长方体体积动态演示：改变长宽高观察体积变化

GeoGebra 命令及参数

1. Line(AA, BB) → a
2. OrthogonalLine(CC, a) → b
3. OrthogonalLine(CC, b) → c
4. Circle(CC, l) → d
5. Circle(CC, br) → e
6. Intersect(d, c) → D, E
7. Intersect(e, b) → F, G
8. OrthogonalLine(G, b) → f
9. OrthogonalLine(D, c) → g
10. OrthogonalLine(F, b) → h
11. OrthogonalLine(E, c) → i
12. Intersect(f, i) → H
13. Intersect(g, f) → I
14. Intersect(g, h) → J
15. Intersect(h, i) → K
16. Polygon(H, I, J, K) → mangekant1, h_1, i_1, j, k
17. OrthogonalLine(Rotate, h_1) → m
18. OrthogonalLine(Rotate, k) → n
19. Intersect(h_1, m) → M
20. Intersect(k, n) → N
21. Distance(Rotate, M) → avstandLM
22. Distance(Rotate, N) → avstandLN
23. OrthogonalLine(O, a) → p
24. OrthogonalLine(O, p) → q
25. Circle(O, size) → r
26. Intersect(r, q) → P, Q
27. Intersect(r, p) → R, S
28. OrthogonalLine(S, p) → s
29. OrthogonalLine(P, q) → t
30. OrthogonalLine(R, p) → a_1
31. OrthogonalLine(Q, q) → b_1
32. Intersect(s, b_1) → T
33. Intersect(s, t) → U
34. Intersect(a_1, t) → V
35. Intersect(a_1, b_1) → W
36. Polygon(U, T, W, V) → mangekant2, u, t_1, w, v
37. Rotate(U, ho, O) → U'
38. Rotate(T, ho, O) → T'
39. Rotate(W, ho, O) → W'
40. Rotate(V, ho, O) → V'
41. Polygon(U', T', W', V') → mangekant2', u', t', w', v'
42. OrthogonalLine(T', q) → c_1
43. OrthogonalLine(W', q) → d_1
44. OrthogonalLine(V', q) → e_1
45. OrthogonalLine(U', q) → f_1
46. OrthogonalLine(T', q) → g_1
47. OrthogonalLine(V', q) → j_1
48. OrthogonalLine(U', q) → k_1
49. OrthogonalLine(W', q) → l_1
50. Intersect(g_1, q) → Z
51. Intersect(l_1, q) → A_1
52. Intersect(q, k_1) → B_1
53. Intersect(q, j_1) → C_1
54. Distance(Z, T') → avstandZT'
55. Distance(B_1, U') → avstandB1U'
56. Dilate(T', l1, Z) → T''
57. Dilate(W', l1, A_1) → W''
58. Dilate(U', l1, B_1) → U''
59. Dilate(V', l1, C_1) → V''
60. Polygon(T'', W'', V'', U'') → mangekant3, t'', w'', v'', u''
61. Midpoint(W'', V'') → D_1
62. Midpoint(V'', U'') → E_1
63. Distance(O, D_1) → avstandOD1
64. Distance(O, E_1) → avstandOE1
65. If(((-π < ve) ∧ (ve < (-π) / 2) ∨ (π / 2 < ve) ∧ (ve < π)) ∧ ((-π) / 2 < ho) ∧ (ho < π / 2) ∨ ((-π) / 2 < ve) ∧ (ve < π / 2) ∧ ((-π < ho) ∧ (ho < (-π) / 2) ∨ (π / 2 < ho) ∧ (ho < π)), van / (size - xp) + 3, (-van) / (size - xp) - 3) → ix
66. Dilate(D_1, ix, O) → F_1
67. If((0 < ho) ∧ (ho < π) ∧ ((-π) / 2 < ve) ∧ (ve < π / 2) ∨ (-π < ho) ∧ (ho < 0) ∧ ((-π < ve) ∧ (ve < (-π) / 2) ∨ (π / 2 < ve) ∧ (ve < π)), van / (size - yp) + 3, (-van) / (size - yp) - 3) → iy
68. Dilate(E_1, iy, O) → G_1
69. If((-π < ve) ∧ (ve < (-π) / 2) ∨ (0 < ve) ∧ (ve < π / 2), (-van) / (size - zp) - 3, van / (size - zp) + 3) → iz
70. Circle(O, size) → p_1
71. Circle(O, zp) → q_1
72. Intersect(q_1, p) → J_1, K_1
73. Dilate(K_1, iz, O) → H_1
74. Dilate(D_1, xpos, O) → I_1
75. Dilate(D_1, xneg, O) → L_1
76. Dilate(E_1, ypos, O) → M_1
77. Dilate(E_1, yneg, O) → N_1
78. Line(M_1, F_1) → m_1
79. Line(N_1, F_1) → n_1
80. Line(L_1, G_1) → r_1
81. Line(I_1, G_1) → s_1
82. Intersect(n_1, r_1) → O_1
83. Intersect(m_1, r_1) → P_1
84. Intersect(s_1, m_1) → Q_1
85. Intersect(s_1, n_1) → R_1
86. Polygon(P_1, O_1, R_1, Q_1) → mangekant4, p_2, o_1, r_2, q_2
87. Dilate(K_1, zpos, O) → S_1
88. Dilate(K_1, zneg, O) → T_1
89. Segment(I_1, L_1) → a_2
90. Segment(N_1, M_1) → b_2
91. Line(F_1, S_1) → c_2
92. Line(T_1, F_1) → d_2
93. Line(S_1, G_1) → e_2
94. Line(T_1, G_1) → f_2
95. Line(H_1, N_1) → g_2
96. Line(H_1, I_1) → h_2
97. Line(H_1, L_1) → i_2
98. Line(H_1, M_1) → j_2
99. Intersect(g_2, e_2) → V_1
100. Intersect(g_2, f_2) → W_1
101. Intersect(e_2, j_2) → Z_1
102. Intersect(f_2, j_2) → A_2
103. Line(V_1, F_1) → k_2
104. Line(Z_1, F_1) → l_2
105. Line(W_1, F_1) → m_2
106. Line(A_2, F_1) → n_2
107. Intersect(i_2, c_2) → B_2
108. Intersect(i_2, d_2) → C_2
109. Intersect(c_2, h_2) → D_2
110. Intersect(h_2, d_2) → E_2
111. Line(B_2, G_1) → s_2
112. Line(D_2, G_1) → t_2
113. Line(E_2, G_1) → a_3
114. Line(C_2, G_1) → b_3
115. Intersect(k_2, s_2) → F_2
116. Intersect(s_2, l_2) → G_2
117. Intersect(t_2, l_2) → H_2
118. Intersect(t_2, k_2) → I_2
119. Intersect(m_2, b_3) → J_2
120. Intersect(m_2, a_3) → K_2
121. Intersect(a_3, n_2) → L_2
122. Intersect(n_2, b_3) → M_2
123. Segment(F_2, G_2) → c_3
124. Segment(G_2, H_2) → d_3
125. Segment(H_2, I_2) → e_3
126. Segment(I_2, F_2) → f_3
127. Segment(F_2, J_2) → g_3
128. Segment(I_2, K_2) → h_3
129. Segment(L_2, H_2) → i_3
130. Segment(G_2, M_2) → j_3
131. Segment(M_2, L_2) → k_3
132. Segment(L_2, K_2) → l_3
133. Segment(K_2, J_2) → m_3
134. Segment(J_2, M_2) → n_3
135. Segment(T_1, S_1) → p_3
136. Dilate(I_1, enxm, O) → S_2
137. Line(S_2, G_1) → g_4
138. Intersect(q_2, g_4) → S_3
139. Intersect(o_1, g_4) → P_4
140. Dilate(M_1, enym, O) → N_5
141. Line(N_5, F_1) → h_6
142. Intersect(p_2, h_6) → H_6
143. Intersect(r_2, h_6) → E_7
144. Dilate(I_1, x1, O) → A
145. Dilate(I_1, x1m, O) → B
146. Dilate(M_1, y1, O) → C
147. Dilate(M_1, y1m, O) → L
148. Line(L, F_1) → q_3
149. Line(C, F_1) → r_3
150. Line(B, G_1) → s_3
151. Line(A, G_1) → t_3
152. Intersect(r_3, s_3) → N_2
153. Intersect(q_3, s_3) → O_2
154. Intersect(r_3, t_3) → P_2
155. Intersect(q_3, t_3) → Q_2
156. Polygon(O_2, Q_2, P_2, N_2) → poly1, o_2, q_4, p_4, n_4
157. Dilate(I_1, x3, O) → R_2
158. Dilate(I_1, x2, O) → T_2
159. Dilate(I_1, x3m, O) → U_2
160. Dilate(I_1, x2m, O) → V_2
161. Dilate(M_1, y3, O) → W_2
162. Dilate(M_1, y2, O) → Z_2
163. Dilate(M_1, y3m, O) → A_3
164. Dilate(M_1, y2m, O) → B_3
165. Dilate(S_1, z1, O) → C_3
166. Line(V_2, G_1) → a_4
167. Line(R_2, G_1) → b_4
168. Line(Z_2, F_1) → c_4
169. Line(B_3, F_1) → d_4
170. Intersect(a_4, d_4) → D_3
171. Intersect(c_4, a_4) → E_3
172. Intersect(c_4, b_4) → F_3
173. Intersect(d_4, b_4) → G_3
174. Polygon(D_3, G_3, F_3, E_3) → poly2, d_5, g_5, f_4, e_4
175. Line(H_1, T_2) → h_4
176. Line(H_1, U_2) → i_4
177. Line(H_1, A_3) → j_4
178. Line(H_1, W_2) → k_4
179. Line(C_3, G_1) → l_4
180. Line(T_2, G_1) → m_4
181. Line(U_2, G_1) → r_4
182. Line(A_3, F_1) → s_4
183. Line(W_2, F_1) → t_4
184. Line(C_3, F_1) → a_5
185. Intersect(i_4, a_5) → H_3
186. Intersect(h_4, a_5) → I_3
187. Intersect(j_4, l_4) → J_3
188. Intersect(k_4, l_4) → K_3
189. Intersect(c_4, m_4) → L_3
190. Intersect(m_4, d_4) → M_3
191. Intersect(r_4, c_4) → N_3
192. Intersect(r_4, d_4) → O_3
193. Intersect(s_4, a_4) → P_3
194. Intersect(b_4, s_4) → Q_3
195. Intersect(t_4, b_4) → R_3
196. Intersect(t_4, a_4) → T_3
197. Line(H_1, Q_3) → b_5
198. Line(H_1, P_3) → c_5
199. Line(H_1, R_3) → e_5
200. Line(H_1, T_3) → f_5
201. Line(H_1, M_3) → h_5
202. Line(H_1, L_3) → i_5
203. Line(H_1, O_3) → j_5
204. Line(H_1, N_3) → k_5
205. Line(I_3, G_1) → l_5
206. Line(H_3, G_1) → m_5
207. Line(J_3, F_1) → n_5
208. Line(K_3, F_1) → p_5
209. Intersect(j_5, m_5) → U_3
210. Intersect(k_5, m_5) → V_3
211. Polygon(D_3, U_3, V_3, E_3) → poly3, d_6, u_3, v_3, e_6
212. Intersect(f_5, p_5) → W_3
213. Intersect(e_5, p_5) → Z_3
214. Polygon(E_3, W_3, Z_3, F_3) → poly4, e_7, w_3, z_3, f_6
215. Intersect(c_5, n_5) → A_4
216. Intersect(b_5, n_5) → B_4
217. Polygon(A_4, D_3, G_3, B_4) → poly5, a_6, d_7, g_6, b_6
218. Intersect(i_5, l_5) → C_4
219. Intersect(h_5, l_5) → D_4
220. Polygon(G_3, D_4, C_4, F_3) → poly6, g_7, d_8, c_6, f_7
221. Intersect(a_4, q_3) → E_4
222. Intersect(b_4, q_3) → F_4
223. Intersect(t_3, d_4) → G_4
224. Intersect(t_3, c_4) → H_4
225. Intersect(r_3, b_4) → I_4
226. Intersect(r_3, a_4) → J_4
227. Intersect(d_4, s_3) → K_4
228. Intersect(s_3, c_4) → L_4
229. Polygon(L_4, E_3, J_4, N_2) → poly7, l_6, e_8, j_6, n_6
230. Polygon(E_4, D_3, K_4, O_2) → poly8, e_9, d_9, k_6, o_3
231. Polygon(I_4, F_3, H_4, P_2) → poly9, i_6, f_8, h_7, p_6
232. Polygon(Q_2, G_4, G_3, F_4) → poly10, q_5, g_8, g_9, f_9
233. Segment(O_2, N_2) → r_5
234. Segment(O_2, Q_2) → s_5
235. Segment(Q_2, P_2) → t_5
236. Segment(P_2, N_2) → m_6
237. Segment(L_4, N_2) → q_6
238. Segment(N_2, J_4) → r_6
239. Segment(K_4, O_2) → s_6
240. Segment(O_2, E_4) → t_6
241. Segment(F_4, Q_2) → a_7
242. Segment(Q_2, G_4) → b_7
243. Segment(H_4, P_2) → c_7
244. Segment(P_2, I_4) → i_7
245. Segment(O, C_3) → j_7
246. Segment(D_3, E_3) → k_7
247. Segment(E_3, F_3) → l_7
248. Segment(F_3, G_3) → m_7
249. Segment(G_3, D_3) → n_7
250. Segment(D_3, K_4) → p_7
251. Segment(D_3, E_4) → q_7
252. Segment(G_3, F_4) → r_7
253. Segment(G_3, G_4) → s_7
254. Segment(F_3, H_4) → t_7
255. Segment(F_3, I_4) → a_8
256. Segment(E_3, J_4) → b_8
257. Segment(E_3, L_4) → c_8
258. Dilate(I_1, hei, O) → M_4
259. Dilate(S_1, vol, O) → N_4
260. Line(N_4, F_1) → h_8
261. Line(H_1, M_4) → i_8
262. Intersect(h_8, i_8) → O_4
263. Locus(O_4, height) → loc1
264. Segment(O, S_1) → j_8
265. Segment(O, I_1) → k_8
266. Segment(O_4, N_4) → l_8
267. Segment(O_4, M_4) → m_8
268. Segment(O, M_4) → n_8
269. Segment(T_3, N_2) → p_8
270. Segment(D_3, U_3) → q_8
271. Segment(U_3, V_3) → r_8
272. Segment(V_3, E_3) → s_8
273. Segment(E_3, W_3) → t_8
274. Segment(W_3, Z_3) → a_9
275. Segment(Z_3, F_3) → b_9
276. Segment(C_4, F_3) → c_9
277. Segment(C_4, D_4) → h_9
278. Segment(D_4, G_3) → i_9
279. Segment(G_3, B_4) → j_9
280. Segment(B_4, A_4) → k_9
281. Segment(A_4, D_3) → l_9
282. Polygon(D_3, E_3, F_3, G_3) → poly11, d_{10}, e_{10}, f_{10}, g_{10}