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能级图示

能级图示
几何画板及绘图内容加载中，请稍等……
2017-03-19 09:41
测试改名0向量几何作图
该范例演示了能级图示，涉及相似三角形和几何作图。通过使用GeoGebra命令如Line, Point, OrthogonalLine等，可以构造出能级图示。适合高中物理和数学教学。

GeoGebra 命令及参数

  1. Line(A, xAxis) → f
  2. Point(f) → K
  3. OrthogonalLine(K, f) → f_2
  4. Point(yAxis) → C
  5. Line(C, xAxis) → h
  6. Intersect(h, f_2) → O_1
  7. Segment(C, O_1) → i_2
  8. If(levelnumber > 3, 1, 0) → testlevel4
  9. If(levelnumber > 5, 1, 0) → testlevel6
  10. If(levelnumber > 4, 1, 0) → testlevel5
  11. Point(yAxis) → B
  12. Point(yAxis) → D
  13. Point(yAxis) → E
  14. Segment(A, K) → g_2
  15. Point(g_2) → G
  16. OrthogonalLine(G, f) → l
  17. Point(l) → endA1
  18. Point(yAxis) → F
  19. Line(F, xAxis) → k
  20. Intersect(k, f_2) → S_2
  21. Segment(F, S_2) → l_2
  22. Line(E, xAxis) → j
  23. Intersect(j, f_2) → Q_1
  24. Segment(E, Q_1) → k_2
  25. Line(D, xAxis) → i
  26. Intersect(i, f_2) → P_1
  27. Segment(D, P_1) → j_2
  28. Line(B, xAxis) → g
  29. Intersect(g, f_2) → N_1
  30. Segment(B, N_1) → h_2
  31. Point(i_2) → S
  32. Point(h_2) → O
  33. OrthogonalLine(O, g) → b
  34. Point(b) → endB2
  35. Point(h_2) → N
  36. OrthogonalLine(N, g) → a
  37. Point(a) → endB1
  38. Point(i_2) → T
  39. OrthogonalLine(S, h) → e
  40. Point(e) → endC3
  41. Vector(O, endB2) → B2
  42. OrthogonalLine(T, h) → f_1
  43. Point(f_1) → endC2
  44. Vector(N, endB1) → B1
  45. Point(i_2) → R
  46. OrthogonalLine(R, h) → d
  47. Point(d) → endC1
  48. Vector(R, endC1) → C1
  49. Point(g_2) → J
  50. OrthogonalLine(J, f) → p
  51. Point(g_2) → I
  52. OrthogonalLine(I, f) → n
  53. Point(g_2) → H_3
  54. OrthogonalLine(H_3, f) → m
  55. Vector(G, endA1) → A1
  56. Point(m) → endA4
  57. Vector(H_3, endA4) → A4
  58. Point(n) → endA5
  59. Vector(I, endA5) → A5
  60. Point(p) → endA2
  61. Vector(J, endA2) → A2
  62. Point(g_2) → P
  63. OrthogonalLine(P, f) → q
  64. Point(q) → endA3
  65. Vector(P, endA3) → A3
  66. If(490 < w < 510, (-((w - 510) / 20)), If[380 < w < 491, 1, 0]) → BCoeff
  67. If(440 < w < 490, (w - 440) / 50, If[580 < w < 645, (-((w - 645) / 65)), If[489 < w < 581, 1, 0]]) → GCoeff
  68. If(380 < w < 440, (w - 440) / 60, If[510 < w < 580, (w - 510) / 70, If[579 < w < 780, 1, 0]]) → RCoeff
  69. Point(h_2) → M
  70. Point(h_2) → Q
  71. Point(h_2) → L
  72. OrthogonalLine(L, g) → s
  73. OrthogonalLine(M, g) → t
  74. OrthogonalLine(Q, g) → c
  75. Point(s) → endB3
  76. Point(t) → endB5
  77. Point(c) → endB4
  78. Vector(L, endB3) → B3
  79. Vector(M, endB5) → B5
  80. Vector(T, endC2) → C2
  81. Vector(S, endC3) → C3
  82. Vector(Q, endB4) → B4
  83. If(abs(y(endA2) - y(B)) < r, testlevel6, If[abs(y(endA2) - y(C)) < r, testlevel5, If[abs(y(endA2) - y(D)) < r, testlevel4, If[abs(y(endA2) - y(E)) < r, 1, If[abs(y(endA2) - y(F)) < r, 1, 0]]]]) → testA2
  84. If(abs(y(endA3) - y(B)) < r, testlevel6, If[abs(y(endA3) - y(C)) < r, testlevel5, If[abs(y(endA3) - y(D)) < r, testlevel4, If[abs(y(endA3) - y(E)) < r, 1, If[abs(y(endA3) - y(F)) < r, 1, 0]]]]) → testA3
  85. If(abs(y(endA4) - y(B)) < r, testlevel6, If[abs(y(endA4) - y(C)) < r, testlevel5, If[abs(y(endA4) - y(D)) < r, testlevel4, If[abs(y(endA4) - y(E)) < r, 1, If[abs(y(endA4) - y(F)) < r, 1, 0]]]]) → testA4
  86. If(abs(y(endA5) - y(B)) < r, testlevel6, If[abs(y(endA5) - y(C)) < r, testlevel5, If[abs(y(endA5) - y(D)) < r, testlevel4, If[abs(y(endA5) - y(E)) < r, 1, If[abs(y(endA5) - y(F)) < r, 1, 0]]]]) → testA5
  87. If(abs(y(endB2) - y(A)) < r, 1, If[abs(y(endB2) - y(C)) < r, testlevel5, If[abs(y(endB2) - y(D)) < r, testlevel4, If[abs(y(endB2) - y(E)) < r, 1, If[abs(y(endB2) - y(F)) < r, 1, 0]]]]) → testB2
  88. If(abs(y(endB1) - y(A)) < r, 1, If[abs(y(endB1) - y(C)) < r, testlevel5, If[abs(y(endB1) - y(D)) < r, testlevel4, If[abs(y(endB1) - y(E)) < r, 1, If[abs(y(endB1) - y(F)) < r, 1, 0]]]]) → testB1
  89. If(abs(y(endB3) - y(A)) < r, 1, If[abs(y(endB3) - y(C)) < r, testlevel5, If[abs(y(endB3) - y(D)) < r, testlevel4, If[abs(y(endB3) - y(E)) < r, 1, If[abs(y(endB3) - y(F)) < r, 1, 0]]]]) → testB3
  90. If(abs(y(endB5) - y(A)) < r, 1, If[abs(y(endB5) - y(C)) < r, testlevel5, If[abs(y(endB5) - y(D)) < r, testlevel4, If[abs(y(endB5) - y(E)) < r, 1, If[abs(y(endB5) - y(F)) < r, 1, 0]]]]) → testB5
  91. If(abs(y(endB4) - y(A)) < r, 1, If[abs(y(endB4) - y(C)) < r, testlevel5, If[abs(y(endB4) - y(D)) < r, testlevel4, If[abs(y(endB4) - y(E)) < r, 1, If[abs(y(endB4) - y(F)) < r, 1, 0]]]]) → testB4
  92. Point(i_2) → U
  93. Point(i_2) → V
  94. Point(j_2) → W
  95. Point(j_2) → Z
  96. Point(j_2) → A_1
  97. Point(j_2) → B_1
  98. Point(k_2) → E_1
  99. Point(k_2) → F_1
  100. Point(k_2) → G_1
  101. Point(k_2) → H_1
  102. Point(l_2) → I_1
  103. Point(l_2) → K_1
  104. Point(l_2) → L_1
  105. Point(l_2) → M_1
  106. OrthogonalLine(U, h) → g_1
  107. OrthogonalLine(V, h) → h_1
  108. Point(j_2) → C_1
  109. OrthogonalLine(C_1, i) → i_1
  110. OrthogonalLine(B_1, i) → j_1
  111. OrthogonalLine(A_1, i) → k_1
  112. OrthogonalLine(Z, i) → l_1
  113. OrthogonalLine(W, i) → m_1
  114. Point(k_2) → D_1
  115. OrthogonalLine(D_1, j) → n_1
  116. OrthogonalLine(E_1, j) → p_1
  117. OrthogonalLine(F_1, j) → q_1
  118. OrthogonalLine(G_1, j) → r_1
  119. OrthogonalLine(H_1, j) → s_1
  120. OrthogonalLine(M_1, k) → t_1
  121. OrthogonalLine(L_1, k) → a_1
  122. OrthogonalLine(K_1, k) → b_1
  123. Point(l_2) → J_1
  124. OrthogonalLine(J_1, k) → c_1
  125. OrthogonalLine(I_1, k) → d_1
  126. Point(h_1) → endC5
  127. Point(g_1) → endC4
  128. Vector(U, endC4) → C4
  129. Vector(V, endC5) → C5
  130. Point(m_1) → endD1
  131. Point(l_1) → endD3
  132. Point(k_1) → endD2
  133. Point(j_1) → endD4
  134. Point(i_1) → endD5
  135. Vector(W, endD1) → D1
  136. Vector(Z, endD3) → D3
  137. Vector(A_1, endD2) → D2
  138. Vector(B_1, endD4) → D4
  139. Vector(C_1, endD5) → D5
  140. Point(n_1) → endE2
  141. Point(p_1) → endE3
  142. Point(q_1) → endE4
  143. Point(r_1) → endE5
  144. Point(s_1) → endE1
  145. Point(t_1) → endF4
  146. Point(a_1) → endF2
  147. Point(b_1) → endF3
  148. Point(c_1) → endF1
  149. Point(d_1) → endF5
  150. Vector(J_1, endF1) → F1
  151. Vector(K_1, endF3) → F3
  152. Vector(L_1, endF2) → F2
  153. Vector(M_1, endF4) → F4
  154. Vector(I_1, endF5) → F5
  155. Vector(D_1, endE2) → E2
  156. Vector(E_1, endE3) → E3
  157. Vector(F_1, endE4) → E4
  158. Vector(G_1, endE5) → E5
  159. Vector(H_1, endE1) → E1
  160. If(abs(y(endC5) - y(A)) < r, 1, If[abs(y(endC5) - y(B)) < r, testlevel6, If[abs(y(endC5) - y(D)) < r, testlevel4, If[abs(y(endC5) - y(E)) < r, 1, If[abs(y(endC5) - y(F)) < r, 1, 0]]]]) → testC5
  161. If(abs(y(endC4) - y(A)) < r, 1, If[abs(y(endC4) - y(B)) < r, testlevel6, If[abs(y(endC4) - y(D)) < r, testlevel4, If[abs(y(endC4) - y(E)) < r, 1, If[abs(y(endC4) - y(F)) < r, 1, 0]]]]) → testC4
  162. If(abs(y(endC3) - y(A)) < r, 1, If[abs(y(endC3) - y(B)) < r, testlevel6, If[abs(y(endC3) - y(D)) < r, testlevel4, If[abs(y(endC3) - y(E)) < r, 1, If[abs(y(endC3) - y(F)) < r, 1, 0]]]]) → testC3
  163. If(abs(y(endC2) - y(A)) < r, 1, If[abs(y(endC2) - y(B)) < r, testlevel6, If[abs(y(endC2) - y(D)) < r, testlevel4, If[abs(y(endC2) - y(E)) < r, 1, If[abs(y(endC2) - y(F)) < r, 1, 0]]]]) → testC2
  164. If(abs(y(endC1) - y(A)) < r, 1, If[abs(y(endC1) - y(B)) < r, testlevel6, If[abs(y(endC1) - y(D)) < r, testlevel4, If[abs(y(endC1) - y(E)) < r, 1, If[abs(y(endC1) - y(F)) < r, 1, 0]]]]) → testC1
  165. If(abs(y(endD1) - y(A)) < r, 1, If[abs(y(endD1) - y(B)) < r, testlevel6, If[abs(y(endD1) - y(C)) < r, testlevel5, If[abs(y(endD1) - y(E)) < r, 1, If[abs(y(endD1) - y(F)) < r, 1, 0]]]]) → testD1
  166. If(abs(y(endD2) - y(A)) < r, 1, If[abs(y(endD2) - y(B)) < r, testlevel6, If[abs(y(endD2) - y(C)) < r, testlevel5, If[abs(y(endD2) - y(E)) < r, 1, If[abs(y(endD2) - y(F)) < r, 1, 0]]]]) → testD2
  167. If(abs(y(endD3) - y(A)) < r, 1, If[abs(y(endD3) - y(B)) < r, testlevel6, If[abs(y(endD3) - y(C)) < r, testlevel5, If[abs(y(endD3) - y(E)) < r, 1, If[abs(y(endD3) - y(F)) < r, 1, 0]]]]) → testD3
  168. If(abs(y(endD4) - y(A)) < r, 1, If[abs(y(endD4) - y(B)) < r, testlevel6, If[abs(y(endD4) - y(C)) < r, testlevel5, If[abs(y(endD4) - y(E)) < r, 1, If[abs(y(endD4) - y(F)) < r, 1, 0]]]]) → testD4
  169. If(abs(y(endD5) - y(A)) < r, 1, If[abs(y(endD5) - y(B)) < r, testlevel6, If[abs(y(endD5) - y(C)) < r, testlevel5, If[abs(y(endD5) - y(E)) < r, 1, If[abs(y(endD5) - y(F)) < r, 1, 0]]]]) → testD5
  170. If(abs(y(endE5) - y(A)) < r, 1, If[abs(y(endE5) - y(B)) < r, testlevel6, If[abs(y(endE5) - y(C)) < r, testlevel5, If[abs(y(endE5) - y(D)) < r, testlevel4, If[abs(y(endE5) - y(F)) < r, 1, 0]]]]) → testE5
  171. If(abs(y(endE1) - y(A)) < r, 1, If[abs(y(endE1) - y(B)) < r, testlevel6, If[abs(y(endE1) - y(C)) < r, testlevel5, If[abs(y(endE1) - y(D)) < r, testlevel4, If[abs(y(endE1) - y(F)) < r, 1, 0]]]]) → testE1
  172. If(abs(y(endE2) - y(A)) < r, 1, If[abs(y(endE2) - y(B)) < r, testlevel6, If[abs(y(endE2) - y(C)) < r, testlevel5, If[abs(y(endE2) - y(D)) < r, testlevel4, If[abs(y(endE2) - y(F)) < r, 1, 0]]]]) → testE2
  173. If(abs(y(endE3) - y(A)) < r, 1, If[abs(y(endE3) - y(B)) < r, testlevel6, If[abs(y(endE3) - y(C)) < r, testlevel5, If[abs(y(endE3) - y(D)) < r, testlevel4, If[abs(y(endE3) - y(F)) < r, 1, 0]]]]) → testE3
  174. If(abs(y(endE4) - y(A)) < r, 1, If[abs(y(endE4) - y(B)) < r, testlevel6, If[abs(y(endE4) - y(C)) < r, testlevel5, If[abs(y(endE4) - y(D)) < r, testlevel4, If[abs(y(endE4) - y(F)) < r, 1, 0]]]]) → testE4
  175. If(abs(y(endF5) - y(A)) < r, 1, If[abs(y(endF5) - y(B)) < r, testlevel6, If[abs(y(endF5) - y(C)) < r, testlevel5, If[abs(y(endF5) - y(D)) < r, testlevel4, If[abs(y(endF5) - y(E)) < r, 1, 0]]]]) → testF5
  176. If(abs(y(endF1) - y(A)) < r, 1, If[abs(y(endF1) - y(B)) < r, testlevel6, If[abs(y(endF1) - y(C)) < r, testlevel5, If[abs(y(endF1) - y(D)) < r, testlevel4, If[abs(y(endF1) - y(E)) < r, 1, 0]]]]) → testF1
  177. If(abs(y(endF2) - y(A)) < r, 1, If[abs(y(endF2) - y(B)) < r, testlevel6, If[abs(y(endF2) - y(C)) < r, testlevel5, If[abs(y(endF2) - y(D)) < r, testlevel4, If[abs(y(endF2) - y(E)) < r, 1, 0]]]]) → testF2
  178. If(abs(y(endF3) - y(A)) < r, 1, If[abs(y(endF3) - y(B)) < r, testlevel6, If[abs(y(endF3) - y(C)) < r, testlevel5, If[abs(y(endF3) - y(D)) < r, testlevel4, If[abs(y(endF3) - y(E)) < r, 1, 0]]]]) → testF3
  179. If(abs(y(endF4) - y(A)) < r, 1, If[abs(y(endF4) - y(B)) < r, testlevel6, If[abs(y(endF4) - y(C)) < r, testlevel5, If[abs(y(endF4) - y(D)) < r, testlevel4, If[abs(y(endF4) - y(E)) < r, 1, 0]]]]) → testF4
  180. If(o > 0, 1, 0) → u
  181. If(abs(y(endA1) - y(B)) < r, testlevel6, If[abs(y(endA1) - y(C)) < r, testlevel5, If[abs(y(endA1) - y(D)) < r, testlevel4, If[abs(y(endA1) - y(E)) < r, 1, If[abs(y(endA1) - y(F)) < r, 1, 0]]]]) → testA1
  182. Point(g_2) → R_1
  183. Point(g_2) → S_1
  184. Point(g_2) → T_1
  185. Point(g_2) → U_1
  186. Point(g_2) → V_1
  187. Point(h_2) → W_1
  188. Point(h_2) → Z_1
  189. Point(h_2) → A_2
  190. Point(h_2) → B_2
  191. Point(i_2) → C_2
  192. Point(i_2) → D_2
  193. Point(i_2) → E_2
  194. Point(j_2) → F_2
  195. Point(j_2) → G_2
  196. Point(k_2) → H_2
  197. OrthogonalLine(R_1, g_2) → m_2
  198. OrthogonalLine(S_1, g_2) → n_2
  199. OrthogonalLine(T_1, g_2) → p_2
  200. OrthogonalLine(U_1, g_2) → q_2
  201. OrthogonalLine(V_1, g_2) → r_2
  202. OrthogonalLine(W_1, h_2) → s_2
  203. OrthogonalLine(Z_1, h_2) → t_2
  204. OrthogonalLine(A_2, h_2) → a_2
  205. OrthogonalLine(B_2, h_2) → b_2
  206. OrthogonalLine(C_2, i_2) → c_2
  207. OrthogonalLine(D_2, i_2) → d_2
  208. OrthogonalLine(E_2, i_2) → e_2
  209. OrthogonalLine(F_2, j_2) → f_3
  210. OrthogonalLine(G_2, j_2) → g_3
  211. OrthogonalLine(H_2, k_2) → h_3
  212. Intersect(m_2, h_2) → endG1
  213. Intersect(n_2, i_2) → endG2
  214. Intersect(p_2, j_2) → endG3
  215. Intersect(q_2, k_2) → endG4
  216. Intersect(r_2, l_2) → endG5
  217. Intersect(s_2, i_2) → endH1
  218. Intersect(t_2, j_2) → endH2
  219. Intersect(a_2, k_2) → endH3
  220. Intersect(b_2, l_2) → endH4
  221. Intersect(c_2, j_2) → endI1
  222. Intersect(d_2, k_2) → endI2
  223. Intersect(e_2, l_2) → endI3
  224. Intersect(f_3, k_2) → endJ1
  225. Intersect(g_3, l_2) → endJ2
  226. Intersect(h_3, l_2) → endK1
  227. Vector(R_1, endG1) → G1
  228. Vector(S_1, endG2) → G2
  229. Vector(T_1, endG3) → G3
  230. Vector(U_1, endG4) → G4
  231. Vector(V_1, endG5) → G5
  232. Vector(W_1, endH1) → H1
  233. Vector(Z_1, endH2) → H2
  234. Vector(A_2, endH3) → H3
  235. Vector(B_2, endH4) → H4
  236. Vector(C_2, endI1) → I1
  237. Vector(D_2, endI2) → I2
  238. Vector(E_2, endI3) → I3
  239. Vector(F_2, endJ1) → J1
  240. Vector(G_2, endJ2) → J2
  241. Vector(H_2, endK1) → K1
  242. Length(G1) → EG1
  243. Length(G2) → EG2
  244. Length(G3) → EG3
  245. Length(G5) → EG5
  246. Length(H1) → EH1
  247. Length(H2) → EH2
  248. Length(H3) → EH3
  249. Length(H4) → EH4
  250. Length(I1) → EI1
  251. Length(I2) → EI2
  252. Length(I3) → EI3
  253. Length(J1) → EJ1
  254. Length(J2) → EJ2
  255. Length(K1) → EK1
  256. Length(G4) → EG4