多级实验设计与数据分析

多级实验设计与数据分析
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2014-09-21 16:12
所属专题 Complex Math
①本范例演示了如何设置多级实验并展示其数据分析过程;②涉及的核心数学概念包括线性代数在Rn空间的应用、几何图形的构造与变换;③作图要点提炼自构造摘要,使用了Line(线)、Point(点)、Circle(圆)、Segment(线段)、OrthogonalLine(垂线)、Polygon(多边形)、Vector(向量)、Translate(平移)、Intersect(交点)、LaTeX(公式)、CircleArc(圆弧)、Rotate(旋转)等GeoGebra命令与对象;④适合高中及以上数学学习者,用于理解实验设计与空间线性代数的实际应用。

GeoGebra 命令及参数

  1. Line(A, B) → a
  2. Point(a) → C
  3. Circle(C, D) → c
  4. Segment(C, D) → b
  5. Line(E, xAxis) → d
  6. OrthogonalLine(F, d) → e
  7. Line(G, e) → f
  8. Line(H, d) → g
  9. Line(I, b) → h
  10. Point(f) → J
  11. Point(d) → L
  12. Point(c) → K
  13. Segment(D, J) → i
  14. Segment(J, K) → j
  15. Segment(K, L) → k
  16. Segment(L, D) → z
  17. Segment(L, C) → m
  18. Polygon(M, N, O, P) → poly1, m_1, n, o, p
  19. Polygon(Q, R, S, T) → poly2, q, r, s, t
  20. Polygon(U, V, W) → poly3, w, u, v
  21. Polygon(Z, A_1, B_1) → poly4, b_1, z_1, a_1
  22. Vector(C_1, D_1) → u_1
  23. Translate(Z, u_1) → Z'
  24. Translate(A_1, u_1) → E_1
  25. Translate(B_1, u_1) → F_1
  26. Vector(G_1, H_1) → v_1
  27. Translate(U, v_1) → U'
  28. Translate(V, v_1) → V'
  29. Translate(W, v_1) → W'
  30. Polygon(U', V', W') → poly3', w', u', v'
  31. Intersect(b, i) → I_1
  32. Intersect(i, j) → L_1
  33. Intersect(k, z) → N_1
  34. Intersect(k, z) → J_1
  35. Segment(J_1, K_1) → c_1
  36. Segment(C, M_1) → d_1
  37. Segment(K_1, M_1) → e_1
  38. Segment(O_1, K_1) → f_1
  39. Segment(O_1, P_1) → g_1
  40. Segment(P_1, M_1) → h_1
  41. Point(f_1) → Q_1
  42. Point(h_1) → R_1
  43. Segment(Q_1, R_1) → i_1
  44. Point(k) → S_1
  45. Point(m) → T_1
  46. Point(m_1) → W_1
  47. Point(m_1) → Z_1
  48. Vector(W_1, Z_1) → w_1
  49. Point(r) → A_2
  50. Point(r) → B_2
  51. Vector(A_2, B_2) → j_1
  52. Polygon(M_2, N_2, O_2, P_2) → poly1_1, m_2, n_1, o_1, p_1
  53. Point(m_2) → W_2
  54. Point(m_2) → Z_2
  55. Polygon(M_3, N_3, O_3, P_3) → poly1_2, m_3, n_2, o_2, p_2
  56. Point(m_3) → W_3
  57. Point(m_3) → Z_3
  58. Polygon(M_4, N_4, O_4, P_4) → poly1_3, m_4, n_3, o_3, p_3
  59. Point(m_4) → W_4
  60. Point(m_4) → Z_4
  61. Point(q) → C_2
  62. Point(q) → D_2
  63. Vector(C_2, D_2) → k_1
  64. Point(n) → E_2
  65. Point(n) → F_2
  66. Vector(E_2, F_2) → l_1
  67. Intersect(m_1, n) → G_2
  68. Vector(G_2, H_2) → l
  69. Vector(I_2, J_2) → q_1
  70. Vector(K_2, L_2) → r_1
  71. Translate(Q, r_1) → Q'
  72. Translate(R, r_1) → R'
  73. Translate(S, r_1) → S'
  74. Translate(T, r_1) → T'
  75. Polygon(Q', R', S', T') → poly2', q', r', s', t'
  76. Vector(Q_2, R_2) → s_1
  77. Translate(M, s_1) → M'
  78. Translate(N, s_1) → N'
  79. Translate(O, s_1) → O'
  80. Translate(P, s_1) → P'
  81. Polygon(M', N', O', P') → poly1', m', n', o', p'
  82. Intersect(o', p') → S_2
  83. Intersect(o, p) → T_2
  84. Segment(S_2, T_2) → t_1
  85. Vector(U_2, V_2) → u_2
  86. Translate(O_1, u_2) → A_3
  87. Translate(P_1, u_2) → B_3
  88. Segment(A_3, B_3) → a_2
  89. Vector(C_3, D_3) → v_2
  90. Translate(C, v_2) → C'
  91. Intersect(m', p') → E_3
  92. Point(r) → F_3
  93. Segment(E_3, F_3) → b_2
  94. Point(r) → G_3
  95. Intersect(m', p') → H_3
  96. Vector(G_3, H_3) → w_2
  97. Vector(I_3, J_3) → c_2
  98. Translate(K, c_2) → K'
  99. Translate(L, c_2) → L'
  100. Segment(K', L') → k'
  101. Vector(K_3, L_3) → d_2
  102. Translate(L, d_2) → L'_1
  103. Translate(C, d_2) → C'_1
  104. Segment(L'_1, C'_1) → m'_1
  105. Vector(Q_3, R_3) → e_2
  106. Translate(A_3, e_2) → S_3
  107. Translate(B_3, e_2) → T_3
  108. Segment(S_3, T_3) → f_2
  109. Polygon(U_3, V_3, A_4, B_4) → poly5, u_3, v_3, a_4, b_4
  110. Vector(G_4, H_4) → g_2
  111. Translate(L, g_2) → L'_2
  112. Translate(D, g_2) → D'
  113. Segment(L'_2, D') → z'
  114. Vector(I_4, J_4) → h_2
  115. Translate(J, h_2) → J'
  116. Translate(K, h_2) → K'_1
  117. Segment(J', K'_1) → j'
  118. Vector(K_4, L_4) → i_2
  119. Translate(C, i_2) → C'_2
  120. Translate(D, i_2) → D'_1
  121. Segment(C'_2, D'_1) → b'
  122. Point(k') → Q_4
  123. Point(z') → R_4
  124. Segment(Q_4, R_4) → j_2
  125. Polygon(S_4, T_4, U_4, V_4) → poly6, s_4, t_4, u_4, v_4
  126. Intersect(u_3, b_4) → A_5
  127. Segment(A_5, B_5) → k_2
  128. Intersect(q, r) → C_5
  129. Segment(B_5, C_5) → l_2
  130. Point(k_2) → D_5
  131. Segment(D_5, E_5) → q_2
  132. Point(l_2) → F_5
  133. Segment(E_5, F_5) → r_2
  134. Intersect(b, i) → G_5
  135. Segment(G_5, H_5) → s_2
  136. Intersect(s_4, v_4) → I_5
  137. Point(v_4) → J_5
  138. Vector(I_5, J_5) → t_2
  139. Intersect(u_3, b_4) → K_5
  140. Point(b_4) → L_5
  141. Vector(K_5, L_5) → w_3
  142. Intersect(u_3, b_4) → M_5
  143. Point(u_3) → N_5
  144. Vector(M_5, N_5) → a_3
  145. Intersect(s_4, v_4) → O_5
  146. Point(s_4) → P_5
  147. Vector(O_5, P_5) → b_3
  148. LaTeX(a_3, true, true) → text7
  149. Vector(Q_5, R_5) → c_3
  150. Translate(L'_1, c_3) → S_5
  151. Vector(U_5, V_5) → e_3
  152. Translate(K', e_3) → K''
  153. Translate(L', e_3) → L''
  154. CircleArc(C, T_5, G_6) → d_3
  155. Translate(d_3, Vector[(0, 0.01366026910730156)]) → f_3
  156. Vector(J_6, K_6) → g_3
  157. Translate(d_3, g_3) → h_3
  158. Line(A_7, B_7) → a_5
  159. Point(a_5) → C_7
  160. CircleArc(C_7, T_6, G_7) → d_4
  161. Vector(J_7, K_7) → g_4
  162. Line(A_8, B_8) → a_6
  163. Point(a_6) → C_8
  164. CircleArc(C_8, T_7, G_8) → d_5
  165. Vector(J_8, K_8) → g_5
  166. Vector(L_6, M_6) → j_3
  167. Translate(d_3, j_3) → k_3
  168. Vector(N_6, O_6) → l_3
  169. Translate(d_3, l_3) → q_3
  170. Vector(P_6, R_6) → r_3
  171. Translate(d_3, r_3) → s_3
  172. Vector(S_6, V_6) → t_3
  173. Translate(d_3, t_3) → c_4
  174. Point(c_4) → W_6
  175. Rotate(c_4, 45*°, W_6) → e_4
  176. Vector(Z_6, D_7) → w_4
  177. Translate(d_3, w_4) → f_4
  178. Vector(E_7, F_7) → h_4
  179. Translate(d_3, h_4) → k_4
  180. Vector(H_7, I_7) → i_4
  181. Translate(d_3, i_4) → p_4
  182. Point(p_4) → L_7
  183. Point(k_4) → M_7
  184. Point(f_4) → N_7
  185. Rotate(p_4, 30*°, L_7) → q_4
  186. Rotate(p_4, 15*°, L_7) → r_4
  187. Rotate(p_4, 40*°, L_7) → c_5
  188. Rotate(f_4, 40*°, N_7) → e_5
  189. Rotate(k_4, 40*°, M_7) → f_5
  190. Point(d_3) → O_7
  191. Rotate(d_3, 40*°, O_7) → h_5
  192. Rotate(d_3, 28*°, O_7) → k_5
  193. Vector(P_7, Q_7) → j_4
  194. Translate(s_3, j_4) → p_5
  195. Point(p_5) → R_7
  196. Rotate(p_5, 34*°, R_7) → q_5
  197. Segment(U_7, V_7) → l_4
  198. Segment(U_8, V_8) → l_5
  199. Segment(W_7, Z_7) → n_4
  200. Segment(D_8, E_8) → b_5
  201. Segment(U_9, V_9) → l_6
  202. Segment(U_{10}, V_{10}) → l_7

AI 绘图提示语参考

画一个多级实验设计和数据分析的几何图形,包含直线、点、圆、线段、正交线、多边形和向量。首先构造一个基础图形,包括一个圆和两条相交的直线,然后通过旋转和平移变换生成多个多边形,展示线性代数和几何变换的应用。最后,连接关键点形成封闭的多边形,并用线段和向量表示空间关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。