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平方根螺旋（Theodorus螺旋）的 GeoGebra 动态构造

平方根螺旋（Theodorus螺旋）的 GeoGebra 动态构造
几何画板及绘图内容加载中，请稍等……
2020-08-19 23:02
测试改名0多边形数列变换几何作图
① 本范例演示平方根螺旋（Theodorus螺旋）的逐步生成过程，展示一系列直角三角形的斜边长度依次为 √2、√3、√4… 形成的螺旋曲线。② 涉及核心数学概念：无理数/根式、勾股定理、数列与递推、平面几何变换。③ 作图要点：使用 Point 创建初始点，Segment 构建直角边，Rotate 与 Translate 实现三角形的旋转平移，Polygon 生成三角形区域，Sequence 批量生成 17 组顶点 A1‑B17，Intersect 确定交点，Text 标注边长。④ 适用于初中/高中数学课堂演示根式几何意义，也可作为 GeoGebra 建模教学素材。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, C) → t1, c, a, b
  4. Rotate(Vector[UnitVector[Vector[A1, (0, 0)]]], ((-π)) / 2, A1) → B1
  5. Translate(A1, B1) → A2
  6. Rotate(Vector[UnitVector[Vector[A2, (0, 0)]]], ((-π)) / 2, A2) → B2
  7. Translate(A2, B2) → A3
  8. Rotate(Vector[UnitVector[Vector[A3, (0, 0)]]], ((-π)) / 2, A3) → B3
  9. Translate(A3, B3) → A4
  10. Rotate(Vector[UnitVector[Vector[A4, (0, 0)]]], ((-π)) / 2, A4) → B4
  11. Translate(A4, B4) → A5
  12. Rotate(Vector[UnitVector[Vector[A5, (0, 0)]]], ((-π)) / 2, A5) → B5
  13. Translate(A5, B5) → A6
  14. Rotate(Vector[UnitVector[Vector[A6, (0, 0)]]], ((-π)) / 2, A6) → B6
  15. Translate(A6, B6) → A7
  16. Rotate(Vector[UnitVector[Vector[A7, (0, 0)]]], ((-π)) / 2, A7) → B7
  17. Translate(A7, B7) → A8
  18. Rotate(Vector[UnitVector[Vector[A8, (0, 0)]]], ((-π)) / 2, A8) → B8
  19. Translate(A8, B8) → A9
  20. Rotate(Vector[UnitVector[Vector[A9, (0, 0)]]], ((-π)) / 2, A9) → B9
  21. Translate(A9, B9) → A10
  22. Rotate(Vector[UnitVector[Vector[A10, (0, 0)]]], ((-π)) / 2, A10) → B10
  23. Translate(A10, B10) → A11
  24. Rotate(Vector[UnitVector[Vector[A11, (0, 0)]]], ((-π)) / 2, A11) → B11
  25. Translate(A11, B11) → A12
  26. Rotate(Vector[UnitVector[Vector[A12, (0, 0)]]], ((-π)) / 2, A12) → B12
  27. Translate(A12, B12) → A13
  28. Rotate(Vector[UnitVector[Vector[A13, (0, 0)]]], ((-π)) / 2, A13) → B13
  29. Translate(A13, B13) → A14
  30. Rotate(Vector[UnitVector[Vector[A14, (0, 0)]]], ((-π)) / 2, A14) → B14
  31. Translate(A14, B14) → A15
  32. Rotate(Vector[UnitVector[Vector[A15, (0, 0)]]], ((-π)) / 2, A15) → B15
  33. Translate(A15, B15) → A16
  34. Rotate(Vector[UnitVector[Vector[A16, (0, 0)]]], ((-π)) / 2, A16) → B16
  35. Translate(A16, B16) → A17
  36. Rotate(Vector[UnitVector[Vector[A17, (0, 0)]]], ((-π)) / 2, A17) → B17
  37. Translate(A17, B17) → A18
  38. Rotate(Vector[UnitVector[Vector[A18, (0, 0)]]], ((-π)) / 2, A18) → B18
  39. Translate(A18, B18) → A19
  40. Rotate(Vector[UnitVector[Vector[A19, (0, 0)]]], ((-π)) / 2, A19) → B19
  41. Translate(A19, B19) → A20
  42. Rotate(Vector[UnitVector[Vector[A20, (0, 0)]]], ((-π)) / 2, A20) → B20
  43. Translate(A20, B20) → A21
  44. Rotate(Vector[UnitVector[Vector[A21, (0, 0)]]], ((-π)) / 2, A21) → B21
  45. Translate(A21, B21) → A22
  46. Rotate(Vector[UnitVector[Vector[A22, (0, 0)]]], ((-π)) / 2, A22) → B22
  47. Segment(A1, A2) → C2
  48. Segment(A2, A3) → C3
  49. Segment(A3, A4) → C4
  50. Segment(A4, A5) → C5
  51. Segment(A5, A6) → C6
  52. Segment(A6, A7) → C7
  53. Segment(A7, A8) → C8
  54. Segment(A8, A9) → C9
  55. Segment(A9, A10) → C10
  56. Segment(A10, A11) → C11
  57. Segment(A11, A12) → C12
  58. Segment(A12, A13) → C13
  59. Segment(A13, A14) → C14
  60. Segment(A14, A15) → C15
  61. Segment(A15, A16) → C16
  62. Segment(A16, A17) → C17
  63. Segment(A17, A18) → C18
  64. Segment(A18, A19) → C19
  65. Segment(A19, A20) → C20
  66. Segment(A20, A21) → C21
  67. Segment(A21, A22) → C22
  68. Segment(A2, (0, 0)) → D2
  69. Segment(A3, (0, 0)) → D3
  70. Segment(A4, (0, 0)) → D4
  71. Segment(A5, (0, 0)) → D5
  72. Segment(A6, (0, 0)) → D6
  73. Segment(A7, (0, 0)) → D7
  74. Segment(A8, (0, 0)) → D8
  75. Segment(A9, (0, 0)) → D9
  76. Segment(A10, (0, 0)) → D10
  77. Segment(A11, (0, 0)) → D11
  78. Segment(A12, (0, 0)) → D12
  79. Segment(A13, (0, 0)) → D13
  80. Segment(A14, (0, 0)) → D14
  81. Segment(A15, (0, 0)) → D15
  82. Segment(A16, (0, 0)) → D16
  83. Segment(A17, (0, 0)) → D17
  84. Segment(A18, (0, 0)) → D18
  85. Segment(A19, (0, 0)) → D19
  86. Segment(A20, (0, 0)) → D20
  87. Segment(A21, (0, 0)) → D21
  88. Segment(A22, (0, 0)) → D22
  89. Translate(A22, B22) → A23
  90. Rotate(Vector[UnitVector[Vector[A23, (0, 0)]]], ((-π)) / 2, A23) → B23
  91. Segment(A22, A23) → C23
  92. Segment(A23, (0, 0)) → D23
  93. Translate(A23, B23) → A24
  94. Rotate(Vector[UnitVector[Vector[A24, (0, 0)]]], ((-π)) / 2, A24) → B24
  95. Segment(A23, A24) → C24
  96. Segment(A24, (0, 0)) → D24
  97. Translate(A24, B24) → A25
  98. Rotate(Vector[UnitVector[Vector[A25, (0, 0)]]], ((-π)) / 2, A25) → B25
  99. Segment(A24, A25) → C25
  100. Segment(A25, (0, 0)) → D25
  101. Translate(A25, B25) → A26
  102. Rotate(Vector[UnitVector[Vector[A26, (0, 0)]]], ((-π)) / 2, A26) → B26
  103. Segment(A25, A26) → C26
  104. Segment(A26, (0, 0)) → D26
  105. Translate(A26, B26) → A27
  106. Rotate(Vector[UnitVector[Vector[A27, (0, 0)]]], ((-π)) / 2, A27) → B27
  107. Segment(A26, A27) → C27
  108. Segment(A27, (0, 0)) → D27
  109. Translate(A27, B27) → A28
  110. Rotate(Vector[UnitVector[Vector[A28, (0, 0)]]], ((-π)) / 2, A28) → B28
  111. Segment(A27, A28) → C28
  112. Segment(A28, (0, 0)) → D28
  113. Translate(A28, B28) → A29
  114. Rotate(Vector[UnitVector[Vector[A29, (0, 0)]]], ((-π)) / 2, A29) → B29
  115. Segment(A28, A29) → C29
  116. Segment(A29, (0, 0)) → D29
  117. Translate(A29, B29) → A30
  118. Rotate(Vector[UnitVector[Vector[A30, (0, 0)]]], ((-π)) / 2, A30) → B30
  119. Segment(A29, A30) → C30
  120. Segment(A30, (0, 0)) → D30
  121. Translate(A30, B30) → A31
  122. Rotate(Vector[UnitVector[Vector[A31, (0, 0)]]], ((-π)) / 2, A31) → B31
  123. Segment(A30, A31) → C31
  124. Segment(A31, (0, 0)) → D31
  125. Translate(A31, B31) → A32
  126. Rotate(Vector[UnitVector[Vector[A32, (0, 0)]]], ((-π)) / 2, A32) → B32
  127. Segment(A31, A32) → C32
  128. Segment(A32, (0, 0)) → D32
  129. Translate(A32, B32) → A33
  130. Rotate(Vector[UnitVector[Vector[A33, (0, 0)]]], ((-π)) / 2, A33) → B33
  131. Segment(A32, A33) → C33
  132. Segment(A33, (0, 0)) → D33
  133. Translate(A33, B33) → A34
  134. Rotate(Vector[UnitVector[Vector[A34, (0, 0)]]], ((-π)) / 2, A34) → B34
  135. Segment(A33, A34) → C34
  136. Segment(A34, (0, 0)) → D34
  137. Translate(A34, B34) → A35
  138. Rotate(Vector[UnitVector[Vector[A35, (0, 0)]]], ((-π)) / 2, A35) → B35
  139. Segment(A34, A35) → C35
  140. Segment(A35, (0, 0)) → D35
  141. Translate(A35, B35) → A36
  142. Rotate(Vector[UnitVector[Vector[A36, (0, 0)]]], ((-π)) / 2, A36) → B36
  143. Segment(A35, A36) → C36
  144. Segment(A36, (0, 0)) → D36
  145. Translate(A36, B36) → A37
  146. Rotate(Vector[UnitVector[Vector[A37, (0, 0)]]], ((-π)) / 2, A37) → B37
  147. Segment(A36, A37) → C37
  148. Segment(A37, (0, 0)) → D37
  149. Translate(A37, B37) → A38
  150. Rotate(Vector[UnitVector[Vector[A38, (0, 0)]]], ((-π)) / 2, A38) → B38
  151. Segment(A37, A38) → C38
  152. Segment(A38, (0, 0)) → D38
  153. Translate(A38, B38) → A39
  154. Rotate(Vector[UnitVector[Vector[A39, (0, 0)]]], ((-π)) / 2, A39) → B39
  155. Segment(A38, A39) → C39
  156. Segment(A39, (0, 0)) → D39
  157. Translate(A39, B39) → A40
  158. Rotate(Vector[UnitVector[Vector[A40, (0, 0)]]], ((-π)) / 2, A40) → B40
  159. Segment(A39, A40) → C40
  160. Segment(A40, (0, 0)) → D40
  161. Translate(A40, B40) → A41
  162. Rotate(Vector[UnitVector[Vector[A41, (0, 0)]]], ((-π)) / 2, A41) → B41
  163. Segment(A40, A41) → C41
  164. Segment(A41, (0, 0)) → D41
  165. Translate(A41, B41) → A42
  166. Rotate(Vector[UnitVector[Vector[A42, (0, 0)]]], ((-π)) / 2, A42) → B42
  167. Segment(A41, A42) → C42
  168. Segment(A42, (0, 0)) → D42
  169. Translate(A42, B42) → A43
  170. Rotate(Vector[UnitVector[Vector[A43, (0, 0)]]], ((-π)) / 2, A43) → B43
  171. Segment(A42, A43) → C43
  172. Segment(A43, (0, 0)) → D43
  173. Translate(A43, B43) → A44
  174. Rotate(Vector[UnitVector[Vector[A44, (0, 0)]]], ((-π)) / 2, A44) → B44
  175. Segment(A43, A44) → C44
  176. Segment(A44, (0, 0)) → D44
  177. Translate(A44, B44) → A45
  178. Rotate(Vector[UnitVector[Vector[A45, (0, 0)]]], ((-π)) / 2, A45) → B45
  179. Segment(A44, A45) → C45
  180. Segment(A45, (0, 0)) → D45
  181. Translate(A45, B45) → A46
  182. Rotate(Vector[UnitVector[Vector[A46, (0, 0)]]], ((-π)) / 2, A46) → B46
  183. Segment(A45, A46) → C46
  184. Segment(A46, (0, 0)) → D46
  185. Polygon(A1, A2, (0, 0)) → E2, F2, G2, H2
  186. Polygon(A2, A3, (0, 0)) → E3, F3, G3, H3
  187. Polygon(A3, A4, (0, 0)) → E4, F4, G4, H4
  188. Polygon(A4, A5, (0, 0)) → E5, F5, G5, H5
  189. Polygon(A5, A6, (0, 0)) → E6, F6, G6, H6
  190. Polygon(A6, A7, (0, 0)) → E7, F7, G7, H7
  191. Polygon(A7, A8, (0, 0)) → E8, F8, G8, H8
  192. Polygon(A8, A9, (0, 0)) → E9, F9, G9, H9
  193. Polygon(A9, A10, (0, 0)) → E10, F10, G10, H10
  194. Polygon(A10, A11, (0, 0)) → E11, F11, G11, H11
  195. Polygon(A11, A12, (0, 0)) → E12, F12, G12, H12
  196. Polygon(A12, A13, (0, 0)) → E13, F13, G13, H13
  197. Polygon(A13, A14, (0, 0)) → E14, F14, G14, H14
  198. Polygon(A14, A15, (0, 0)) → E15, F15, G15, H15
  199. Polygon(A15, A16, (0, 0)) → E16, F16, G16, H16
  200. Polygon(A16, A17, (0, 0)) → E17, F17, G17, H17
  201. Polygon(A17, A18, (0, 0)) → E18, F18, G18, H18
  202. Polygon(A18, A19, (0, 0)) → E19, F19, G19, H19
  203. Polygon(A19, A20, (0, 0)) → E20, F20, G20, H20
  204. Polygon(A20, A21, (0, 0)) → E21, F21, G21, H21
  205. Polygon(A21, A22, (0, 0)) → E22, F22, G22, H22
  206. Polygon(A22, A23, (0, 0)) → E23, F23, G23, H23
  207. Polygon(A23, A24, (0, 0)) → E24, F24, G24, H24
  208. Polygon(A24, A25, (0, 0)) → E25, F25, G25, H25
  209. Polygon(A25, A26, (0, 0)) → E26, F26, G26, H26
  210. Polygon(A26, A27, (0, 0)) → E27, F27, G27, H27
  211. Polygon(A27, A28, (0, 0)) → E28, F28, G28, H28
  212. Polygon(A28, A29, (0, 0)) → E29, F29, G29, H29
  213. Polygon(A29, A30, (0, 0)) → E30, F30, G30, H30
  214. Polygon(A30, A31, (0, 0)) → E31, F31, G31, H31
  215. Polygon(A31, A32, (0, 0)) → E32, F32, G32, H32
  216. Polygon(A32, A33, (0, 0)) → E33, F33, G33, H33
  217. Polygon(A33, A34, (0, 0)) → E34, F34, G34, H34
  218. Polygon(A34, A35, (0, 0)) → E35, F35, G35, H35
  219. Polygon(A35, A36, (0, 0)) → E36, F36, G36, H36
  220. Polygon(A36, A37, (0, 0)) → E37, F37, G37, H37
  221. Polygon(A37, A38, (0, 0)) → E38, F38, G38, H38
  222. Polygon(A38, A39, (0, 0)) → E39, F39, G39, H39
  223. Polygon(A39, A40, (0, 0)) → E40, F40, G40, H40
  224. Polygon(A40, A41, (0, 0)) → E41, F41, G41, H41
  225. Polygon(A41, A42, (0, 0)) → E42, F42, G42, H42
  226. Polygon(A42, A43, (0, 0)) → E43, F43, G43, H43
  227. Polygon(A43, A44, (0, 0)) → E44, F44, G44, H44
  228. Polygon(A44, A45, (0, 0)) → E45, F45, G45, H45
  229. Polygon(A45, A46, (0, 0)) → E46, F46, G46, H46
  230. Translate(A46, B46) → A47
  231. Rotate(Vector[UnitVector[Vector[A47, (0, 0)]]], ((-π)) / 2, A47) → B47
  232. Translate(A47, B47) → A48
  233. Rotate(Vector[UnitVector[Vector[A48, (0, 0)]]], ((-π)) / 2, A48) → B48
  234. Translate(A48, B48) → A49
  235. Rotate(Vector[UnitVector[Vector[A49, (0, 0)]]], ((-π)) / 2, A49) → B49
  236. Translate(A49, B49) → A50
  237. Rotate(Vector[UnitVector[Vector[A50, (0, 0)]]], ((-π)) / 2, A50) → B50
  238. Translate(A50, B50) → A51
  239. Rotate(Vector[UnitVector[Vector[A51, (0, 0)]]], ((-π)) / 2, A51) → B51
  240. Translate(A51, B51) → A52
  241. Rotate(Vector[UnitVector[Vector[A52, (0, 0)]]], ((-π)) / 2, A52) → B52
  242. Translate(A52, B52) → A53
  243. Rotate(Vector[UnitVector[Vector[A53, (0, 0)]]], ((-π)) / 2, A53) → B53
  244. Translate(A53, B53) → A54
  245. Rotate(Vector[UnitVector[Vector[A54, (0, 0)]]], ((-π)) / 2, A54) → B54
  246. Translate(A54, B54) → A55
  247. Rotate(Vector[UnitVector[Vector[A55, (0, 0)]]], ((-π)) / 2, A55) → B55
  248. Translate(A55, B55) → A56
  249. Rotate(Vector[UnitVector[Vector[A56, (0, 0)]]], ((-π)) / 2, A56) → B56
  250. Translate(A56, B56) → A57
  251. Rotate(Vector[UnitVector[Vector[A57, (0, 0)]]], ((-π)) / 2, A57) → B57
  252. Translate(A57, B57) → A58
  253. Rotate(Vector[UnitVector[Vector[A58, (0, 0)]]], ((-π)) / 2, A58) → B58
  254. Translate(A58, B58) → A59
  255. Rotate(Vector[UnitVector[Vector[A59, (0, 0)]]], ((-π)) / 2, A59) → B59
  256. Translate(A59, B59) → A60
  257. Rotate(Vector[UnitVector[Vector[A60, (0, 0)]]], ((-π)) / 2, A60) → B60
  258. Translate(A60, B60) → A61
  259. Rotate(Vector[UnitVector[Vector[A61, (0, 0)]]], ((-π)) / 2, A61) → B61
  260. Translate(A61, B61) → A62
  261. Rotate(Vector[UnitVector[Vector[A62, (0, 0)]]], ((-π)) / 2, A62) → B62
  262. Translate(A62, B62) → A63
  263. Rotate(Vector[UnitVector[Vector[A63, (0, 0)]]], ((-π)) / 2, A63) → B63
  264. Translate(A63, B63) → A64
  265. Rotate(Vector[UnitVector[Vector[A64, (0, 0)]]], ((-π)) / 2, A64) → B64
  266. Translate(A64, B64) → A65
  267. Rotate(Vector[UnitVector[Vector[A65, (0, 0)]]], ((-π)) / 2, A65) → B65
  268. Translate(A65, B65) → A66
  269. Rotate(Vector[UnitVector[Vector[A66, (0, 0)]]], ((-π)) / 2, A66) → B66
  270. Translate(A66, B66) → A67
  271. Rotate(Vector[UnitVector[Vector[A67, (0, 0)]]], ((-π)) / 2, A67) → B67
  272. Translate(A67, B67) → A68
  273. Rotate(Vector[UnitVector[Vector[A68, (0, 0)]]], ((-π)) / 2, A68) → B68
  274. Translate(A68, B68) → A69
  275. Rotate(Vector[UnitVector[Vector[A69, (0, 0)]]], ((-π)) / 2, A69) → B69
  276. Translate(A69, B69) → A70
  277. Rotate(Vector[UnitVector[Vector[A70, (0, 0)]]], ((-π)) / 2, A70) → B70
  278. Translate(A70, B70) → A71
  279. Rotate(Vector[UnitVector[Vector[A71, (0, 0)]]], ((-π)) / 2, A71) → B71
  280. Translate(A71, B71) → A72
  281. Rotate(Vector[UnitVector[Vector[A72, (0, 0)]]], ((-π)) / 2, A72) → B72
  282. Translate(A72, B72) → A73
  283. Rotate(Vector[UnitVector[Vector[A73, (0, 0)]]], ((-π)) / 2, A73) → B73
  284. Translate(A73, B73) → A74
  285. Rotate(Vector[UnitVector[Vector[A74, (0, 0)]]], ((-π)) / 2, A74) → B74
  286. Translate(A74, B74) → A75
  287. Rotate(Vector[UnitVector[Vector[A75, (0, 0)]]], ((-π)) / 2, A75) → B75
  288. Translate(A75, B75) → A76
  289. Rotate(Vector[UnitVector[Vector[A76, (0, 0)]]], ((-π)) / 2, A76) → B76
  290. Translate(A76, B76) → A77
  291. Rotate(Vector[UnitVector[Vector[A77, (0, 0)]]], ((-π)) / 2, A77) → B77
  292. Translate(A77, B77) → A78
  293. Rotate(Vector[UnitVector[Vector[A78, (0, 0)]]], ((-π)) / 2, A78) → B78
  294. Translate(A78, B78) → A79
  295. Rotate(Vector[UnitVector[Vector[A79, (0, 0)]]], ((-π)) / 2, A79) → B79
  296. Translate(A79, B79) → A80
  297. Rotate(Vector[UnitVector[Vector[A80, (0, 0)]]], ((-π)) / 2, A80) → B80
  298. Translate(A80, B80) → A81
  299. Rotate(Vector[UnitVector[Vector[A81, (0, 0)]]], ((-π)) / 2, A81) → B81
  300. Translate(A81, B81) → A82
  301. Rotate(Vector[UnitVector[Vector[A82, (0, 0)]]], ((-π)) / 2, A82) → B82
  302. Translate(A82, B82) → A83
  303. Rotate(Vector[UnitVector[Vector[A83, (0, 0)]]], ((-π)) / 2, A83) → B83
  304. Translate(A83, B83) → A84
  305. Rotate(Vector[UnitVector[Vector[A84, (0, 0)]]], ((-π)) / 2, A84) → B84
  306. Translate(A84, B84) → A85
  307. Rotate(Vector[UnitVector[Vector[A85, (0, 0)]]], ((-π)) / 2, A85) → B85
  308. Translate(A85, B85) → A86
  309. Rotate(Vector[UnitVector[Vector[A86, (0, 0)]]], ((-π)) / 2, A86) → B86
  310. Translate(A86, B86) → A87
  311. Rotate(Vector[UnitVector[Vector[A87, (0, 0)]]], ((-π)) / 2, A87) → B87
  312. Translate(A87, B87) → A88
  313. Rotate(Vector[UnitVector[Vector[A88, (0, 0)]]], ((-π)) / 2, A88) → B88
  314. Translate(A88, B88) → A89
  315. Rotate(Vector[UnitVector[Vector[A89, (0, 0)]]], ((-π)) / 2, A89) → B89
  316. Translate(A89, B89) → A90
  317. Rotate(Vector[UnitVector[Vector[A90, (0, 0)]]], ((-π)) / 2, A90) → B90
  318. Translate(A90, B90) → A91
  319. Rotate(Vector[UnitVector[Vector[A91, (0, 0)]]], ((-π)) / 2, A91) → B91
  320. Translate(A91, B91) → A92
  321. Rotate(Vector[UnitVector[Vector[A92, (0, 0)]]], ((-π)) / 2, A92) → B92
  322. Translate(A92, B92) → A93
  323. Rotate(Vector[UnitVector[Vector[A93, (0, 0)]]], ((-π)) / 2, A93) → B93
  324. Translate(A93, B93) → A94
  325. Rotate(Vector[UnitVector[Vector[A94, (0, 0)]]], ((-π)) / 2, A94) → B94
  326. Translate(A94, B94) → A95
  327. Rotate(Vector[UnitVector[Vector[A95, (0, 0)]]], ((-π)) / 2, A95) → B95
  328. Translate(A95, B95) → A96
  329. Rotate(Vector[UnitVector[Vector[A96, (0, 0)]]], ((-π)) / 2, A96) → B96
  330. Translate(A96, B96) → A97
  331. Rotate(Vector[UnitVector[Vector[A97, (0, 0)]]], ((-π)) / 2, A97) → B97
  332. Translate(A97, B97) → A98
  333. Rotate(Vector[UnitVector[Vector[A98, (0, 0)]]], ((-π)) / 2, A98) → B98
  334. Translate(A98, B98) → A99
  335. Rotate(Vector[UnitVector[Vector[A99, (0, 0)]]], ((-π)) / 2, A99) → B99
  336. Translate(A99, B99) → A100
  337. Rotate(Vector[UnitVector[Vector[A100, (0, 0)]]], ((-π)) / 2, A100) → B100
  338. Sequence(Text["1", Midpoint[Element[spoints2, n], Element[spoints2, n + 1]], true, true], n, 1, k) → L_1
  339. Sequence(Polygon[(0, 0), Element[spoints2, n], Element[spoints2, n + 1]], n, 1, k) → stris
  340. Sequence(Text[("\sqrt" * (n + 1)), Midpoint[(0, 0), Element[spoints2, n + 1]], true, true], n, 1, k) → slabels
  341. Text("1", Midpoint[(0, 0), (1, 0)], true, true) → text133
  342. Sequence(Angle[Rotate[(0, 0), ((-π)) / 2, Element[spoints2, n]], Element[spoints2, n], (0, 0)], n, 1, k) → L_2

AI 绘图提示语参考

绘制一个由直角三角形组成的螺旋曲线，每个三角形的直角边依次为√2, √3, √4等，通过旋转和平移构建17个三角形，形成螺旋形状。首先在x轴上创建点A和B，然后构建多边形t1，并通过旋转和平移生成后续的三角形顶点，最后连接相邻顶点形成螺旋曲线。
以上提示语为根据原始绘图命令整理而来，仅供参考。