Multilevel Experiment Design and Data Analysis

Multilevel Experiment Design and Data Analysis
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2014-09-21 16:12
In collections Complex Math
This example demonstrates the setup of a multilevel experiment and its data analysis process. It involves core mathematical concepts such as linear algebra in Rn space, geometric constructions, and transformations. Key GeoGebra commands and objects used include Line, Point, Circle, Segment, OrthogonalLine, Polygon, Vector, Translate, Intersect, LaTeX, CircleArc, and Rotate, as outlined in the construction summary. It is suitable for high school and above students to understand the practical application of experimental design and spatial linear algebra.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Draw a geometric representation of multilevel experiment design and data analysis, including lines, points, circles, segments, orthogonal lines, polygons, and vectors. Start by constructing a basic shape with a circle and two intersecting lines, then generate multiple polygons through rotations and translations to demonstrate the application of linear algebra and geometric transformations. Finally, connect key points to form closed polygons and use segments and vectors to represent spatial relationships.
The prompt above was compiled from the original drawing commands and is for reference only.