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圆柱的表面积展开图

圆柱的表面积展开图
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2021-11-06 00:55
立体几何几何作图滑块动画
所属专题 Visual Geometry for Grade 9
这个范例演示了圆柱的展开图。核心数学概念包括立体几何和几何作图。通过使用GeoGebra命令如Point, Circle, Intersect, Polygon等，可以构造出圆柱的展开图。适合初中及以上学生学习立体几何。

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, 2.0) → K
  26. Circle(K, I) → d_1
  27. Circle(J, r) → e_1
  28. Intersect(e_1, j, 1.0) → L
  29. Circle(L, J) → f_1
  30. Intersect(f_1, j, 2.0) → M
  31. Intersect(d_1, j, 2.0) → 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, 1.0) → P
  41. Intersect(d_1, m, 1.0) → 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, 1.0) → U
  51. Vector(T, U) → v_1
  52. Translate(T, Vector[v_1 * n]) → T'
  53. Intersect(f_1, l, 1.0) → V
  54. Intersect(f_1, m, 1.0) → W
  55. Intersect(f_1, a_1, 2.0) → 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 - 1.0)]) → B'
  61. Translate(A_1, Vector[z_1 * (n - 1.0)]) → C_1
  62. Translate(O, Vector[w * (n - 1.0)]) → O'
  63. Translate(C, Vector[b_1 * (n - 1.0)]) → C'
  64. If(n < 1.0, B'', P) → B_1
  65. If(n < 1.0, T', U) → D_1
  66. If(n < 1.0, H'_1, N) → E_1
  67. If(n < 1.0, 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 < 1.0, B, If[n < 2.0, B', V]) → G_1
  71. If(n < 1.0, A_1, If[n < 2.0, C_1, Z]) → H_1
  72. If(n < 1.0, O, If[n < 2.0, O', M]) → I_1
  73. If(n < 1.0, C, If[n < 2.0, 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 - 2.0)]) → H'
  77. If(n < 2.0, H, If[n < 3.0, 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, 1.0) → L_1
  88. Intersect(t_1, l_1, 2.0) → 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, 2.0) → T_1
  95. Circle(T_1, H) → d_2
  96. OrthogonalLine(H, j) → b_2
  97. Intersect(d_2, l_1, 1.0) → U_1
  98. OrthogonalLine(T_1, j) → e_2
  99. Intersect(d_2, e_2, 1.0) → V_1
  100. Angle(U_1, T_1, V_1) → β
  101. Circle(L_1, r) → f_2
  102. Intersect(f_2, l_1, 2.0) → W_1
  103. Vector(I, W_1) → u_2
  104. Translate(d_2, Vector[u_2 * (n - 3.0)]) → 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 < 3.0, H, If[n < 4.0, 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 - 3.0)]) → J_2
  119. If(n < 3.0, C'_1, If[n < 4.0, 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, 2.0) → A_3
  135. Intersect(q_2, e_3, 2.0) → 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(N_2, H_4) → j_5
  213. Segment(M_2, G_4) → l_5
  214. Segment(E_3, D_3) → m_5
  215. Segment(H_3, I_3) → n_5

AI 绘图提示语参考

画一个圆柱体的展开图，包含一个矩形和两个圆形，矩形的一边与圆形相接，展示圆柱体的侧面和上下底面。使用滑块调整圆柱体的高度和半径，动态展示展开图的变化。首先画出底面的圆形，然后画出与圆形相接的矩形，最后连接矩形的对边形成侧面。
以上提示语为根据原始绘图命令整理而来，仅供参考。