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Slide 7: Statistical Characteristics, Secant Lines, Confidence Intervals, Median

Slide 7: Statistical Characteristics, Secant Lines, Confidence Intervals, Median
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2014-04-06 11:06
TrigonometryTransformation
In collections Phebe Tanner Tessellation Rotation
① This GeoGebra example presents a dynamic composite figure that integrates statistical characteristics, secant lines, confidence intervals, median values, and cosine functions, likely illustrating how geometric constructions can represent statistical concepts. ② Core mathematical concepts include statistical measures (median), secant lines (lines through two points on a curve), confidence intervals (range estimating a parameter), cosine functions, and geometric transformations like rotation. ③ Construction details: from the summary, commands Polygon, Segment, and Rotate are used, creating multiple points (A, B, C, D...) and segments (a, b, c, d...), with rotations generating symmetric or dynamic configurations, possibly to show how confidence intervals shift or how secant slopes relate to cosine curves. ④ Suitable for high school or undergraduate students, this example helps visualize the intersection of statistics and geometry, and serves as a template for interactive lessons on data-driven geometric interpretations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 3) → poly1, a, b, c, C
  2. Segment(B, D) → d
  3. Segment(D, E) → e
  4. Segment(E, F) → f
  5. Segment(F, G) → g
  6. Segment(G, H) → h
  7. Segment(H, I) → i
  8. Segment(I, J) → j
  9. Segment(J, K) → k
  10. Segment(K, L) → l
  11. Segment(L, M) → m
  12. Segment(M, N) → n
  13. Segment(N, O) → p
  14. Segment(O, P) → q
  15. Segment(P, Q) → r
  16. Segment(Q, R) → s
  17. Segment(R, S) → t
  18. Segment(S, T) → a_1
  19. Segment(T, U) → b_1
  20. Segment(U, V) → c_1
  21. Segment(V, W) → d_1
  22. Segment(W, Z) → e_1
  23. Segment(Z, A_1) → f_1
  24. Segment(A_1, B_1) → g_1
  25. Segment(B_1, C) → h_1
  26. Rotate(B, 60*°, B) → B'
  27. Rotate(D, 60*°, B) → D'
  28. Segment(B', D') → d'
  29. Rotate(D, 60*°, B) → D'_1
  30. Rotate(E, 60*°, B) → E'
  31. Segment(D'_1, E') → e'
  32. Rotate(E, 60*°, B) → E'_1
  33. Rotate(F, 60*°, B) → F'
  34. Segment(E'_1, F') → f'
  35. Rotate(F, 60*°, B) → F'_1
  36. Rotate(G, 60*°, B) → G'
  37. Segment(F'_1, G') → g'
  38. Rotate(G, 60*°, B) → G'_1
  39. Rotate(H, 60*°, B) → H'
  40. Segment(G'_1, H') → h'
  41. Rotate(H, 60*°, B) → H'_1
  42. Rotate(I, 60*°, B) → I'
  43. Segment(H'_1, I') → i'
  44. Rotate(I, 60*°, B) → I'_1
  45. Rotate(J, 60*°, B) → J'
  46. Segment(I'_1, J') → j'
  47. Rotate(J, 60*°, B) → J'_1
  48. Rotate(K, 60*°, B) → K'
  49. Segment(J'_1, K') → k'
  50. Rotate(K, 60*°, B) → K'_1
  51. Rotate(L, 60*°, B) → L'
  52. Segment(K'_1, L') → l'
  53. Rotate(L, 60*°, B) → L'_1
  54. Rotate(M, 60*°, B) → M'
  55. Segment(L'_1, M') → m'
  56. Rotate(M, 60*°, B) → M'_1
  57. Rotate(N, 60*°, B) → N'
  58. Segment(M'_1, N') → n'
  59. Rotate(N, 60*°, B) → N'_1
  60. Rotate(O, 60*°, B) → O'
  61. Segment(N'_1, O') → p'
  62. Rotate(O, 60*°, B) → O'_1
  63. Rotate(P, 60*°, B) → P'
  64. Segment(O'_1, P') → q'
  65. Rotate(P, 60*°, B) → P'_1
  66. Rotate(Q, 60*°, B) → Q'
  67. Segment(P'_1, Q') → r'
  68. Rotate(Q, 60*°, B) → Q'_1
  69. Rotate(R, 60*°, B) → R'
  70. Segment(Q'_1, R') → s'
  71. Rotate(R, 60*°, B) → R'_1
  72. Rotate(S, 60*°, B) → S'
  73. Segment(R'_1, S') → t'
  74. Rotate(S, 60*°, B) → S'_1
  75. Rotate(T, 60*°, B) → T'
  76. Segment(S'_1, T') → i_1
  77. Rotate(T, 60*°, B) → T'_1
  78. Rotate(U, 60*°, B) → U'
  79. Segment(T'_1, U') → j_1
  80. Rotate(U, 60*°, B) → U'_1
  81. Rotate(V, 60*°, B) → V'
  82. Segment(U'_1, V') → k_1
  83. Rotate(V, 60*°, B) → V'_1
  84. Rotate(W, 60*°, B) → W'
  85. Segment(V'_1, W') → l_1
  86. Rotate(W, 60*°, B) → W'_1
  87. Rotate(Z, 60*°, B) → Z'
  88. Segment(W'_1, Z') → m_1
  89. Rotate(Z, 60*°, B) → Z'_1
  90. Rotate(A_1, 60*°, B) → C_1
  91. Segment(Z'_1, C_1) → n_1
  92. Rotate(A_1, 60*°, B) → D_1
  93. Rotate(B_1, 60*°, B) → E_1
  94. Segment(D_1, E_1) → p_1
  95. Rotate(B_1, 60*°, B) → F_1
  96. Rotate(C, 60*°, B) → C'
  97. Segment(F_1, C') → q_1
  98. Rotate(B', 60*°, A) → B''
  99. Rotate(D', 60*°, A) → D''
  100. Segment(B'', D'') → d''
  101. Rotate(D'_1, 60*°, A) → G_1
  102. Rotate(E', 60*°, A) → E''
  103. Segment(G_1, E'') → e''
  104. Rotate(E'_1, 60*°, A) → H_1
  105. Rotate(F', 60*°, A) → F''
  106. Segment(H_1, F'') → f''
  107. Rotate(F'_1, 60*°, A) → I_1
  108. Rotate(G', 60*°, A) → G''
  109. Segment(I_1, G'') → g''
  110. Rotate(G'_1, 60*°, A) → J_1
  111. Rotate(H', 60*°, A) → H''
  112. Segment(J_1, H'') → h''
  113. Rotate(H'_1, 60*°, A) → K_1
  114. Rotate(I', 60*°, A) → I''
  115. Segment(K_1, I'') → i''
  116. Rotate(I'_1, 60*°, A) → L_1
  117. Rotate(J', 60*°, A) → J''
  118. Segment(L_1, J'') → j''
  119. Rotate(J'_1, 60*°, A) → M_1
  120. Rotate(K', 60*°, A) → K''
  121. Segment(M_1, K'') → k''
  122. Rotate(K'_1, 60*°, A) → N_1
  123. Rotate(L', 60*°, A) → L''
  124. Segment(N_1, L'') → l''
  125. Rotate(L'_1, 60*°, A) → O_1
  126. Rotate(M', 60*°, A) → M''
  127. Segment(O_1, M'') → m''
  128. Rotate(M'_1, 60*°, A) → P_1
  129. Rotate(N', 60*°, A) → N''
  130. Segment(P_1, N'') → n''
  131. Rotate(N'_1, 60*°, A) → Q_1
  132. Rotate(O', 60*°, A) → O''
  133. Segment(Q_1, O'') → p''
  134. Rotate(O'_1, 60*°, A) → R_1
  135. Rotate(P', 60*°, A) → P''
  136. Segment(R_1, P'') → q''
  137. Rotate(P'_1, 60*°, A) → S_1
  138. Rotate(Q', 60*°, A) → Q''
  139. Segment(S_1, Q'') → r''
  140. Rotate(Q'_1, 60*°, A) → T_1
  141. Rotate(R', 60*°, A) → R''
  142. Segment(T_1, R'') → s''
  143. Rotate(R'_1, 60*°, A) → U_1
  144. Rotate(S', 60*°, A) → S''
  145. Segment(U_1, S'') → t''
  146. Rotate(S'_1, 60*°, A) → V_1
  147. Rotate(T', 60*°, A) → T''
  148. Segment(V_1, T'') → r_1
  149. Rotate(T'_1, 60*°, A) → W_1
  150. Rotate(U', 60*°, A) → U''
  151. Segment(W_1, U'') → s_1
  152. Rotate(U'_1, 60*°, A) → Z_1
  153. Rotate(V', 60*°, A) → V''
  154. Segment(Z_1, V'') → t_1
  155. Rotate(V'_1, 60*°, A) → A_2
  156. Rotate(W', 60*°, A) → W''
  157. Segment(A_2, W'') → a_2
  158. Rotate(W'_1, 60*°, A) → B_2
  159. Rotate(Z', 60*°, A) → Z''
  160. Segment(B_2, Z'') → b_2
  161. Rotate(Z'_1, 60*°, A) → C_2
  162. Rotate(C_1, 60*°, A) → D_2
  163. Segment(C_2, D_2) → c_2
  164. Rotate(D_1, 60*°, A) → E_2
  165. Rotate(E_1, 60*°, A) → F_2
  166. Segment(E_2, F_2) → d_2
  167. Rotate(F_1, 60*°, A) → G_2
  168. Rotate(C', 60*°, A) → C''
  169. Segment(G_2, C'') → e_2
  170. Rotate(B, 60*°, A) → B'_1
  171. Polygon(B, D', M', M'_1, O', P', Q', R', S', T', U', V', E', W', Z', C_1, E_1, A, F_2, D_2, Z'', W'', V'', F', U'', T'', S'', R'', Q'', P'', O'', N'', M'', L'', G', K'', J'', I'', H'', G'', E'', H_1, D'', C, B_1, H', A_1, Z, W, V, U, T, S, R, Q, P, I', O, N, M, L, K, J, I, H, G, F, J', E, D, K', L') → poly2, b_3, l'_1, m'_1, m'_2, o', p'_1, q'_1, r'_1, s'_1, t'_1, u', d'_1, v', w', z', c_3, e_3, a_3, f_2, d_3, z'', w'', e'_1, v'', u'', t''_1, s''_1, r''_1, q''_1, p''_1, o'', n''_1, m''_1, f'_1, l''_1, k''_1, j''_1, i''_1, h''_1, g''_1, e''_1, h_2, d''_1, c_4, g'_1, b_4, a_4, z, w, v, u, t_2, s_2, r_2, q_2, h'_1, p_2, o, n_2, m_2, l_2, k_2, j_2, i_2, h_3, g_2, i'_1, f_3, e_4, d_4, j'_1, k'_1
  172. Rotate(B, 60*°, A) → B'_2
  173. Rotate(D', 60*°, A) → D''_1
  174. Rotate(E', 60*°, A) → E''_1
  175. Rotate(F', 60*°, A) → F''_1
  176. Rotate(G', 60*°, A) → G''_1
  177. Rotate(H', 60*°, A) → H''_1
  178. Rotate(I', 60*°, A) → I''_1
  179. Rotate(J', 60*°, A) → J''_1
  180. Rotate(K', 60*°, A) → K''_1
  181. Rotate(L', 60*°, A) → L''_1
  182. Rotate(M', 60*°, A) → M''_1
  183. Rotate(M'_1, 60*°, A) → H_2
  184. Rotate(O', 60*°, A) → O''_1
  185. Rotate(P', 60*°, A) → P''_1
  186. Rotate(Q', 60*°, A) → Q''_1
  187. Rotate(R', 60*°, A) → R''_1
  188. Rotate(S', 60*°, A) → S''_1
  189. Rotate(T', 60*°, A) → T''_1
  190. Rotate(U', 60*°, A) → U''_1
  191. Rotate(V', 60*°, A) → V''_1
  192. Rotate(W', 60*°, A) → W''_1
  193. Rotate(Z', 60*°, A) → Z''_1
  194. Rotate(C_1, 60*°, A) → I_2
  195. Rotate(E_1, 60*°, A) → J_2
  196. Rotate(A, 60*°, A) → A'
  197. Rotate(F_2, 60*°, A) → K_2
  198. Rotate(D_2, 60*°, A) → L_2
  199. Rotate(Z'', 60*°, A) → Z'''
  200. Rotate(W'', 60*°, A) → W'''
  201. Rotate(V'', 60*°, A) → V'''
  202. Rotate(U'', 60*°, A) → U'''
  203. Rotate(T'', 60*°, A) → T'''
  204. Rotate(S'', 60*°, A) → S'''
  205. Rotate(R'', 60*°, A) → R'''
  206. Rotate(Q'', 60*°, A) → Q'''
  207. Rotate(P'', 60*°, A) → P'''
  208. Rotate(O'', 60*°, A) → O'''
  209. Rotate(N'', 60*°, A) → N'''
  210. Rotate(M'', 60*°, A) → M'''
  211. Rotate(L'', 60*°, A) → L'''
  212. Rotate(K'', 60*°, A) → K'''
  213. Rotate(J'', 60*°, A) → J'''
  214. Rotate(I'', 60*°, A) → I'''
  215. Rotate(H'', 60*°, A) → H'''
  216. Rotate(G'', 60*°, A) → G'''
  217. Rotate(E'', 60*°, A) → E'''
  218. Rotate(H_1, 60*°, A) → M_2
  219. Rotate(D'', 60*°, A) → D'''
  220. Rotate(C, 60*°, A) → C'_1
  221. Rotate(B_1, 60*°, A) → N_2
  222. Rotate(A_1, 60*°, A) → O_2
  223. Rotate(Z, 60*°, A) → Z'_2
  224. Rotate(W, 60*°, A) → W'_2
  225. Rotate(V, 60*°, A) → V'_2
  226. Rotate(U, 60*°, A) → U'_2
  227. Rotate(T, 60*°, A) → T'_2
  228. Rotate(S, 60*°, A) → S'_2
  229. Rotate(R, 60*°, A) → R'_2
  230. Rotate(Q, 60*°, A) → Q'_2
  231. Rotate(P, 60*°, A) → P'_2
  232. Rotate(O, 60*°, A) → O'_2
  233. Rotate(N, 60*°, A) → N'_2
  234. Rotate(M, 60*°, A) → M'_2
  235. Rotate(L, 60*°, A) → L'_2
  236. Rotate(K, 60*°, A) → K'_2
  237. Rotate(J, 60*°, A) → J'_2
  238. Rotate(I, 60*°, A) → I'_2
  239. Rotate(H, 60*°, A) → H'_2
  240. Rotate(G, 60*°, A) → G'_2
  241. Rotate(F, 60*°, A) → F'_2
  242. Rotate(E, 60*°, A) → E'_2
  243. Rotate(D, 60*°, A) → D'_2
  244. Polygon(B'_2, D''_1, M''_1, H_2, O''_1, P''_1, Q''_1, R''_1, S''_1, T''_1, U''_1, V''_1, E''_1, W''_1, Z''_1, I_2, J_2, A', K_2, L_2, Z''', W''', V''', F''_1, U''', T''', S''', R''', Q''', P''', O''', N''', M''', L''', G''_1, K''', J''', I''', H''', G''', E''', M_2, D''', C'_1, N_2, H''_1, O_2, Z'_2, W'_2, V'_2, U'_2, T'_2, S'_2, R'_2, Q'_2, P'_2, I''_1, O'_2, N'_2, M'_2, L'_2, K'_2, J'_2, I'_2, H'_2, G'_2, F'_2, J''_1, E'_2, D'_2, K''_1, L''_1) → poly2', b'_2, l''_2, m''_2, h_4, o''_1, p''_2, q''_2, r''_2, s''_2, t''_2, u''_1, d''_2, v''_1, w''_1, z''_1, i_3, j_3, a', k_3, l_3, z''', w''', e''_2, v''', u''', t''', s''', r''', q''', p''', o''', n''', m''', f''_1, l''', k''', j''', i''', h''', g''', e''', m_3, d''', c'_1, g''_2, n_3, o_2, z'_2, w'_2, v'_2, u'_2, t'_2, s'_2, r'_2, q'_2, h''_2, p'_2, o'_2, n'_2, m'_3, l'_2, k'_2, j'_2, i'_2, h'_2, g'_2, i''_2, f'_2, e'_2, d'_2, j''_2, k''_2
  245. Rotate(B, 60*°, A) → B'_3
  246. Rotate(D, 60*°, A) → D'_3
  247. Segment(B'_3, D'_3) → d'_3
  248. Rotate(D, 60*°, A) → D'_4
  249. Rotate(E, 60*°, A) → E'_3
  250. Segment(D'_4, E'_3) → e'_3
  251. Rotate(E, 60*°, A) → E'_4
  252. Rotate(F, 60*°, A) → F'_3
  253. Segment(E'_4, F'_3) → f'_3
  254. Rotate(F, 60*°, A) → F'_4
  255. Rotate(G, 60*°, A) → G'_3
  256. Segment(F'_4, G'_3) → g'_3
  257. Rotate(G, 60*°, A) → G'_4
  258. Rotate(H, 60*°, A) → H'_3
  259. Segment(G'_4, H'_3) → h'_3
  260. Rotate(H, 60*°, A) → H'_4
  261. Rotate(I, 60*°, A) → I'_3
  262. Segment(H'_4, I'_3) → i'_3
  263. Rotate(I, 60*°, A) → I'_4
  264. Rotate(J, 60*°, A) → J'_3
  265. Segment(I'_4, J'_3) → j'_3
  266. Rotate(J, 60*°, A) → J'_4
  267. Rotate(K, 60*°, A) → K'_3
  268. Segment(J'_4, K'_3) → k'_3
  269. Rotate(K, 60*°, A) → K'_4
  270. Rotate(L, 60*°, A) → L'_3
  271. Segment(K'_4, L'_3) → l'_3
  272. Rotate(L, 60*°, A) → L'_4
  273. Rotate(M, 60*°, A) → M'_3
  274. Segment(L'_4, M'_3) → m'_4
  275. Rotate(M, 60*°, A) → M'_4
  276. Rotate(N, 60*°, A) → N'_3
  277. Segment(M'_4, N'_3) → n'_1
  278. Rotate(N, 60*°, A) → N'_4
  279. Rotate(O, 60*°, A) → O'_3
  280. Segment(N'_4, O'_3) → p'_3
  281. Rotate(O, 60*°, A) → O'_4
  282. Rotate(P, 60*°, A) → P'_3
  283. Segment(O'_4, P'_3) → q'_3
  284. Rotate(P, 60*°, A) → P'_4
  285. Rotate(Q, 60*°, A) → Q'_3
  286. Segment(P'_4, Q'_3) → r'_3
  287. Rotate(Q, 60*°, A) → Q'_4
  288. Rotate(R, 60*°, A) → R'_3
  289. Segment(Q'_4, R'_3) → s'_3
  290. Rotate(R, 60*°, A) → R'_4
  291. Rotate(S, 60*°, A) → S'_3
  292. Segment(R'_4, S'_3) → t'_3
  293. Rotate(S, 60*°, A) → S'_4
  294. Rotate(T, 60*°, A) → T'_3
  295. Segment(S'_4, T'_3) → g_3
  296. Rotate(T, 60*°, A) → T'_4
  297. Rotate(U, 60*°, A) → U'_3
  298. Segment(T'_4, U'_3) → p_3
  299. Rotate(U, 60*°, A) → U'_4
  300. Rotate(V, 60*°, A) → V'_3
  301. Segment(U'_4, V'_3) → q_3
  302. Rotate(V, 60*°, A) → V'_4
  303. Rotate(W, 60*°, A) → W'_3
  304. Segment(V'_4, W'_3) → r_3
  305. Rotate(W, 60*°, A) → W'_4
  306. Rotate(Z, 60*°, A) → Z'_3
  307. Segment(W'_4, Z'_3) → s_3
  308. Rotate(Z, 60*°, A) → Z'_4
  309. Rotate(A_1, 60*°, A) → P_2
  310. Segment(Z'_4, P_2) → t_3
  311. Rotate(A_1, 60*°, A) → Q_2
  312. Rotate(B_1, 60*°, A) → R_2
  313. Segment(Q_2, R_2) → f_4
  314. Rotate(B_1, 60*°, A) → S_2
  315. Rotate(C, 60*°, A) → C'_2
  316. Segment(S_2, C'_2) → g_4
  317. Rotate(B', 60*°, A) → B''_1
  318. Rotate(D', 60*°, A) → D''_2
  319. Segment(B''_1, D''_2) → d''_3
  320. Rotate(D'_1, 60*°, A) → T_2
  321. Rotate(E', 60*°, A) → E''_2
  322. Segment(T_2, E''_2) → e''_3
  323. Rotate(E'_1, 60*°, A) → U_2
  324. Rotate(F', 60*°, A) → F''_2
  325. Segment(U_2, F''_2) → f''_2
  326. Rotate(F'_1, 60*°, A) → V_2
  327. Rotate(G', 60*°, A) → G''_2
  328. Segment(V_2, G''_2) → g''_3
  329. Rotate(G'_1, 60*°, A) → W_2
  330. Rotate(H', 60*°, A) → H''_2
  331. Segment(W_2, H''_2) → h''_3
  332. Rotate(H'_1, 60*°, A) → Z_2
  333. Rotate(I', 60*°, A) → I''_2
  334. Segment(Z_2, I''_2) → i''_3
  335. Rotate(I'_1, 60*°, A) → A_3
  336. Rotate(J', 60*°, A) → J''_2
  337. Segment(A_3, J''_2) → j''_3
  338. Rotate(J'_1, 60*°, A) → B_3
  339. Rotate(K', 60*°, A) → K''_2
  340. Segment(B_3, K''_2) → k''_3
  341. Rotate(K'_1, 60*°, A) → C_3
  342. Rotate(L', 60*°, A) → L''_2
  343. Segment(C_3, L''_2) → l''_3
  344. Rotate(L'_1, 60*°, A) → D_3
  345. Rotate(M', 60*°, A) → M''_2
  346. Segment(D_3, M''_2) → m''_3
  347. Rotate(M'_1, 60*°, A) → E_3
  348. Rotate(N', 60*°, A) → N''_1
  349. Segment(E_3, N''_1) → n''_2
  350. Rotate(N'_1, 60*°, A) → F_3
  351. Rotate(O', 60*°, A) → O''_2
  352. Segment(F_3, O''_2) → p''_3
  353. Rotate(O'_1, 60*°, A) → G_3
  354. Rotate(P', 60*°, A) → P''_2
  355. Segment(G_3, P''_2) → q''_3
  356. Rotate(P'_1, 60*°, A) → H_3
  357. Rotate(Q', 60*°, A) → Q''_2
  358. Segment(H_3, Q''_2) → r''_3
  359. Rotate(Q'_1, 60*°, A) → I_3
  360. Rotate(R', 60*°, A) → R''_2
  361. Segment(I_3, R''_2) → s''_3
  362. Rotate(R'_1, 60*°, A) → J_3
  363. Rotate(S', 60*°, A) → S''_2
  364. Segment(J_3, S''_2) → t''_3
  365. Rotate(S'_1, 60*°, A) → K_3
  366. Rotate(T', 60*°, A) → T''_2
  367. Segment(K_3, T''_2) → i_4
  368. Rotate(T'_1, 60*°, A) → L_3
  369. Rotate(U', 60*°, A) → U''_2
  370. Segment(L_3, U''_2) → j_4
  371. Rotate(U'_1, 60*°, A) → M_3
  372. Rotate(V', 60*°, A) → V''_2
  373. Segment(M_3, V''_2) → k_4
  374. Rotate(V'_1, 60*°, A) → N_3
  375. Rotate(W', 60*°, A) → W''_2
  376. Segment(N_3, W''_2) → l_4
  377. Rotate(W'_1, 60*°, A) → O_3
  378. Rotate(Z', 60*°, A) → Z''_2
  379. Segment(O_3, Z''_2) → m_4
  380. Rotate(Z'_1, 60*°, A) → P_3
  381. Rotate(C_1, 60*°, A) → Q_3
  382. Segment(P_3, Q_3) → n_4
  383. Rotate(D_1, 60*°, A) → R_3
  384. Rotate(E_1, 60*°, A) → S_3
  385. Segment(R_3, S_3) → p_4
  386. Rotate(F_1, 60*°, A) → T_3
  387. Rotate(C', 60*°, A) → C''_1
  388. Segment(T_3, C''_1) → q_4
  389. Rotate(B'', 60*°, A) → B'''
  390. Rotate(D'', 60*°, A) → D'''_1
  391. Segment(B''', D'''_1) → d'''_1
  392. Rotate(G_1, 60*°, A) → U_3
  393. Rotate(E'', 60*°, A) → E'''_1
  394. Segment(U_3, E'''_1) → e'''_1
  395. Rotate(H_1, 60*°, A) → V_3
  396. Rotate(F'', 60*°, A) → F'''
  397. Segment(V_3, F''') → f'''
  398. Rotate(I_1, 60*°, A) → W_3
  399. Rotate(G'', 60*°, A) → G'''_1
  400. Segment(W_3, G'''_1) → g'''_1
  401. Rotate(J_1, 60*°, A) → Z_3
  402. Rotate(H'', 60*°, A) → H'''_1
  403. Segment(Z_3, H'''_1) → h'''_1
  404. Rotate(K_1, 60*°, A) → A_4
  405. Rotate(I'', 60*°, A) → I'''_1
  406. Segment(A_4, I'''_1) → i'''_1
  407. Rotate(L_1, 60*°, A) → B_4
  408. Rotate(J'', 60*°, A) → J'''_1
  409. Segment(B_4, J'''_1) → j'''_1
  410. Rotate(M_1, 60*°, A) → C_4
  411. Rotate(K'', 60*°, A) → K'''_1
  412. Segment(C_4, K'''_1) → k'''_1
  413. Rotate(N_1, 60*°, A) → D_4
  414. Rotate(L'', 60*°, A) → L'''_1
  415. Segment(D_4, L'''_1) → l'''_1
  416. Rotate(O_1, 60*°, A) → E_4
  417. Rotate(M'', 60*°, A) → M'''_1
  418. Segment(E_4, M'''_1) → m'''_1
  419. Rotate(P_1, 60*°, A) → F_4
  420. Rotate(N'', 60*°, A) → N'''_1
  421. Segment(F_4, N'''_1) → n'''_1
  422. Rotate(Q_1, 60*°, A) → G_4
  423. Rotate(O'', 60*°, A) → O'''_1
  424. Segment(G_4, O'''_1) → p'''_1
  425. Rotate(R_1, 60*°, A) → H_4
  426. Rotate(P'', 60*°, A) → P'''_1
  427. Segment(H_4, P'''_1) → q'''_1
  428. Rotate(S_1, 60*°, A) → I_4
  429. Rotate(Q'', 60*°, A) → Q'''_1
  430. Segment(I_4, Q'''_1) → r'''_1
  431. Rotate(T_1, 60*°, A) → J_4
  432. Rotate(R'', 60*°, A) → R'''_1
  433. Segment(J_4, R'''_1) → s'''_1
  434. Rotate(U_1, 60*°, A) → K_4
  435. Rotate(S'', 60*°, A) → S'''_1
  436. Segment(K_4, S'''_1) → t'''_1
  437. Rotate(V_1, 60*°, A) → L_4
  438. Rotate(T'', 60*°, A) → T'''_1
  439. Segment(L_4, T'''_1) → r_4
  440. Rotate(W_1, 60*°, A) → M_4
  441. Rotate(U'', 60*°, A) → U'''_1
  442. Segment(M_4, U'''_1) → s_4
  443. Rotate(Z_1, 60*°, A) → N_4
  444. Rotate(V'', 60*°, A) → V'''_1
  445. Segment(N_4, V'''_1) → t_4
  446. Rotate(A_2, 60*°, A) → O_4
  447. Rotate(W'', 60*°, A) → W'''_1
  448. Segment(O_4, W'''_1) → a_5
  449. Rotate(B_2, 60*°, A) → P_4
  450. Rotate(Z'', 60*°, A) → Z'''_1
  451. Segment(P_4, Z'''_1) → b_5
  452. Rotate(C_2, 60*°, A) → Q_4
  453. Rotate(D_2, 60*°, A) → R_4
  454. Segment(Q_4, R_4) → c_5
  455. Rotate(E_2, 60*°, A) → S_4
  456. Rotate(F_2, 60*°, A) → T_4
  457. Segment(S_4, T_4) → d_5
  458. Rotate(G_2, 60*°, A) → U_4
  459. Rotate(C'', 60*°, A) → C'''
  460. Segment(U_4, C''') → e_5
  461. Rotate(B'_1, 60*°, A) → V_4

AI Drawing Prompt Reference

Create a dynamic composite figure illustrating statistical characteristics, secant lines, confidence intervals, and median values, incorporating cosine functions. The figure should consist of multiple closed polygons formed by line segments, with rotations generating symmetric or dynamic configurations. Show secant lines passing through two points on a curve and confidence intervals estimating parameter ranges. The design should visualize the intersection of statistical concepts and geometric constructions, suitable for high school or undergraduate students.
The prompt above was compiled from the original drawing commands and is for reference only.