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Spiraling Squares with Reflections

Spiraling Squares with Reflections
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2018-07-23 20:02
Coordinate GeometryTransformationGeometric Construction
This example demonstrates the process of drawing spiraling squares and their reflections. Key mathematical concepts include geometric transformations such as reflection and rotation. Using GeoGebra commands like Intersect, Point, Polygon, Rotate, etc., complex geometric shapes can be constructed. Suitable for middle school and above students to learn geometric transformations and figure construction.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  4. Rotate(B, a, A) → B'
  5. Line(A1, B1) → C1
  6. Intersect(C1, D1) → E1
  7. Rotate(C1, ((-π)) / 2 + a, E1) → C2
  8. Segment(E1, A1) → F1
  9. Intersect(C2, D2) → E2
  10. Segment(E2, A2) → F2
  11. Rotate(C2, ((-π)) / 2 + a, E2) → C3
  12. Intersect(C3, D3) → E3
  13. Segment(E3, A3) → F3
  14. Rotate(C3, ((-π)) / 2 + a, E3) → C4
  15. Intersect(C4, F1) → E4
  16. Segment(E4, A4) → F4
  17. Rotate(C4, ((-π)) / 2 + a, E4) → C5
  18. Intersect(C5, F2) → E5
  19. Segment(E5, A5) → F5
  20. Rotate(C5, ((-π)) / 2 + a, E5) → C6
  21. Intersect(C6, F3) → E6
  22. Segment(E6, A6) → F6
  23. Rotate(C6, ((-π)) / 2 + a, E6) → C7
  24. Intersect(C7, F4) → E7
  25. Segment(E7, A7) → F7
  26. Rotate(C7, ((-π)) / 2 + a, E7) → C8
  27. Intersect(C8, F5) → E8
  28. Segment(E8, A8) → F8
  29. Rotate(C8, ((-π)) / 2 + a, E8) → C9
  30. Intersect(C9, F6) → E9
  31. Segment(E9, A9) → F9
  32. Rotate(C9, ((-π)) / 2 + a, E9) → C10
  33. Intersect(C10, F7) → E10
  34. Segment(E10, A10) → F10
  35. Rotate(C10, ((-π)) / 2 + a, E10) → C11
  36. Intersect(C11, F8) → E11
  37. Segment(E11, A11) → F11
  38. Rotate(C11, ((-π)) / 2 + a, E11) → C12
  39. Intersect(C12, F9) → E12
  40. Segment(E12, A12) → F12
  41. Rotate(C12, ((-π)) / 2 + a, E12) → C13
  42. Intersect(C13, F10) → E13
  43. Segment(E13, A13) → F13
  44. Rotate(C13, ((-π)) / 2 + a, E13) → C14
  45. Intersect(C14, F11) → E14
  46. Segment(E14, A14) → F14
  47. Rotate(C14, ((-π)) / 2 + a, E14) → C15
  48. Intersect(C15, F12) → E15
  49. Segment(E15, A15) → F15
  50. Rotate(C15, ((-π)) / 2 + a, E15) → C16
  51. Intersect(C16, F13) → E16
  52. Segment(E16, A16) → F16
  53. Rotate(C16, ((-π)) / 2 + a, E16) → C17
  54. Intersect(C17, F14) → E17
  55. Segment(E17, A17) → F17
  56. Rotate(C17, ((-π)) / 2 + a, E17) → C18
  57. Intersect(C18, F15) → E18
  58. Segment(E18, A18) → F18
  59. Rotate(C18, ((-π)) / 2 + a, E18) → C19
  60. Intersect(C19, F16) → E19
  61. Segment(E19, A19) → F19
  62. Rotate(C19, ((-π)) / 2 + a, E19) → C20
  63. Intersect(C20, F17) → E20
  64. Segment(E20, A20) → F20
  65. Rotate(C20, ((-π)) / 2 + a, E20) → C21
  66. Intersect(C21, F18) → E21
  67. Segment(E21, A21) → F21
  68. Rotate(C21, ((-π)) / 2 + a, E21) → C22
  69. Intersect(C22, F19) → E22
  70. Segment(E22, A22) → F22
  71. Rotate(C22, ((-π)) / 2 + a, E22) → C23
  72. Intersect(C23, F20) → E23
  73. Segment(E23, A23) → F23
  74. Rotate(C23, ((-π)) / 2 + a, E23) → C24
  75. Intersect(C24, F21) → E24
  76. Segment(E24, A24) → F24
  77. Rotate(C24, ((-π)) / 2 + a, E24) → C25
  78. Intersect(C25, F22) → E25
  79. Segment(E25, A25) → F25
  80. Rotate(C25, ((-π)) / 2 + a, E25) → C26
  81. Intersect(C26, F23) → E26
  82. Segment(E26, A26) → F26
  83. Rotate(C26, ((-π)) / 2 + a, E26) → C27
  84. Intersect(C27, F24) → E27
  85. Segment(E27, A27) → F27
  86. Rotate(C27, ((-π)) / 2 + a, E27) → C28
  87. Intersect(C28, F25) → E28
  88. Segment(E28, A28) → F28
  89. Rotate(C28, ((-π)) / 2 + a, E28) → C29
  90. Intersect(C29, F26) → E29
  91. Segment(E29, A29) → F29
  92. Rotate(C29, ((-π)) / 2 + a, E29) → C30
  93. Intersect(C30, F27) → E30
  94. Segment(E30, A30) → F30
  95. Rotate(C30, ((-π)) / 2 + a, E30) → C31
  96. Intersect(C31, F28) → E31
  97. Segment(E31, A31) → F31
  98. Rotate(C31, ((-π)) / 2 + a, E31) → C32
  99. Intersect(C32, F29) → E32
  100. Segment(E32, A32) → F32
  101. Rotate(C32, ((-π)) / 2 + a, E32) → C33
  102. Intersect(C33, F30) → E33
  103. Segment(E33, A33) → F33
  104. Rotate(C33, ((-π)) / 2 + a, E33) → C34
  105. Intersect(C34, F31) → E34
  106. Segment(E34, A34) → F34
  107. Rotate(C34, ((-π)) / 2 + a, E34) → C35
  108. Intersect(C35, F32) → E35
  109. Segment(E35, A35) → F35
  110. Rotate(C35, ((-π)) / 2 + a, E35) → C36
  111. Intersect(C36, F33) → E36
  112. Segment(E36, A36) → F36
  113. Rotate(C36, ((-π)) / 2 + a, E36) → C37
  114. Intersect(C37, F34) → E37
  115. Segment(E37, A37) → F37
  116. Rotate(C37, ((-π)) / 2 + a, E37) → C38
  117. Intersect(C38, F35) → E38
  118. Segment(E38, A38) → F38
  119. Rotate(C38, ((-π)) / 2 + a, E38) → C39
  120. Intersect(C39, F36) → E39
  121. Segment(E39, A39) → F39
  122. Rotate(C39, ((-π)) / 2 + a, E39) → C40
  123. Intersect(C40, F37) → E40
  124. Segment(E40, A40) → F40
  125. Rotate(C40, ((-π)) / 2 + a, E40) → C41
  126. Intersect(C41, F38) → E41
  127. Segment(E41, A41) → F41
  128. Rotate(C41, ((-π)) / 2 + a, E41) → C42
  129. Intersect(C42, F39) → E42
  130. Segment(E42, A42) → F42
  131. Rotate(C42, ((-π)) / 2 + a, E42) → C43
  132. Intersect(C43, F40) → E43
  133. Segment(E43, A43) → F43
  134. Rotate(C43, ((-π)) / 2 + a, E43) → C44
  135. Intersect(C44, F41) → E44
  136. Segment(E44, A44) → F44
  137. Rotate(C44, ((-π)) / 2 + a, E44) → C45
  138. Intersect(C45, F42) → E45
  139. Segment(E45, A45) → F45
  140. Rotate(C45, ((-π)) / 2 + a, E45) → C46
  141. Intersect(C46, F43) → E46
  142. Segment(E46, A46) → F46
  143. Rotate(C46, ((-π)) / 2 + a, E46) → C47
  144. Intersect(C47, F44) → E47
  145. Segment(E47, A47) → F47
  146. Rotate(C47, ((-π)) / 2 + a, E47) → C48
  147. Intersect(C48, F45) → E48
  148. Segment(E48, A48) → F48
  149. Rotate(C48, ((-π)) / 2 + a, E48) → C49
  150. Intersect(C49, F46) → E49
  151. Segment(E49, A49) → F49
  152. Rotate(C49, ((-π)) / 2 + a, E49) → C50
  153. Intersect(C50, F47) → E50
  154. Segment(E50, A50) → F50
  155. Rotate(C50, ((-π)) / 2 + a, E50) → C51
  156. Intersect(C51, F48) → E51
  157. Segment(E51, A51) → F51
  158. Rotate(C51, ((-π)) / 2 + a, E51) → C52
  159. Intersect(C52, F49) → E52
  160. Segment(E52, A52) → F52
  161. Rotate(C52, ((-π)) / 2 + a, E52) → C53
  162. Intersect(C53, F50) → E53
  163. Segment(E53, A53) → F53
  164. Rotate(C53, ((-π)) / 2 + a, E53) → C54
  165. Intersect(C54, F51) → E54
  166. Segment(E54, A54) → F54
  167. Rotate(C54, ((-π)) / 2 + a, E54) → C55
  168. Intersect(C55, F52) → E55
  169. Segment(E55, A55) → F55
  170. Rotate(C55, ((-π)) / 2 + a, E55) → C56
  171. Intersect(C56, F53) → E56
  172. Segment(E56, A56) → F56
  173. Rotate(C56, ((-π)) / 2 + a, E56) → C57
  174. Intersect(C57, F54) → E57
  175. Segment(E57, A57) → F57
  176. Rotate(C57, ((-π)) / 2 + a, E57) → C58
  177. Intersect(C58, F55) → E58
  178. Segment(E58, A58) → F58
  179. Rotate(C58, ((-π)) / 2 + a, E58) → C59
  180. Intersect(C59, F56) → E59
  181. Segment(E59, A59) → F59
  182. Rotate(C59, ((-π)) / 2 + a, E59) → C60
  183. Intersect(C60, F57) → E60
  184. Segment(E60, A60) → F60
  185. Rotate(C60, ((-π)) / 2 + a, E60) → C61
  186. Intersect(C61, F58) → E61
  187. Segment(E61, A61) → F61
  188. Rotate(C61, ((-π)) / 2 + a, E61) → C62
  189. Intersect(C62, F59) → E62
  190. Segment(E62, A62) → F62
  191. Rotate(C62, ((-π)) / 2 + a, E62) → C63
  192. Intersect(C63, F60) → E63
  193. Segment(E63, A63) → F63
  194. Rotate(C63, ((-π)) / 2 + a, E63) → C64
  195. Intersect(C64, F61) → E64
  196. Segment(E64, A64) → F64
  197. Rotate(C64, ((-π)) / 2 + a, E64) → C65
  198. Intersect(C65, F62) → E65
  199. Segment(E65, A65) → F65
  200. Rotate(C65, ((-π)) / 2 + a, E65) → C66
  201. Intersect(C66, F63) → E66
  202. Segment(E66, A66) → F66
  203. Rotate(C66, ((-π)) / 2 + a, E66) → C67
  204. Intersect(C67, F64) → E67
  205. Segment(E67, A67) → F67
  206. Rotate(C67, ((-π)) / 2 + a, E67) → C68
  207. Intersect(C68, F65) → E68
  208. Segment(E68, A68) → F68
  209. Rotate(C68, ((-π)) / 2 + a, E68) → C69
  210. Intersect(C69, F66) → E69
  211. Segment(E69, A69) → F69
  212. Rotate(C69, ((-π)) / 2 + a, E69) → C70
  213. Intersect(C70, F67) → E70
  214. Segment(E70, A70) → F70
  215. Rotate(C70, ((-π)) / 2 + a, E70) → C71
  216. Intersect(C71, F68) → E71
  217. Segment(E71, A71) → F71
  218. Rotate(C71, ((-π)) / 2 + a, E71) → C72
  219. Intersect(C72, F69) → E72
  220. Segment(E72, A72) → F72
  221. Rotate(C72, ((-π)) / 2 + a, E72) → C73
  222. Intersect(C73, F70) → E73
  223. Segment(E73, A73) → F73
  224. Rotate(C73, ((-π)) / 2 + a, E73) → C74
  225. Intersect(C74, F71) → E74
  226. Segment(E74, A74) → F74
  227. Rotate(C74, ((-π)) / 2 + a, E74) → C75
  228. Intersect(C75, F72) → E75
  229. Segment(E75, A75) → F75
  230. Rotate(C75, ((-π)) / 2 + a, E75) → C76
  231. Intersect(C76, F73) → E76
  232. Segment(E76, A76) → F76
  233. Rotate(C76, ((-π)) / 2 + a, E76) → C77
  234. Intersect(C77, F74) → E77
  235. Segment(E77, A77) → F77
  236. Rotate(C77, ((-π)) / 2 + a, E77) → C78
  237. Intersect(C78, F75) → E78
  238. Segment(E78, A78) → F78
  239. Rotate(C78, ((-π)) / 2 + a, E78) → C79
  240. Intersect(C79, F76) → E79
  241. Segment(E79, A79) → F79
  242. Rotate(C79, ((-π)) / 2 + a, E79) → C80
  243. Intersect(C80, F77) → E80
  244. Segment(E80, A80) → F80
  245. Rotate(C80, ((-π)) / 2 + a, E80) → C81
  246. Intersect(C81, F78) → E81
  247. Segment(E81, A81) → F81
  248. Rotate(C81, ((-π)) / 2 + a, E81) → C82
  249. Intersect(C82, F79) → E82
  250. Segment(E82, A82) → F82
  251. Rotate(C82, ((-π)) / 2 + a, E82) → C83
  252. Intersect(C83, F80) → E83
  253. Segment(E83, A83) → F83
  254. Rotate(C83, ((-π)) / 2 + a, E83) → C84
  255. Intersect(C84, F81) → E84
  256. Segment(E84, A84) → F84
  257. Rotate(C84, ((-π)) / 2 + a, E84) → C85
  258. Intersect(C85, F82) → E85
  259. Segment(E85, A85) → F85
  260. Rotate(C85, ((-π)) / 2 + a, E85) → C86
  261. Intersect(C86, F83) → E86
  262. Segment(E86, A86) → F86
  263. Rotate(C86, ((-π)) / 2 + a, E86) → C87
  264. Intersect(C87, F84) → E87
  265. Segment(E87, A87) → F87
  266. Rotate(C87, ((-π)) / 2 + a, E87) → C88
  267. Intersect(C88, F85) → E88
  268. Segment(E88, A88) → F88
  269. Rotate(C88, ((-π)) / 2 + a, E88) → C89
  270. Intersect(C89, F86) → E89
  271. Segment(E89, A89) → F89
  272. Rotate(C89, ((-π)) / 2 + a, E89) → C90
  273. Intersect(C90, F87) → E90
  274. Segment(E90, A90) → F90
  275. Rotate(C90, ((-π)) / 2 + a, E90) → C91
  276. Intersect(C91, F88) → E91
  277. Segment(E91, A91) → F91
  278. Rotate(C91, ((-π)) / 2 + a, E91) → C92
  279. Intersect(C92, F89) → E92
  280. Segment(E92, A92) → F92
  281. Rotate(C92, ((-π)) / 2 + a, E92) → C93
  282. Intersect(C93, F90) → E93
  283. Segment(E93, A93) → F93
  284. Rotate(C93, ((-π)) / 2 + a, E93) → C94
  285. Intersect(C94, F91) → E94
  286. Segment(E94, A94) → F94
  287. Rotate(C94, ((-π)) / 2 + a, E94) → C95
  288. Intersect(C95, F92) → E95
  289. Segment(E95, A95) → F95
  290. Rotate(C95, ((-π)) / 2 + a, E95) → C96
  291. Intersect(C96, F93) → E96
  292. Segment(E96, A96) → F96
  293. Rotate(C96, ((-π)) / 2 + a, E96) → C97
  294. Intersect(C97, F94) → E97
  295. Segment(E97, A97) → F97
  296. Rotate(C97, ((-π)) / 2 + a, E97) → C98
  297. Intersect(C98, F95) → E98
  298. Segment(E98, A98) → F98
  299. Rotate(C98, ((-π)) / 2 + a, E98) → C99
  300. Intersect(C99, F96) → E99
  301. Segment(E99, A99) → F99
  302. Rotate(C99, ((-π)) / 2 + a, E99) → C100
  303. Intersect(C100, F97) → E100
  304. Segment(E100, A100) → F100
  305. Rotate(C100, ((-π)) / 2 + a, E100) → C101
  306. Intersect(C101, F98) → E101
  307. Segment(E101, A101) → F101
  308. Rotate(C101, ((-π)) / 2 + a, E101) → C102
  309. Intersect(C102, F99) → E102
  310. Segment(E102, A102) → F102
  311. Rotate(C102, ((-π)) / 2 + a, E102) → C103
  312. Intersect(C103, F100) → E103
  313. Segment(E103, A103) → F103
  314. Rotate(C103, ((-π)) / 2 + a, E103) → C104
  315. Intersect(C104, F101) → E104
  316. Segment(E104, A104) → F104
  317. Rotate(C104, ((-π)) / 2 + a, E104) → C105
  318. Intersect(C105, F102) → E105
  319. Segment(E105, A105) → F105
  320. Rotate(C105, ((-π)) / 2 + a, E105) → C106
  321. Intersect(C106, F103) → E106
  322. Segment(E106, A106) → F106
  323. Rotate(C106, ((-π)) / 2 + a, E106) → C107
  324. Intersect(C107, F104) → E107
  325. Segment(E107, A107) → F107
  326. Rotate(C107, ((-π)) / 2 + a, E107) → C108
  327. Intersect(C108, F105) → E108
  328. Segment(E108, A108) → F108
  329. Rotate(C108, ((-π)) / 2 + a, E108) → C109
  330. Intersect(C109, F106) → E109
  331. Segment(E109, A109) → F109
  332. Rotate(C109, ((-π)) / 2 + a, E109) → C110
  333. Intersect(C110, F107) → E110
  334. Segment(E110, A110) → F110
  335. Rotate(C110, ((-π)) / 2 + a, E110) → C111
  336. Intersect(C111, F108) → E111
  337. Segment(E111, A111) → F111
  338. Rotate(C111, ((-π)) / 2 + a, E111) → C112
  339. Intersect(C112, F109) → E112
  340. Segment(E112, A112) → F112
  341. Rotate(C112, ((-π)) / 2 + a, E112) → C113
  342. Intersect(C113, F110) → E113
  343. Segment(E113, A113) → F113
  344. Rotate(C113, ((-π)) / 2 + a, E113) → C114
  345. Intersect(C114, F111) → E114
  346. Segment(E114, A114) → F114
  347. Rotate(C114, ((-π)) / 2 + a, E114) → C115
  348. Intersect(C115, F112) → E115
  349. Segment(E115, A115) → F115
  350. Rotate(C115, ((-π)) / 2 + a, E115) → C116
  351. Intersect(C116, F113) → E116
  352. Segment(E116, A116) → F116
  353. Rotate(C116, ((-π)) / 2 + a, E116) → C117
  354. Intersect(C117, F114) → E117
  355. Segment(E117, A117) → F117
  356. Rotate(C117, ((-π)) / 2 + a, E117) → C118
  357. Intersect(C118, F115) → E118
  358. Segment(E118, A118) → F118
  359. Rotate(C118, ((-π)) / 2 + a, E118) → C119
  360. Intersect(C119, F116) → E119
  361. Segment(E119, A119) → F119
  362. Rotate(C119, ((-π)) / 2 + a, E119) → C120
  363. Intersect(C120, F117) → E120
  364. Segment(E120, A120) → F120
  365. Rotate(C120, ((-π)) / 2 + a, E120) → C121
  366. Intersect(C121, F118) → E121
  367. Segment(E121, A121) → F121
  368. Rotate(C121, ((-π)) / 2 + a, E121) → C122
  369. Intersect(C122, F119) → E122
  370. Segment(E122, A122) → F122
  371. Rotate(C122, ((-π)) / 2 + a, E122) → C123
  372. Intersect(C123, F120) → E123
  373. Segment(E123, A123) → F123
  374. Rotate(C123, ((-π)) / 2 + a, E123) → C124
  375. Intersect(C124, F121) → E124
  376. Segment(E124, A124) → F124
  377. Rotate(C124, ((-π)) / 2 + a, E124) → C125
  378. Intersect(C125, F122) → E125
  379. Segment(E125, A125) → F125
  380. Rotate(C125, ((-π)) / 2 + a, E125) → C126
  381. Intersect(C126, F123) → E126
  382. Segment(E126, A126) → F126
  383. Rotate(C126, ((-π)) / 2 + a, E126) → C127
  384. Intersect(C127, F124) → E127
  385. Segment(E127, A127) → F127
  386. Rotate(C127, ((-π)) / 2 + a, E127) → C128
  387. Intersect(C128, F125) → E128
  388. Segment(E128, A128) → F128
  389. Rotate(C128, ((-π)) / 2 + a, E128) → C129
  390. Intersect(C129, F126) → E129
  391. Segment(E129, A129) → F129
  392. Rotate(C129, ((-π)) / 2 + a, E129) → C130
  393. Intersect(C130, F127) → E130
  394. Segment(E130, A130) → F130
  395. Rotate(C130, ((-π)) / 2 + a, E130) → C131
  396. Intersect(C131, F128) → E131
  397. Segment(E131, A131) → F131
  398. Rotate(C131, ((-π)) / 2 + a, E131) → C132
  399. Intersect(C132, F129) → E132
  400. Segment(E132, A132) → F132
  401. Rotate(C132, ((-π)) / 2 + a, E132) → C133
  402. Intersect(C133, F130) → E133
  403. Segment(E133, A133) → F133
  404. Rotate(C133, ((-π)) / 2 + a, E133) → C134
  405. Intersect(C134, F131) → E134
  406. Segment(E134, A134) → F134
  407. Rotate(C134, ((-π)) / 2 + a, E134) → C135
  408. Intersect(C135, F132) → E135
  409. Segment(E135, A135) → F135
  410. Rotate(C135, ((-π)) / 2 + a, E135) → C136
  411. Intersect(C136, F133) → E136
  412. Segment(E136, A136) → F136
  413. Rotate(C136, ((-π)) / 2 + a, E136) → C137
  414. Intersect(C137, F134) → E137
  415. Segment(E137, A137) → F137
  416. Rotate(C137, ((-π)) / 2 + a, E137) → C138
  417. Intersect(C138, F135) → E138
  418. Segment(E138, A138) → F138
  419. Rotate(C138, ((-π)) / 2 + a, E138) → C139
  420. Intersect(C139, F136) → E139
  421. Segment(E139, A139) → F139
  422. Rotate(C139, ((-π)) / 2 + a, E139) → C140
  423. Intersect(C140, F137) → E140
  424. Segment(E140, A140) → F140
  425. Rotate(C140, ((-π)) / 2 + a, E140) → C141
  426. Intersect(C141, F138) → E141
  427. Segment(E141, A141) → F141
  428. Rotate(C141, ((-π)) / 2 + a, E141) → C142
  429. Intersect(C142, F139) → E142
  430. Segment(E142, A142) → F142
  431. Rotate(C142, ((-π)) / 2 + a, E142) → C143
  432. Intersect(C143, F140) → E143
  433. Segment(E143, A143) → F143
  434. Rotate(C143, ((-π)) / 2 + a, E143) → C144
  435. Intersect(C144, F141) → E144
  436. Segment(E144, A144) → F144
  437. Rotate(C144, ((-π)) / 2 + a, E144) → C145
  438. Intersect(C145, F142) → E145
  439. Segment(E145, A145) → F145
  440. Rotate(C145, ((-π)) / 2 + a, E145) → C146
  441. Intersect(C146, F143) → E146
  442. Segment(E146, A146) → F146
  443. Rotate(C146, ((-π)) / 2 + a, E146) → C147
  444. Intersect(C147, F144) → E147
  445. Segment(E147, A147) → F147
  446. Rotate(C147, ((-π)) / 2 + a, E147) → C148
  447. Intersect(C148, F145) → E148
  448. Segment(E148, A148) → F148
  449. Rotate(C148, ((-π)) / 2 + a, E148) → C149
  450. Intersect(C149, F146) → E149
  451. Segment(E149, A149) → F149
  452. Rotate(C149, ((-π)) / 2 + a, E149) → C150
  453. Intersect(C150, F147) → E150
  454. Segment(E150, A150) → F150
  455. Rotate(C150, ((-π)) / 2 + a, E150) → C151
  456. Intersect(((-(x(C151) / y(C151))) * x) - z(C151) / y(C151), F148, (0.5265817173569335, 0.47481312661645786)) → E151
  457. Segment(E151, A151) → F151
  458. Rotate(C151, ((-π)) / 2 + a, E151) → C152
  459. Intersect(((-(x(C152) / y(C152))) * x) - z(C152) / y(C152), F149, (0.5285001561850211, 0.5218160651670214)) → E152
  460. Segment(E152, A152) → F152
  461. Rotate(C152, ((-π)) / 2 + a, E152) → C153
  462. Intersect(((-(x(C153) / y(C153))) * x) - z(C153) / y(C153), F150, (0.4724819049488805, 0.5229585843397063)) → E153
  463. Segment(E153, A153) → F153
  464. Rotate(C153, ((-π)) / 2 + a, E153) → C154
  465. Intersect(((-(x(C154) / y(C154))) * x) - z(C154) / y(C154), F151, (0.4724822342945369, 0.4781277558286092)) → E154
  466. Segment(E154, A154) → F154
  467. Rotate(C154, ((-π)) / 2 + a, E154) → C155
  468. Intersect(((-(x(C155) / y(C155))) * x) - z(C155) / y(C155), F152, (0.5267622227376747, 0.47923562015382776)) → E155
  469. Segment(E155, A155) → F155
  470. Rotate(C155, ((-π)) / 2 + a, E155) → C156
  471. Intersect(((-(x(C156) / y(C156))) * x) - z(C156) / y(C156), F153, (0.5250207651658653, 0.5218870290200694)) → E156
  472. Segment(E156, A156) → F156
  473. Rotate(C156, ((-π)) / 2 + a, E156) → C157
  474. Intersect(((-(x(C157) / y(C157))) * x) - z(C157) / y(C157), F154, (0.47248193647482045, 0.5186672449266323)) → E157
  475. Segment(E157, A157) → F157
  476. Rotate(C157, ((-π)) / 2 + a, E157) → C158
  477. Intersect(((-(x(C158) / y(C158))) * x) - z(C158) / y(C158), F155, (0.47579209518340027, 0.47819531068455845)) → E158
  478. Segment(E158, A158) → F158
  479. Rotate(C158, ((-π)) / 2 + a, E158) → C159
  480. Intersect(((-(x(C159) / y(C159))) * x) - z(C159) / y(C159), F156, (0.5265923804296099, 0.48339536187900245)) → E159
  481. Segment(E159, A159) → F159
  482. Rotate(C159, ((-π)) / 2 + a, E159) → C160
  483. Intersect(((-(x(C160) / y(C160))) * x) - z(C160) / y(C160), F157, (0.5218807169433148, 0.5216945946325611)) → E160
  484. Segment(E160, A160) → F160
  485. Rotate(C160, ((-π)) / 2 + a, E160) → C161
  486. Intersect(((-(x(C161) / y(C161))) * x) - z(C161) / y(C161), F158, (0.4728113938637827, 0.5146391064125786)) → E161
  487. Segment(E161, A161) → F161
  488. Rotate(C161, ((-π)) / 2 + a, E161) → C162
  489. Intersect(((-(x(C162) / y(C162))) * x) - z(C162) / y(C162), F159, (0.47876259694626144, 0.47849937908033935)) → E162
  490. Segment(E162, A162) → F162
  491. Rotate(C162, ((-π)) / 2 + a, E162) → C163
  492. Intersect(((-(x(C163) / y(C163))) * x) - z(C163) / y(C163), F160, (0.5261129714394467, 0.48729228629896904)) → E163
  493. Segment(E163, A163) → F163
  494. Rotate(C163, ((-π)) / 2 + a, E163) → C164
  495. Intersect(((-(x(C164) / y(C164))) * x) - z(C164) / y(C164), F161, (0.5190789779968878, 0.5212917434234678)) → E164
  496. Segment(E164, A164) → F164
  497. Rotate(C164, ((-π)) / 2 + a, E164) → C165
  498. Intersect(((-(x(C165) / y(C165))) * x) - z(C165) / y(C165), F162, (0.47343162322205024, 0.5108726545572846)) → E165
  499. Segment(E165, A165) → F165
  500. Rotate(C165, ((-π)) / 2 + a, E165) → C166
  501. Intersect(((-(x(C166) / y(C166))) * x) - z(C166) / y(C166), F163, (0.4813968445217981, 0.4789885556659641)) → E166
  502. Segment(E166, A166) → F166
  503. Rotate(C166, ((-π)) / 2 + a, E166) → C167
  504. Intersect(((-(x(C167) / y(C167))) * x) - z(C167) / y(C167), F164, (0.5253605223517758, 0.4909293184775717)) → E167
  505. Segment(E167, A167) → F167
  506. Rotate(C167, ((-π)) / 2 + a, E167) → C168
  507. Intersect(((-(x(C168) / y(C168))) * x) - z(C168) / y(C168), F165, (0.5166104905042127, 0.5207283068195692)) → E168
  508. Segment(E168, A168) → F168
  509. Rotate(C168, ((-π)) / 2 + a, E168) → C169
  510. Intersect(((-(x(C169) / y(C169))) * x) - z(C169) / y(C169), F166, (0.47430821875585116, 0.5073637176884135)) → E169
  511. Segment(E169, A169) → F169
  512. Rotate(C169, ((-π)) / 2 + a, E169) → C170
  513. Intersect(((-(x(C170) / y(C170))) * x) - z(C170) / y(C170), F167, (0.4837017367742911, 0.47961457635057947)) → E170
  514. Segment(E170, A170) → F170
  515. Rotate(C170, ((-π)) / 2 + a, E170) → C171
  516. Intersect(((-(x(C171) / y(C171))) * x) - z(C171) / y(C171), F168, (0.5243673310402107, 0.49431171717397226)) → E171
  517. Segment(E171, A171) → F171
  518. Rotate(C171, ((-π)) / 2 + a, E171) → C172
  519. Intersect(((-(x(C172) / y(C172))) * x) - z(C172) / y(C172), F169, (0.514466619718183, 0.5200509920792173)) → E172
  520. Segment(E172, A172) → F172
  521. Rotate(C172, ((-π)) / 2 + a, E172) → C173
  522. Intersect(((-(x(C173) / y(C173))) * x) - z(C173) / y(C173), F170, (0.47541097162960166, 0.5041061048010673)) → E173
  523. Segment(E173, A173) → F173
  524. Rotate(C173, ((-π)) / 2 + a, E173) → C174
  525. Intersect(((-(x(C174) / y(C174))) * x) - z(C174) / y(C174), F171, (0.4856875458266052, 0.48033227680023716)) → E174
  526. Segment(E174, A174) → F174
  527. Rotate(C174, ((-π)) / 2 + a, E174) → C175
  528. Intersect(((-(x(C175) / y(C175))) * x) - z(C175) / y(C175), F172, (0.5231615418761095, 0.4974464554531839)) → E175
  529. Segment(E175, A175) → F175
  530. Rotate(C175, ((-π)) / 2 + a, E175) → C176
  531. Intersect(((-(x(C176) / y(C176))) * x) - z(C176) / y(C176), F173, (0.5126355480455106, 0.5193034374271281)) → E176
  532. Segment(E176, A176) → F176
  533. Rotate(C176, ((-π)) / 2 + a, E176) → C177
  534. Intersect(((-(x(C177) / y(C177))) * x) - z(C177) / y(C177), F174, (0.47671377196942666, 0.5010922063360094)) → E177
  535. Segment(E177, A177) → F177
  536. Rotate(C177, ((-π)) / 2 + a, E177) → C178
  537. Intersect(((-(x(C178) / y(C178))) * x) - z(C178) / y(C178), F175, (0.48736754936989024, 0.4810995256610032)) → E178
  538. Segment(E178, A178) → F178
  539. Rotate(C178, ((-π)) / 2 + a, E178) → C179
  540. Intersect(((-(x(C179) / y(C179))) * x) - z(C179) / y(C179), F176, (0.5217672653177532, 0.5003416383777769)) → E179
  541. Segment(E179, A179) → F179
  542. Rotate(C179, ((-π)) / 2 + a, E179) → C180
  543. Intersect(((-(x(C180) / y(C180))) * x) - z(C180) / y(C180), F177, (0.5111026166237308, 0.5185262885381166)) → E180
  544. Segment(E180, A180) → F180
  545. Rotate(C180, ((-π)) / 2 + a, E180) → C181
  546. Intersect(((-(x(C181) / y(C181))) * x) - z(C181) / y(C181), F178, (0.4781944687927023, 0.49831355819540224)) → E181
  547. Segment(E181, A181) → F181
  548. Rotate(C181, ((-π)) / 2 + a, E181) → C182
  549. Intersect(((-(x(C182) / y(C182))) * x) - z(C182) / y(C182), F179, (0.4887577148537453, 0.4818771402487473)) → E182
  550. Segment(E182, A182) → F182
  551. Rotate(C182, ((-π)) / 2 + a, E182) → C183
  552. Intersect(((-(x(C183) / y(C183))) * x) - z(C183) / y(C183), F180, (0.5202047374334833, 0.5030059570774752)) → E183
  553. Segment(E183, A183) → F183
  554. Rotate(C183, ((-π)) / 2 + a, E183) → C184
  555. Intersect(((-(x(C184) / y(C184))) * x) - z(C184) / y(C184), F181, (0.5098506157777354, 0.5177572888478607)) → E184
  556. Segment(E184, A184) → F184
  557. Rotate(C184, ((-π)) / 2 + a, E184) → C185
  558. Intersect(((-(x(C185) / y(C185))) * x) - z(C185) / y(C185), F182, (0.47983469197896067, 0.49576136981889973)) → E185
  559. Segment(E185, A185) → F185
  560. Rotate(C185, ((-π)) / 2 + a, E185) → C186
  561. Intersect(((-(x(C186) / y(C186))) * x) - z(C186) / y(C186), F183, (0.4898764339044062, 0.48262879200987363)) → E186
  562. Segment(E186, A186) → F186
  563. Rotate(C186, ((-π)) / 2 + a, E186) → C187
  564. Intersect(((-(x(C187) / y(C187))) * x) - z(C187) / y(C187), F184, (0.518490515570705, 0.5054481782785198)) → E187
  565. Segment(E187, A187) → F187
  566. Rotate(C187, ((-π)) / 2 + a, E187) → C188
  567. Intersect(((-(x(C188) / y(C188))) * x) - z(C188) / y(C188), F185, (0.508860026267391, 0.5170313766018616)) → E188
  568. Segment(E188, A188) → F188
  569. Rotate(C188, ((-π)) / 2 + a, E188) → C189
  570. Intersect(((-(x(C189) / y(C189))) * x) - z(C189) / y(C189), F186, (0.4816196397478476, 0.49342701730974414)) → E189
  571. Segment(E189, A189) → F189
  572. Rotate(C189, ((-π)) / 2 + a, E189) → C190
  573. Intersect(((-(x(C190) / y(C190))) * x) - z(C190) / y(C190), F187, (0.49074430481146736, 0.4833209086289044)) → E190
  574. Segment(E190, A190) → F190
  575. Rotate(C190, ((-π)) / 2 + a, E190) → C191
  576. Intersect(((-(x(C191) / y(C191))) * x) - z(C191) / y(C191), F188, (0.5166377070216949, 0.5076766682547229)) → E191
  577. Segment(E191, A191) → F191
  578. Rotate(C191, ((-π)) / 2 + a, E191) → C192
  579. Intersect(((-(x(C192) / y(C192))) * x) - z(C192) / y(C192), F189, (0.5081092137233985, 0.5163807819769756)) → E192
  580. Segment(E192, A192) → F192
  581. Rotate(C192, ((-π)) / 2 + a, E192) → C193
  582. Intersect(((-(x(C193) / y(C193))) * x) - z(C193) / y(C193), F190, (0.4835378344830586, 0.4913025026749718)) → E193
  583. Segment(E193, A193) → F193
  584. Rotate(C193, ((-π)) / 2 + a, E193) → C194
  585. Intersect(((-(x(C194) / y(C194))) * x) - z(C194) / y(C194), F191, (0.4913839604574867, 0.4839225792410264)) → E194
  586. Segment(E194, A194) → F194
  587. Rotate(C194, ((-π)) / 2 + a, E194) → C195
  588. Intersect(((-(x(C195) / y(C195))) * x) - z(C195) / y(C195), F192, (0.5146562281501004, 0.5096989501318777)) → E195
  589. Segment(E195, A195) → F195
  590. Rotate(C195, ((-π)) / 2 + a, E195) → C196
  591. Intersect(((-(x(C196) / y(C196))) * x) - z(C196) / y(C196), F193, (0.5075745791173564, 0.515835118022026)) → E196
  592. Segment(E196, A196) → F196
  593. Rotate(C196, ((-π)) / 2 + a, E196) → C197
  594. Intersect(((-(x(C197) / y(C197))) * x) - z(C197) / y(C197), F194, (0.48558084914371913, 0.48938088023107457)) → E197
  595. Segment(E197, A197) → F197
  596. Rotate(C197, ((-π)) / 2 + a, E197) → C198
  597. Intersect(((-(x(C198) / y(C198))) * x) - z(C198) / y(C198), F195, (0.49181993863148515, 0.48440546880132684)) → E198
  598. Segment(E198, A198) → F198
  599. Rotate(C198, ((-π)) / 2 + a, E198) → C199
  600. Intersect(((-(x(C199) / y(C199))) * x) - z(C199) / y(C199), F196, (0.5125530920224594, 0.5115212935317536)) → E199
  601. Segment(E199, A199) → F199
  602. Rotate(C199, ((-π)) / 2 + a, E199) → C200
  603. Intersect(((-(x(C200) / y(C200))) * x) - z(C200) / y(C200), F197, (0.507230668531766, 0.5154214595647779)) → E200
  604. Segment(E200, A200) → F200
  605. First(L_1, n) → seglist
  606. Mirror(seglist, g) → seglist'
  607. Mirror(poly1, g) → poly1'
  608. Mirror(poly1, f) → poly1'_1
  609. Mirror(seglist, f) → seglist'_1
  610. Rotate(poly1, π, B) → poly1'_2
  611. Rotate(seglist, π, B) → seglist'_2