圆柱体展开图与表面积计算

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