n_4, i_2) → U_3
  190. Intersect(i, i_2) → V_3
  191. Intersect(m_4, i_2) → W_3
  192. Ellipse(T_3, V_3, W_3) → q_5
  193. Polygon(U_3, W_3, Q_3, P_3) → poly6, u_4, w_6, q_6, p_6
  194. Ellipse(T_3, V_3, W_3) → r_5
  195. Arc(k_5, Q_3, P_3) → s_5
  196. Arc(k_5, P_3, Q_3) → t_5
  197. Center(q_5) → Z_3
  198. Segment(O_3, Z_3) → b_5
  199. Segment(Z_3, W_3) → i_5
  200. Angle(W_3, Z_3, O_3) → γ
  201. Intersect(k_1, f_4) → A_4,
  202. Intersect(k_1, e_4) → B_4,
  203. Intersect(g_3, k_1) → C_4, D_4, E_4, F_4
  204. Polygon(Z_2, C_4, B_4) → poly7, b_6, z_4, c_6
  205. Polygon(F_4, A_4, W_2) → poly8, w_7, f_6, a_6
  206. Arc(q_2, W_2, F_4) → d_6
  207. Arc(q_2, C_4, Z_2) → e_6
  208. Arc(q_2, W_2, F_4) → g_6
  209. Arc(q_2, C_4, Z_2) → k_6
  210. Arc(k_1, G_3, J_3) → r_6
  211. Intersect(k_1, b) → G_4, H_4
  212. Segment(E_3, D_3) → m_5
  213. Segment(H_3, I_3) → n_5
  214. Point(c_3) → J_4
  215. Point(k_2) → K_4
  216. Point(c_3) → N_4
  217. Vector(M_4, N_4) → u_5
  218. Segment(D_2, C_2) → i_6
  219. Intersect(h_1, i_6) → O_4, V_4
  220. If(4 < n ≤ 5, Dilate[O_4, 5 - n, C_2]) → P_4
  221. Vector(O_4, P_4) → v_5
  222. Translate(h_1, v_5) → s_6
  223. Translate(E_1, v_5) → Q_4
  224. Center(s_6) → R_4
  225. Segment(O_4, P_4) → l_6
  226. Segment(O_4, P_4) → m_6
  227. If(4 < n ≤ 5, Rotate[Q_4, ((-(n - 4)) * 180°), R_4]) → S_4
  228. CircleArc(R_4, P_4, S_4) → t_6
  229. Mirror(O_4, j_6) → T_4
  230. Mirror(P_4, j_6) → U_4
  231. Segment(T_4, U_4) → n_6
  232. Mirror(t_6, j_6) → c_7
  233. Segment(D_2, C_2) → a_7
  234. Segment(D_2, C_2) → j_5

AI 绘图提示语参考

绘制一个直圆柱体。先在水平轴上取一点作为底面圆心，以给定半径画圆，圆与轴交于两点。再画一个椭圆作为顶面，并沿竖直方向平移整个底面圆和椭圆，形成柱体。连接底面与顶面的对应点，构成长方形侧面。画出顶面和底面的圆弧，以及连接上下底面的线段。在柱体内部构造若干辅助圆和交点，以展示圆柱的几何性质。最后标出上下底面的中点并连线，作为圆柱的轴。
以上提示语为根据原始绘图命令整理而来，仅供参考。