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我的第二个螺旋和多边形星星

我的第二个螺旋和多边形星星
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2020-01-29 04:16
多边形角向量变换
①这个范例演示了一个由多边形和星星组成的螺旋图形；②涉及的核心数学概念包括线段、几何变换、菱形、逻辑、分数、减法等；③作图要点使用了GeoGebra的Circle（圆）、Line（线）、Intersect（交点）、If（条件）、Rotate（旋转）、Angle（角度）、Segment（线段）、Textfield（文本框）等命令和对象；④适合初中及以上学生学习和探索几何图形的构造与变换规律。

GeoGebra 命令及参数

  1. Circle(P0, r0) → c0
  2. Line(P0, A) → s0
  3. Intersect(c0, s0, 2) → P1
  4. If(x(Bc1) > (-To), 2, 1) → SnDx1
  5. Rotate(C0, α, P1) → W0
  6. Circle(P0, W0) → c1
  7. Intersect(c1, s0, If[KK, SnDx1, 2]) → B1
  8. Rotate(C1, α, B1) → F1
  9. Circle(P0, F1) → c2
  10. If(x(Bc2) > (-To), 2, 1) → SnDx2
  11. Intersect(c2, s0, If[KK, SnDx2, 2]) → B2
  12. Rotate(C2, α, B2) → F2
  13. Circle(P0, F2) → c3
  14. If(x(Bc3) > (-To), 2, 1) → SnDx3
  15. Intersect(c3, s0, If[KK, SnDx3, 2]) → B3
  16. Rotate(C3, α, B3) → F3
  17. Circle(P0, F3) → c4
  18. If(x(Bc4) > (-To), 2, 1) → SnDx4
  19. Intersect(c4, s0, If[KK, SnDx4, 2]) → B4
  20. Rotate(C4, α, B4) → F4
  21. Circle(P0, F4) → c5
  22. If(x(Bc5) > (-To), 2, 1) → SnDx5
  23. Intersect(c5, s0, If[KK, SnDx5, 2]) → B5
  24. Rotate(C5, α, B5) → F5
  25. Circle(P0, F5) → c6
  26. If(x(Bc6) > (-To), 2, 1) → SnDx6
  27. Intersect(c6, s0, If[KK, SnDx6, 2]) → B6
  28. Rotate(C6, α, B6) → F6
  29. Circle(P0, F6) → c7
  30. If(x(Bc7) > (-To), 2, 1) → SnDx7
  31. Intersect(c7, s0, If[KK, SnDx7, 2]) → B7
  32. Rotate(C7, α, B7) → F7
  33. Circle(P0, F7) → c8
  34. If(x(Bc8) > (-To), 2, 1) → SnDx8
  35. Intersect(c8, s0, If[KK, SnDx8, 2]) → B8
  36. Rotate(C8, α, B8) → F8
  37. Circle(P0, F8) → c9
  38. If(x(Bc9) > (-To), 2, 1) → SnDx9
  39. Intersect(c9, s0, If[KK, SnDx9, 2]) → B9
  40. Rotate(C9, α, B9) → F9
  41. Circle(P0, F9) → c10
  42. If(x(Bc10) > (-To), 2, 1) → SnDx10
  43. Intersect(c10, s0, If[KK, SnDx10, 2]) → B10
  44. Rotate(C10, α, B10) → F10
  45. Circle(P0, F10) → c11
  46. If(x(Bc11) > (-To), 2, 1) → SnDx11
  47. Intersect(c11, s0, If[KK, SnDx11, 2]) → B11
  48. Rotate(C11, α, B11) → F11
  49. Circle(P0, F11) → c12
  50. If(x(Bc12) > (-To), 2, 1) → SnDx12
  51. Intersect(c12, s0, If[KK, SnDx12, 2]) → B12
  52. Rotate(C12, α, B12) → F12
  53. Circle(P0, F12) → c13
  54. If(x(Bc13) > (-To), 2, 1) → SnDx13
  55. Intersect(c13, s0, If[KK, SnDx13, 2]) → B13
  56. Rotate(C13, α, B13) → F13
  57. Circle(P0, F13) → c14
  58. If(x(Bc14) > (-To), 2, 1) → SnDx14
  59. Intersect(c14, s0, If[KK, SnDx14, 2]) → B14
  60. Rotate(C14, α, B14) → F14
  61. Circle(P0, F14) → c15
  62. If(x(Bc15) > (-To), 2, 1) → SnDx15
  63. Intersect(c15, s0, If[KK, SnDx15, 2]) → B15
  64. Rotate(C15, α, B15) → F15
  65. Circle(P0, F15) → c16
  66. If(x(Bc16) > (-To), 2, 1) → SnDx16
  67. Intersect(c16, s0, If[KK, SnDx16, 2]) → B16
  68. Rotate(C16, α, B16) → F16
  69. Circle(P0, F16) → c17
  70. If(x(Bc17) > (-To), 2, 1) → SnDx17
  71. Intersect(c17, s0, If[KK, SnDx17, 2]) → B17
  72. Rotate(C17, α, B17) → F17
  73. Circle(P0, F17) → c18
  74. If(x(Bc18) > (-To), 2, 1) → SnDx18
  75. Intersect(c18, s0, If[KK, SnDx18, 2]) → B18
  76. Rotate(C18, α, B18) → F18
  77. Circle(P0, F18) → c19
  78. If(x(Bc19) > (-To), 2, 1) → SnDx19
  79. Intersect(c19, s0, If[KK, SnDx19, 2]) → B19
  80. Rotate(C19, α, B19) → F19
  81. Circle(P0, F19) → c20
  82. If(x(Bc20) > (-To), 2, 1) → SnDx20
  83. Intersect(c20, s0, If[KK, SnDx20, 2]) → B20
  84. Rotate(C20, α, B20) → F20
  85. Circle(P0, F20) → c21
  86. If(x(Bc21) > (-To), 2, 1) → SnDx21
  87. Intersect(c21, s0, If[KK, SnDx21, 2]) → B21
  88. Rotate(C21, α, B21) → F21
  89. Circle(P0, F21) → c22
  90. If(x(Bc22) > (-To), 2, 1) → SnDx22
  91. Intersect(c22, s0, If[KK, SnDx22, 2]) → B22
  92. Rotate(C22, α, B22) → F22
  93. Circle(P0, F22) → c23
  94. If(x(Bc23) > (-To), 2, 1) → SnDx23
  95. Intersect(c23, s0, If[KK, SnDx23, 2]) → B23
  96. Rotate(C23, α, B23) → F23
  97. Circle(P0, F23) → c24
  98. If(x(Bc24) > (-To), 2, 1) → SnDx24
  99. Intersect(c24, s0, If[KK, SnDx24, 2]) → B24
  100. Rotate(C24, α, B24) → F24
  101. Circle(P0, F24) → c25
  102. If(x(Bc25) > (-To), 2, 1) → SnDx25
  103. Intersect(c25, s0, If[KK, SnDx25, 2]) → B25
  104. Rotate(C25, α, B25) → F25
  105. Circle(P0, F25) → c26
  106. If(x(Bc26) > (-To), 2, 1) → SnDx26
  107. Intersect(c26, s0, If[KK, SnDx26, 2]) → B26
  108. Rotate(C26, α, B26) → F26
  109. Circle(P0, F26) → c27
  110. If(x(Bc27) > (-To), 2, 1) → SnDx27
  111. Intersect(c27, s0, If[KK, SnDx27, 2]) → B27
  112. Rotate(C27, α, B27) → F27
  113. Circle(P0, F27) → c28
  114. If(x(Bc28) > (-To), 2, 1) → SnDx28
  115. Intersect(c28, s0, If[KK, SnDx28, 2]) → B28
  116. Rotate(C28, α, B28) → F28
  117. Circle(P0, F28) → c29
  118. If(x(Bc29) > (-To), 2, 1) → SnDx29
  119. Intersect(c29, s0, If[KK, SnDx29, 2]) → B29
  120. Rotate(C29, α, B29) → F29
  121. Circle(P0, F29) → c30
  122. If(x(Bc30) > (-To), 2, 1) → SnDx30
  123. Intersect(c30, s0, If[KK, SnDx30, 2]) → B30
  124. Rotate(C30, α, B30) → F30
  125. Circle(P0, F30) → c31
  126. If(x(Bc31) > (-To), 2, 1) → SnDx31
  127. Intersect(c31, s0, If[KK, SnDx31, 2]) → B31
  128. Rotate(C31, α, B31) → F31
  129. Circle(P0, F31) → c32
  130. If(x(Bc32) > (-To), 2, 1) → SnDx32
  131. Intersect(c32, s0, If[KK, SnDx32, 2]) → B32
  132. Rotate(C32, α, B32) → F32
  133. Circle(P0, F32) → c33
  134. If(x(Bc33) > (-To), 2, 1) → SnDx33
  135. Intersect(c33, s0, If[KK, SnDx33, 2]) → B33
  136. Rotate(C33, α, B33) → F33
  137. Circle(P0, F33) → c34
  138. If(x(Bc34) > (-To), 2, 1) → SnDx34
  139. Intersect(c34, s0, If[KK, SnDx34, 2]) → B34
  140. Rotate(C34, α, B34) → F34
  141. Circle(P0, F34) → c35
  142. If(x(Bc35) > (-To), 2, 1) → SnDx35
  143. Intersect(c35, s0, If[KK, SnDx35, 2]) → B35
  144. Rotate(C35, α, B35) → F35
  145. Circle(P0, F35) → c36
  146. If(x(Bc36) > (-To), 2, 1) → SnDx36
  147. Angle(B1, P0, W0) → β1
  148. Rotate(P1_0, α, P1) → P1'
  149. Segment(P1, W0) → g
  150. Segment(B2, F2) → l
  151. Segment(P0, W0) → t
  152. Segment(P0, F1) → a
  153. Segment(P0, F2) → b
  154. Segment(B3, F3) → j_1
  155. Segment(P0, F3) → m_1
  156. Segment(B4, F4) → r_1
  157. Segment(P0, F4) → b_1
  158. Segment(B5, F5) → h_2
  159. Segment(P0, F5) → j_2
  160. Segment(B6, F6) → m_2
  161. Segment(P0, F6) → s_2
  162. Segment(B7, F7) → b_2
  163. Segment(P0, F7) → g_3
  164. Segment(B8, F8) → j_3
  165. Segment(P0, F8) → m_3
  166. Segment(B9, F9) → b_3
  167. Segment(P0, F9) → f_4
  168. Segment(B10, F10) → j_4
  169. Segment(P0, F10) → l_4
  170. Segment(B11, F11) → t_4
  171. Segment(P0, F11) → a_4
  172. Segment(B12, F12) → g_5
  173. Segment(P0, F12) → i_5
  174. Segment(B13, F13) → m_5
  175. Segment(P0, F13) → n_5
  176. Segment(B14, F14) → b_5
  177. Segment(P0, F14) → f_6
  178. Segment(B15, F15) → l_6
  179. Segment(P0, F15) → n_6
  180. Segment(B16, F16) → t_6
  181. Segment(P0, F16) → b_6
  182. Segment(B17, F17) → j_7
  183. Segment(P0, F17) → k_7
  184. Segment(B18, F18) → n_7
  185. Segment(P0, F18) → t_7
  186. Segment(B19, F19) → g_8
  187. Segment(P0, F19) → h_8
  188. Segment(B20, F20) → l_8
  189. Segment(P0, F20) → n_8
  190. Segment(B21, F21) → b_8
  191. Segment(P0, F21) → f_9
  192. Segment(B22, F22) → i_9
  193. Segment(P0, F22) → l_9
  194. Segment(B23, F23) → a_9
  195. Segment(P0, F23) → b_9
  196. Segment(B24, F24) → h_{10}
  197. Segment(P0, F24) → i_{10}
  198. Segment(B25, F25) → n_{10}
  199. Segment(P0, F25) → s_{10}
  200. Segment(B26, F26) → f_{11}
  201. Segment(P0, F26) → g_{11}
  202. Segment(B27, F27) → j_{11}
  203. Segment(P0, F27) → l_{11}
  204. Segment(B28, F28) → a_{11}
  205. Segment(P0, F28) → b_{11}
  206. Segment(B29, F29) → i_{12}
  207. Segment(P0, F29) → j_{12}
  208. Segment(B30, F30) → s_{12}
  209. Segment(P0, F30) → t_{12}
  210. Segment(B31, F31) → g_{13}
  211. Segment(P0, F31) → h_{13}
  212. Segment(B32, F32) → l_{13}
  213. Segment(P0, F32) → m_{13}
  214. Segment(B33, F33) → a_{13}
  215. Segment(P0, F33) → b_{13}
  216. Segment(B34, F34) → i_{14}
  217. Segment(P0, F34) → l_{14}
  218. Segment(B35, F35) → s_{14}
  219. Intersect(c36, s0, If[KK, SnDx36, 2]) → B36
  220. Segment(P0, F35) → b_{14}
  221. Segment(B1, F1) → i
  222. Line(W0, F35) → f
  223. Rotate(F1, β1, P0) → W1
  224. Segment(W0, W1) → h
  225. Angle(B2, P0, W1) → β2
  226. Rotate(F2, β2, P0) → W2
  227. Segment(W1, W2) → j
  228. Angle(B3, P0, W2) → β3
  229. Rotate(F3, β3, P0) → W3
  230. Segment(W2, W3) → k
  231. Angle(B4, P0, W3) → β4
  232. Rotate(F4, β4, P0) → W4
  233. Segment(W3, W4) → m
  234. Angle(B5, P0, W4) → β5
  235. Rotate(F5, β5, P0) → W5
  236. Segment(W4, W5) → n
  237. Angle(B6, P0, W5) → β6
  238. Rotate(F6, β6, P0) → W6
  239. Segment(W5, W6) → p
  240. Angle(B7, P0, W6) → β7
  241. Rotate(F7, β7, P0) → W7
  242. Segment(W6, W7) → q
  243. Angle(B8, P0, W7) → β8
  244. Rotate(F8, β8, P0) → W8
  245. Segment(W7, W8) → r
  246. Angle(B9, P0, W8) → β9
  247. Rotate(F9, β9, P0) → W9
  248. Segment(W8, W9) → s
  249. Angle(B10, P0, W9) → β10
  250. Rotate(F10, β10, P0) → W10
  251. Segment(W9, W10) → c
  252. Angle(B11, P0, W10) → β11
  253. Rotate(F11, β11, P0) → W11
  254. Segment(W10, W11) → d
  255. Angle(B12, P0, W11) → β12
  256. Rotate(F12, β12, P0) → W12
  257. Segment(W11, W12) → e
  258. Angle(B13, P0, W12) → β13
  259. Rotate(F13, β13, P0) → W13
  260. Segment(W12, W13) → f_1
  261. Angle(B14, P0, W13) → β14
  262. Rotate(F14, β14, P0) → W14
  263. Segment(W13, W14) → g_1
  264. Angle(B15, P0, W14) → β15
  265. Rotate(F15, β15, P0) → W15
  266. Segment(W14, W15) → h_1
  267. Angle(B16, P0, W15) → β16
  268. Rotate(F16, β16, P0) → W16
  269. Segment(W15, W16) → i_1
  270. Angle(B17, P0, W16) → β17
  271. Rotate(F17, β17, P0) → W17
  272. Segment(W16, W17) → k_1
  273. Angle(B18, P0, W17) → β18
  274. Rotate(F18, β18, P0) → W18
  275. Segment(W17, W18) → l_1
  276. Angle(B19, P0, W18) → β19
  277. Rotate(F19, β19, P0) → W19
  278. Segment(W18, W19) → n_1
  279. Angle(B20, P0, W19) → β20
  280. Rotate(F20, β20, P0) → W20
  281. Segment(W19, W20) → p_1
  282. Angle(B21, P0, W20) → β21
  283. Rotate(F21, β21, P0) → W21
  284. Segment(W20, W21) → q_1
  285. Angle(B22, P0, W21) → β22
  286. Rotate(F22, β22, P0) → W22
  287. Segment(W21, W22) → s_1
  288. Angle(B23, P0, W22) → β23
  289. Rotate(F23, β23, P0) → W23
  290. Segment(W22, W23) → t_1
  291. Angle(B24, P0, W23) → β24
  292. Rotate(F24, β24, P0) → W24
  293. Segment(W23, W24) → a_1
  294. Angle(B25, P0, W24) → β25
  295. Rotate(F25, β25, P0) → W25
  296. Segment(W24, W25) → c_1
  297. Angle(B26, P0, W25) → β26
  298. Rotate(F26, β26, P0) → W26
  299. Segment(W25, W26) → d_1
  300. Angle(B27, P0, W26) → β27
  301. Rotate(F27, β27, P0) → W27
  302. Segment(W26, W27) → e_1
  303. Angle(B28, P0, W27) → β28
  304. Rotate(F28, β28, P0) → W28
  305. Segment(W27, W28) → f_2
  306. Angle(B29, P0, W28) → β29
  307. Rotate(F29, β29, P0) → W29
  308. Segment(W28, W29) → g_2
  309. Angle(B30, P0, W29) → β30
  310. Rotate(F30, β30, P0) → W30
  311. Segment(W29, W30) → i_2
  312. Angle(B31, P0, W30) → β31
  313. Rotate(F31, β31, P0) → W31
  314. Segment(W30, W31) → k_2
  315. Angle(B32, P0, W31) → β32
  316. Rotate(F32, β32, P0) → W32
  317. Segment(W31, W32) → l_2
  318. Angle(B33, P0, W32) → β33
  319. Rotate(F33, β33, P0) → W33
  320. Segment(W32, W33) → n_2
  321. Angle(B34, P0, W33) → β34
  322. Rotate(F34, β34, P0) → W34
  323. Segment(W33, W34) → p_2
  324. Angle(B35, P0, W34) → β35
  325. Rotate(F35, β35, P0) → W35
  326. Segment(W34, W35) → q_2
  327. Segment(P0, W1) → r_2
  328. Segment(P0, W2) → t_2
  329. Segment(P0, W3) → a_2
  330. Segment(P0, W4) → c_2
  331. Segment(P0, W5) → d_2
  332. Segment(P0, W6) → e_2
  333. Segment(P0, W7) → f_3
  334. Segment(P0, W8) → h_3
  335. Segment(P0, W9) → i_3
  336. Segment(P0, W10) → k_3
  337. Segment(P0, W11) → l_3
  338. Segment(P0, W12) → n_3
  339. Segment(P0, W13) → p_3
  340. Segment(P0, W14) → q_3
  341. Segment(P0, W15) → r_3
  342. Segment(P0, W16) → s_3
  343. Segment(P0, W17) → t_3
  344. Segment(P0, W18) → a_3
  345. Segment(P0, W19) → c_3
  346. Segment(P0, W20) → d_3
  347. Segment(P0, W21) → e_3
  348. Segment(P0, W22) → g_4
  349. Segment(P0, W23) → h_4
  350. Segment(P0, W24) → i_4
  351. Segment(P0, W25) → k_4
  352. Segment(P0, W26) → m_4
  353. Segment(P0, W27) → n_4
  354. Segment(P0, W28) → p_4
  355. Segment(P0, W29) → q_4
  356. Segment(P0, W30) → r_4
  357. Segment(P0, W31) → s_4
  358. Segment(P0, W32) → b_4
  359. Segment(P0, W33) → c_4
  360. Segment(P0, W34) → d_4
  361. Segment(P0, W35) → e_4
  362. If(abs(x(B36)) > x(P1), (-abs(x(B36))), (-x(P1))) → y1
  363. If(abs(x(B36)) > x(P1), abs(x(B36)), x(P1)) → y2
  364. Textfield(α) → CampoInserimento1
  365. Textfield(r0) → CampoInserimento2
  366. Textfield(IS) → CampoInserimento3

AI 绘图提示语参考

绘制一个由多个星形多边形组成的螺旋图形。首先画一个圆，然后画一条通过圆心的直线。接着在圆上选择一个点，沿着直线旋转该点形成新的圆，重复此过程多次，每次旋转角度相同，形成螺旋效果。每个圆上选择一个点，再次旋转形成新的星形多边形，重复此过程多次，形成螺旋状的星形多边形序列。
以上提示语为根据原始绘图命令整理而来，仅供参考。