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对数/黄金多边形螺旋

对数/黄金多边形螺旋
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2020-06-13 21:09
多边形函数三角函数变换几何作图
这个范例展示了对数/黄金比例多边形螺旋的构造。它涉及对数增长、黄金比例和多边形的概念。通过旋转、交点、条件语句等命令，构造了多个多边形，展示了螺旋的生成过程。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. Rotate(A, α, P1) → P1'
  2. Line(P1, P1') → rt0
  3. Line(P0, A) → rp0
  4. Rotate(A, θ, P0) → A1
  5. Line(P0, A1) → rp1
  6. Intersect(rt0, rp1) → W1
  7. If(x(W1) ≥ 0, 1, 2) → INT1
  8. Circle(P0, W1) → c0
  9. Rotate(A, (2 * θ), P0) → A2
  10. Rotate(A, (3 * θ), P0) → A3
  11. Rotate(A, (4 * θ), P0) → A4
  12. Rotate(A, (5 * θ), P0) → A5
  13. Rotate(A, (6 * θ), P0) → A6
  14. Rotate(A, (7 * θ), P0) → A7
  15. Rotate(A, (8 * θ), P0) → A8
  16. Rotate(A, (9 * θ), P0) → A9
  17. Rotate(A, (10 * θ), P0) → A10
  18. Rotate(A, (11 * θ), P0) → A11
  19. Rotate(A, (12 * θ), P0) → A12
  20. Rotate(A, (13 * θ), P0) → A13
  21. Rotate(A, (14 * θ), P0) → A14
  22. Rotate(A, (15 * θ), P0) → A15
  23. Rotate(A, (16 * θ), P0) → A16
  24. Rotate(A, (17 * θ), P0) → A17
  25. Rotate(A, (18 * θ), P0) → A18
  26. Rotate(A, (19 * θ), P0) → A19
  27. Rotate(A, (20 * θ), P0) → A20
  28. Rotate(A, (21 * θ), P0) → A21
  29. Rotate(A, (22 * θ), P0) → A22
  30. Rotate(A, (23 * θ), P0) → A23
  31. Rotate(A, (24 * θ), P0) → A24
  32. Rotate(A, (25 * θ), P0) → A25
  33. Rotate(A, (26 * θ), P0) → A26
  34. Rotate(A, (27 * θ), P0) → A27
  35. Rotate(A, (28 * θ), P0) → A28
  36. Rotate(A, (29 * θ), P0) → A29
  37. Rotate(A, (30 * θ), P0) → A30
  38. Rotate(A, (31 * θ), P0) → A31
  39. Rotate(A, (32 * θ), P0) → A32
  40. Rotate(A, (33 * θ), P0) → A33
  41. Rotate(A, (34 * θ), P0) → A34
  42. Rotate(A, (35 * θ), P0) → A35
  43. Rotate(A, (36 * θ), P0) → A36
  44. Line(P0, A14) → rp14
  45. Line(P0, A33) → rp33
  46. Line(P0, A15) → rp15
  47. Line(P0, A34) → rp34
  48. Line(P0, A16) → rp16
  49. Line(P0, A35) → rp35
  50. Line(P0, A17) → rp17
  51. Line(P0, A36) → rp36
  52. Line(P0, A18) → rp18
  53. Line(P0, A19) → rp19
  54. Line(P0, A20) → rp20
  55. Line(P0, A2) → rp2
  56. Line(P0, A21) → rp21
  57. Line(P0, A3) → rp3
  58. Line(P0, A22) → rp22
  59. Line(P0, A4) → rp4
  60. Line(P0, A23) → rp23
  61. Line(P0, A5) → rp5
  62. Line(P0, A24) → rp24
  63. Line(P0, A6) → rp6
  64. Line(P0, A25) → rp25
  65. Line(P0, A7) → rp7
  66. Line(P0, A26) → rp26
  67. Line(P0, A8) → rp8
  68. Line(P0, A27) → rp27
  69. Line(P0, A9) → rp9
  70. Line(P0, A28) → rp28
  71. Line(P0, A10) → rp10
  72. Line(P0, A29) → rp29
  73. Line(P0, A11) → rp11
  74. Line(P0, A30) → rp30
  75. Line(P0, A12) → rp12
  76. Line(P0, A31) → rp31
  77. Line(P0, A13) → rp13
  78. Line(P0, A32) → rp32
  79. Intersect(c0, rp0, 1) → B1
  80. Line(B1, rt0) → rt1
  81. Intersect(rt1, rp1) → F1
  82. Circle(P0, F1) → c1
  83. Intersect(c1, rp0, 1) → B2
  84. Line(B2, rt0) → rt2
  85. Intersect(rt2, rp1) → F2
  86. Intersect(c1, rp2, 1) → W2
  87. Circle(P0, F2) → c2
  88. Intersect(c2, rp0, 1) → B3
  89. Line(B3, rt0) → rt3
  90. Intersect(rt3, rp1) → F3
  91. Circle(P0, F3) → c3
  92. Intersect(c3, rp0, 1) → B4
  93. Line(B4, rt0) → rt4
  94. Intersect(rt4, rp1) → F4
  95. Circle(P0, F4) → c4
  96. Intersect(c4, rp0, 1) → B5
  97. Line(B5, rt0) → rt5
  98. Intersect(rt5, rp1) → F5
  99. Circle(P0, F5) → c5
  100. Intersect(c5, rp0, 1) → B6
  101. Line(B6, rt0) → rt6
  102. Intersect(rt6, rp1) → F6
  103. Circle(P0, F6) → c6
  104. Intersect(c6, rp0, 1) → B7
  105. Line(B7, rt0) → rt7
  106. Intersect(rt7, rp1) → F7
  107. Circle(P0, F7) → c7
  108. Intersect(c7, rp0, 1) → B8
  109. Line(B8, rt0) → rt8
  110. Intersect(rt8, rp1) → F8
  111. Circle(P0, F8) → c8
  112. Intersect(c8, rp0, 1) → B9
  113. Line(B9, rt0) → rt9
  114. Intersect(rt9, rp1) → F9
  115. Circle(P0, F9) → c9
  116. Intersect(c9, rp0, 1) → B10
  117. Line(B10, rt0) → rt10
  118. Intersect(rt10, rp1) → F10
  119. Circle(P0, F10) → c10
  120. Intersect(c10, rp0, 1) → B11
  121. Line(B11, rt0) → rt11
  122. Intersect(rt11, rp1) → F11
  123. Circle(P0, F11) → c11
  124. Intersect(c11, rp0, 1) → B12
  125. Line(B12, rt0) → rt12
  126. Intersect(rt12, rp1) → F12
  127. Circle(P0, F12) → c12
  128. Intersect(c12, rp0, 1) → B13
  129. Line(B13, rt0) → rt13
  130. Intersect(rt13, rp1) → F13
  131. Circle(P0, F13) → c13
  132. Intersect(c13, rp0, 1) → B14
  133. Line(B14, rt0) → rt14
  134. Intersect(rt14, rp1) → F14
  135. Circle(P0, F14) → c14
  136. Intersect(c14, rp0, 1) → B15
  137. Line(B15, rt0) → rt15
  138. Intersect(rt15, rp1) → F15
  139. Circle(P0, F15) → c15
  140. Intersect(c15, rp0, 1) → B16
  141. Line(B16, rt0) → rt16
  142. Intersect(rt16, rp1) → F16
  143. Circle(P0, F16) → c16
  144. Intersect(c16, rp0, 1) → B17
  145. Line(B17, rt0) → rt17
  146. Intersect(rt17, rp1) → F17
  147. Circle(P0, F17) → c17
  148. Intersect(c17, rp0, 1) → B18
  149. Line(B18, rt0) → rt18
  150. Intersect(rt18, rp1) → F18
  151. Circle(P0, F18) → c18
  152. Intersect(c18, rp0, 1) → B19
  153. Line(B19, rt0) → rt19
  154. Intersect(rt19, rp1) → F19
  155. Circle(P0, F19) → c19
  156. Intersect(c19, rp0, 1) → B20
  157. Line(B20, rt0) → rt20
  158. Intersect(rt20, rp1) → F20
  159. Circle(P0, F20) → c20
  160. Intersect(c20, rp0, 1) → B21
  161. Line(B21, rt0) → rt21
  162. Intersect(rt21, rp1) → F21
  163. Circle(P0, F21) → c21
  164. Intersect(c21, rp0, 1) → B22
  165. Line(B22, rt0) → rt22
  166. Intersect(rt22, rp1) → F22
  167. Circle(P0, F22) → c22
  168. Intersect(c22, rp0, 1) → B23
  169. Line(B23, rt0) → rt23
  170. Intersect(rt23, rp1) → F23
  171. Circle(P0, F23) → c23
  172. Intersect(c23, rp0, 1) → B24
  173. Line(B24, rt0) → rt24
  174. Intersect(rt24, rp1) → F24
  175. Circle(P0, F24) → c24
  176. Intersect(c24, rp0, 1) → B25
  177. Line(B25, rt0) → rt25
  178. Intersect(rt25, rp1) → F25
  179. Circle(P0, F25) → c25
  180. Intersect(c25, rp0, 1) → B26
  181. Line(B26, rt0) → rt26
  182. Intersect(rt26, rp1) → F26
  183. Circle(P0, F26) → c26
  184. Intersect(c26, rp0, 1) → B27
  185. Line(B27, rt0) → rt27
  186. Intersect(rt27, rp1) → F27
  187. Circle(P0, F27) → c27
  188. Intersect(c27, rp0, 1) → B28
  189. Line(B28, rt0) → rt28
  190. Intersect(rt28, rp1) → F28
  191. Circle(P0, F28) → c28
  192. Intersect(c28, rp0, 1) → B29
  193. Line(B29, rt0) → rt29
  194. Intersect(rt29, rp1) → F29
  195. Circle(P0, F29) → c29
  196. Intersect(c29, rp0, 1) → B30
  197. Line(B30, rt0) → rt30
  198. Intersect(rt30, rp1) → F30
  199. Circle(P0, F30) → c30
  200. Intersect(c30, rp0, 1) → B31
  201. Line(B31, rt0) → rt31
  202. Intersect(rt31, rp1) → F31
  203. Circle(P0, F31) → c31
  204. Intersect(c31, rp0, 1) → B32
  205. Line(B32, rt0) → rt32
  206. Intersect(rt32, rp1) → F32
  207. Circle(P0, F32) → c32
  208. Intersect(c32, rp0, 1) → B33
  209. Line(B33, rt0) → rt33
  210. Intersect(rt33, rp1) → F33
  211. Circle(P0, F33) → c33
  212. Intersect(c33, rp0, 1) → B34
  213. Line(B34, rt0) → rt34
  214. Intersect(rt34, rp1) → F34
  215. Circle(P0, F34) → c34
  216. Intersect(c34, rp0, 1) → B35
  217. Line(B35, rt0) → rt35
  218. Intersect(rt35, rp1) → F35
  219. Circle(P0, F35) → c35
  220. Intersect(c2, rp3, 1) → W3
  221. Intersect(c3, rp4, 1) → W4
  222. Intersect(c4, rp5, 1) → W5
  223. Intersect(c5, rp6, 1) → W6
  224. Intersect(c6, rp7, 1) → W7
  225. Intersect(c7, rp8, 1) → W8
  226. Intersect(c8, rp9, 1) → W9
  227. Intersect(c9, rp10, 1) → W10
  228. Intersect(c10, rp11, 1) → W11
  229. Intersect(c11, rp12, 1) → W12
  230. Intersect(c12, rp13, 1) → W13
  231. Intersect(c13, rp14, 1) → W14
  232. Intersect(c14, rp15, 1) → W15
  233. Intersect(c15, rp16, 1) → W16
  234. Intersect(c16, rp17, 1) → W17
  235. Intersect(c17, rp18, 1) → W18
  236. Intersect(c18, rp19, 1) → W19
  237. Intersect(c19, rp20, 1) → W20
  238. Intersect(c20, rp21, 1) → W21
  239. Intersect(c21, rp22, 1) → W22
  240. Intersect(c22, rp23, 1) → W23
  241. Intersect(c23, rp24, 1) → W24
  242. Intersect(c24, rp25, 1) → W25
  243. Intersect(c25, rp26, 1) → W26
  244. Intersect(c26, rp27, 1) → W27
  245. Intersect(c27, rp28, 1) → W28
  246. Intersect(c28, rp29, 1) → W29
  247. Intersect(c29, rp30, 1) → W30
  248. Intersect(c30, rp31, 1) → W31
  249. Intersect(c31, rp32, 1) → W32
  250. Intersect(c32, rp33, 1) → W33
  251. Intersect(c33, rp34, 1) → W34
  252. Intersect(c34, rp35, 1) → W35
  253. Intersect(c35, rp36, 1) → W36
  254. Segment(P1, W1) → f
  255. Segment(W1, W2) → g
  256. Segment(W2, W3) → h
  257. Segment(W3, W4) → i
  258. Segment(W4, W5) → j
  259. Segment(W5, W6) → k
  260. Segment(W6, W7) → l
  261. Segment(W7, W8) → m
  262. Segment(W8, W9) → n
  263. Segment(W9, W10) → p
  264. Segment(W10, W11) → q
  265. Segment(W11, W12) → r
  266. Segment(W12, W13) → s
  267. Segment(W13, W14) → t
  268. Segment(W14, W15) → a
  269. Segment(W15, W16) → b
  270. Segment(W16, W17) → c
  271. Segment(W17, W18) → d
  272. Segment(W18, W19) → e
  273. Segment(W19, W20) → f_1
  274. Segment(W20, W21) → g_1
  275. Segment(W21, W22) → h_1
  276. Segment(W22, W23) → i_1
  277. Segment(W23, W24) → j_1
  278. Segment(W24, W25) → k_1
  279. Segment(W25, W26) → l_1
  280. Segment(W26, W27) → m_1
  281. Segment(W27, W28) → n_1
  282. Segment(W28, W29) → p_1
  283. Segment(W29, W30) → q_1
  284. Segment(W30, W31) → r_1
  285. Segment(W31, W32) → s_1
  286. Segment(W32, W33) → t_1
  287. Segment(W33, W34) → a_1
  288. Segment(W34, W35) → b_1
  289. Segment(W35, W36) → c_1
  290. Segment(B1, F1) → d_1
  291. Segment(B2, F2) → e_1
  292. Segment(B3, F3) → f_2
  293. Segment(B4, F4) → g_2
  294. Segment(B5, F5) → h_2
  295. Segment(B6, F6) → i_2
  296. Segment(B7, F7) → j_2
  297. Segment(B8, F8) → k_2
  298. Segment(B9, F9) → l_2
  299. Segment(B10, F10) → m_2
  300. Segment(B11, F11) → n_2
  301. Segment(B12, F12) → p_2
  302. Segment(B13, F13) → q_2
  303. Segment(B14, F14) → r_2
  304. Segment(B15, F15) → s_2
  305. Segment(B16, F16) → t_2
  306. Segment(B17, F17) → a_2
  307. Segment(B18, F18) → b_2
  308. Segment(B19, F19) → c_2
  309. Segment(B20, F20) → d_2
  310. Segment(B21, F21) → e_2
  311. Segment(B22, F22) → f_3
  312. Segment(B23, F23) → g_3
  313. Segment(B24, F24) → h_3
  314. Segment(B25, F25) → i_3
  315. Segment(B26, F26) → j_3
  316. Segment(B27, F27) → k_3
  317. Segment(B28, F28) → l_3
  318. Segment(B29, F29) → m_3
  319. Segment(B30, F30) → n_3
  320. Segment(B31, F31) → p_3
  321. Segment(B32, F32) → q_3
  322. Segment(B33, F33) → r_3
  323. Segment(B34, F34) → s_3
  324. Segment(B35, F35) → t_3
  325. Intersect(c35, rp0, 1) → B36
  326. Segment(P0, W2) → s2
  327. Segment(P0, W3) → s3
  328. Segment(P0, W4) → s4
  329. Segment(P0, W5) → s5
  330. Segment(P0, W6) → s6
  331. Segment(P0, W7) → s7
  332. Segment(P0, W8) → s8
  333. Segment(P0, W9) → s9
  334. Segment(P0, W10) → s10
  335. Segment(P0, W11) → s11
  336. Segment(P0, W12) → s12
  337. Segment(P0, W13) → s13
  338. Segment(P0, W14) → s14
  339. Segment(P0, W15) → s15
  340. Segment(P0, W16) → s16
  341. Segment(P0, W17) → s17
  342. Segment(P0, W18) → s18
  343. Segment(P0, W19) → s19
  344. Segment(P0, W20) → s20
  345. Segment(P0, W21) → s21
  346. Segment(P0, W22) → s22
  347. Segment(P0, W23) → s23
  348. Segment(P0, W24) → s24
  349. Segment(P0, W25) → s25
  350. Segment(P0, W26) → s26
  351. Segment(P0, W27) → s27
  352. Segment(P0, W28) → s28
  353. Segment(P0, W29) → s29
  354. Segment(P0, W30) → s30
  355. Segment(P0, W31) → s31
  356. Segment(P0, W32) → s32
  357. Segment(P0, W33) → s33
  358. Segment(P0, W34) → s34
  359. Segment(P0, W35) → s35
  360. Segment(P0, W36) → s36
  361. If(x(B36) > x(P1), (-x(B36)), (-x(P1))) → y1
  362. If(x(B36) > x(P1), x(B36), x(P1)) → y2
  363. Segment(P0, F35) → s1
  364. Segment(P0, B36) → s0
  365. Segment(P0, P1) → s0'
  366. Segment(P0, W1) → s1'
  367. Textfield(r0) → CampoInserimento1
  368. Textfield(α) → CampoInserimento2

AI 绘图提示语参考

绘制一个对数/黄金比例多边形螺旋。首先，围绕点P0旋转点A，生成一系列多边形。接着，通过点P0和旋转后的点A绘制多条射线，与前一条射线相交得到新的点，这些点用于绘制螺旋。螺旋由多个多边形组成，每个多边形的边数逐渐增加，形成对数增长。
以上提示语为根据原始绘图命令整理而来，仅供参考。