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My second spiral and polygonal stars

My second spiral and polygonal stars
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2020-01-29 04:16
PolygonAngleVectorTransformation
This example demonstrates a spiral composed of polygonal stars. It involves core mathematical concepts such as line segments, geometric transformations, kites, logic, fractions, and subtraction. The construction utilizes GeoGebra commands and objects like Circle, Line, Intersect, If, Rotate, Angle, Segment, and Textfield. It is suitable for middle school students and above to explore geometric constructions and transformations.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Draw a spiral composed of multiple polygonal stars. Start by drawing a circle and a line passing through its center. Choose a point on the circle and rotate it along the line to form a new circle. Repeat this process multiple times with a fixed rotation angle to create a spiral effect. On each circle, choose a point and rotate it to form a new polygonal star. Repeat this process multiple times to create a sequence of polygonal stars in a spiral pattern.
The prompt above was compiled from the original drawing commands and is for reference only.