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Dynamic Construction of the Square‑Root (Theodorus) Spiral in GeoGebra

Dynamic Construction of the Square‑Root (Theodorus) Spiral in GeoGebra
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2020-08-19 23:02
TrianglePolygonSequenceTransformationGeometric Construction
① This example demonstrates the step‑by‑step construction of the square‑root spiral (Theodorus spiral), showing how successive right triangles with hypotenuses √2, √3, √4 … form a spiral curve. ② Core mathematical concepts: surds/irrational numbers, Pythagorean theorem, sequences and recursion, planar geometric transformations. ③ Construction highlights: Points created with Point; legs built with Segment; triangles rotated and translated via Rotate and Translate; Polygon forms each triangle; Sequence generates 17 vertex pairs A1‑B17; Intersect finds intersection points; Text labels side lengths. ④ Suitable for middle‑school or high‑school lessons on the geometric meaning of surds, and as a GeoGebra modeling resource.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Draw a spiral curve formed by right triangles with legs of √2, √3, √4, etc., using rotation and translation to generate 17 triangle vertices, creating a spiral shape. Start by creating points A and B on the x-axis, then build a polygon t1, and use rotation and translation to generate the subsequent triangle vertices, finally connecting adjacent vertices to form the spiral curve.
The prompt above was compiled from the original drawing commands and is for reference only.