Set Demonstration

Set Demonstration
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2017-08-07 01:21
This example dynamically visualizes set operations like intersections and unions, illustrating the geometric meaning of set theory. It involves core concepts including set theory, similarity transformation, congruence, orthocenter, and logic. GeoGebra commands used in construction include Polygon, Circle, Intersect, and CircleArc. Suitable for high school mathematics teaching to help students understand abstract set operations and geometric transformations.

GeoGebra Commands & Parameters

  1. Polygon(A_1, B_1, C, D) → Back, a_2, b_2, c_2, d_2
  2. Polygon(E, F, G, H) → Backblue, e_3, f_3, g_3, h_3
  3. Polygon(I, J, K, L) → OutlneBox, i, j, k, l
  4. Circle(M, N) → A'
  5. Circle(O, P) → B'
  6. Circle(Q, R) → A
  7. Circle(S, T) → B
  8. Circle(U, V) → OutlineA
  9. Circle(W, Z) → OutlineB
  10. Circle(Q_1, R_1) → A_2
  11. Circle(S_1, T_1) → B_2
  12. Polygon(E_1, F_1, G_1, H_1) → Backblue_1, e_1, f_1, g_1, h_1
  13. Circle(M_1, N_1) → A'_1
  14. Circle(O_1, P_1) → B'_1
  15. Circle(C_1, D_1) → p
  16. Circle(I_1, J_1) → q
  17. Intersect(p, q, 2) → K_1
  18. Intersect(p, q, 1) → L_1
  19. CircleArc(C_1, K_1, L_1) → Intersect1
  20. CircleArc(I_1, L_1, K_1) → Intersect2
  21. Circle(C_2, D_2) → p_1
  22. Circle(I_2, J_2) → q_1
  23. Intersect(p_1, q_1, 2) → K_2
  24. Intersect(p_1, q_1, 1) → L_2
  25. CircleArc(C_2, K_2, L_2) → Intersect1_1
  26. CircleArc(I_2, L_2, K_2) → Intersect2_1
  27. Polygon(A_3, B_3, C_3, D_3) → Back_1, a_1, b_1, c_1, d_1
  28. Polygon(E_2, F_2, G_2, H_2) → Backblue_2, e_2, f_2, g_2, h_2
  29. Circle(S_3, T_3) → B_4
  30. Circle(Q_3, R_3) → A_4
  31. Circle(C_4, D_4) → p_3
  32. Circle(I_3, J_3) → q_2
  33. Intersect(p_3, q_2, 2) → K_3
  34. Intersect(p_3, q_2, 1) → L_3
  35. CircleArc(C_4, K_3, L_3) → Intersect1_2
  36. CircleArc(I_3, L_3, K_3) → Intersect2_2
  37. Circle(C_5, D_5) → p_4
  38. Circle(I_4, J_4) → q_3
  39. Intersect(p_4, q_3, 2) → K_4
  40. Intersect(p_4, q_3, 1) → L_4
  41. CircleArc(C_5, K_4, L_4) → Intersect1_3
  42. CircleArc(I_4, L_4, K_4) → Intersect2_3
  43. Circle(C_6, D_6) → p_5
  44. Circle(I_5, J_5) → q_4
  45. Intersect(p_5, q_4, 2) → K_5
  46. Intersect(p_5, q_4, 1) → L_5
  47. CircleArc(C_6, K_5, L_5) → Intersect1_4
  48. CircleArc(I_5, L_5, K_5) → Intersect2_4
  49. Circle(C_7, D_7) → p_6
  50. Circle(I_6, J_6) → q_5
  51. Intersect(p_6, q_5, 2) → K_6
  52. Intersect(p_6, q_5, 1) → L_6
  53. CircleArc(C_7, K_6, L_6) → Intersect1_5
  54. CircleArc(I_6, L_6, K_6) → Intersect2_5
  55. Circle(Q_4, R_4) → A_5
  56. Circle(S_4, T_4) → B_5
  57. Circle(M_3, N_3) → A'_2
  58. Polygon(A_6, B_6, C_{13}, D_{13}) → Back_2, a_3, b_3, c_3, d_3
  59. Polygon(E_3, F_3, G_3, H_3) → Backblue_3, e_4, f_4, g_4, h_4
  60. Circle(O_3, P_3) → B'_2
  61. Polygon(A_8, B_8, C_{15}, D_{15}) → Back_4, a_5, b_5, c_5, d_5
  62. Polygon(A_9, B_9, C_{16}, D_{16}) → Back_3, a_4, b_4, c_4, d_4
  63. Polygon(E_4, F_4, G_4, H_4) → Backblue_4, e_5, f_5, g_5, h_5
  64. Circle(C_{18}, D_{18}) → p_7
  65. Circle(I_7, J_7) → q_6
  66. Intersect(p_7, q_6, 2) → K_7
  67. Intersect(p_7, q_6, 1) → L_7
  68. CircleArc(C_{18}, K_7, L_7) → Intersect1_6
  69. CircleArc(I_7, L_7, K_7) → Intersect2_6
  70. Circle(C_{19}, D_{19}) → p_8
  71. Circle(I_8, J_8) → q_7
  72. Intersect(p_8, q_7, 2) → K_8
  73. Intersect(p_8, q_7, 1) → L_8
  74. CircleArc(C_{19}, K_8, L_8) → Intersect1_7
  75. CircleArc(I_8, L_8, K_8) → Intersect2_7
  76. Polygon(A_{11}, B_{11}, C_{20}, D_{20}) → Back_5, a_6, b_6, c_6, d_6
  77. Polygon(E_6, F_6, G_6, H_6) → Backblue_5, e_6, f_6, g_6, h_6
  78. Circle(C_{24}, D_{24}) → p_9
  79. Circle(I_9, J_9) → q_8
  80. Intersect(p_9, q_8, 2) → K_9
  81. Intersect(p_9, q_8, 1) → L_9
  82. Circle(C_{25}, D_{25}) → p_{10}
  83. Circle(I_{10}, J_{10}) → q_9
  84. Intersect(p_{10}, q_9, 2) → K_{10}
  85. Intersect(p_{10}, q_9, 1) → L_{10}
  86. CircleArc(C_{25}, K_{10}, L_{10}) → Intersect1_8
  87. CircleArc(I_{10}, L_{10}, K_{10}) → LeftWIntersection
  88. Intersect(OutlineA, OutlineB, 2) → V_2
  89. Intersect(OutlineA, OutlineB, 1) → W_2
  90. CircleArc(U_2, V_2, W_2) → RightWIntersection
  91. Circle(M_5, N_5) → A'_3
  92. Circle(Q_8, R_8) → A_{15}
  93. Circle(M_8, N_8) → A'_4
  94. Circle(O_4, P_4) → B'_3
  95. Circle(C_{34}, D_{34}) → p_{11}
  96. Circle(I_{11}, J_{11}) → q_{10}
  97. Intersect(p_{11}, q_{10}, 2) → K_{11}
  98. Intersect(p_{11}, q_{10}, 1) → L_{11}
  99. CircleArc(C_{34}, K_{11}, L_{11}) → Intersect1_9
  100. Polygon(A_{16}, B_{15}, C_{42}, D_{42}) → Back_6, a_7, b_7, c_7, d_7
  101. Circle(O_5, P_5) → B'_4
  102. Circle(S_9, T_9) → B_{20}
  103. Circle(O_7, P_7) → B'_5
  104. Circle(O_{10}, P_{10}) → B'_6
  105. Circle(O_{13}, P_{13}) → B'_7
  106. Circle(S_{18}, T_{18}) → B_{21}
  107. Circle(M_{12}, N_{12}) → A'_6
  108. Circle(M_{13}, N_{13}) → A'_5
  109. Circle(Q_{14}, R_{14}) → A_{21}
  110. Circle(M_{19}, N_{19}) → A'_7
  111. Circle(O_{16}, P_{16}) → B'_8
  112. Circle(C_{63}, D_{63}) → p_{12}
  113. Circle(I_{51}, J_{51}) → q_{11}
  114. Intersect(p_{12}, q_{11}, 2) → K_{12}
  115. Intersect(p_{12}, q_{11}, 1) → L_{12}
  116. CircleArc(C_{63}, K_{12}, L_{12}) → Intersect1_{10}
  117. CircleArc(I_{51}, L_{12}, K_{12}) → LeftWIntersection_2
  118. Circle(M_{26}, N_{26}) → A'_9
  119. Circle(M_{25}, N_{25}) → A'_8
  120. Circle(O_{20}, P_{20}) → B'_9
  121. Polygon(E_8, F_8, G_8, H_8) → Backblue_6, e_7, f_7, g_7, h_7
  122. Circle(O_{25}, P_{25}) → B'_{10}
  123. Circle(M_{37}, N_{37}) → A'_{10}
  124. Circle(O_{35}, P_{35}) → B'_{11}
  125. Polygon(A_{22}, B_{22}, C_{103}, D_{103}) → Back_7, a_8, b_8, c_8, d_8
  126. Polygon(E_9, F_9, G_9, H_9) → Backblue_7, e_8, f_8, g_8, h_8
  127. Circle(M_{51}, N_{51}) → A'_{12}
  128. Circle(O_{51}, P_{51}) → B'_{13}
  129. Circle(M_{52}, N_{52}) → A'_{11}
  130. Circle(O_{52}, P_{52}) → B'_{12}
  131. Circle(C_{109}, D_{109}) → p_{13}
  132. Circle(I_{107}, J_{107}) → q_{12}
  133. Intersect(p_{13}, q_{12}, 2) → K_{13}
  134. Intersect(p_{13}, q_{12}, 1) → L_{13}
  135. CircleArc(C_{109}, K_{13}, L_{13}) → Intersect1_{11}
  136. CircleArc(I_{107}, L_{13}, K_{13}) → LeftWIntersection_1
  137. Circle(M_{65}, N_{65}) → A'_{15}
  138. Circle(M_{66}, N_{66}) → A'_{14}
  139. Circle(M_{67}, N_{67}) → A'_{13}
  140. Circle(Q_{41}, R_{41}) → A_{28}
  141. Circle(S_{48}, T_{48}) → B_{28}
  142. Circle(O_{73}, P_{73}) → B'_{14}
  143. Circle(M_{92}, N_{92}) → A'_{16}
  144. Circle(O_{83}, P_{83}) → B'_{15}
  145. Circle(C_{157}, D_{157}) → p_{14}
  146. Circle(I_{147}, J_{147}) → q_{13}
  147. Intersect(p_{14}, q_{13}, 2) → K_{14}
  148. Intersect(p_{14}, q_{13}, 1) → L_{14}
  149. CircleArc(C_{157}, K_{14}, L_{14}) → Intersect1_{12}
  150. CircleArc(I_{147}, L_{14}, K_{14}) → LeftWIntersection_3
  151. Circle(U_{61}, V_{25}) → OutlineA_1
  152. Circle(W_{32}, Z_{38}) → OutlineB_1
  153. Intersect(OutlineA_1, OutlineB_1, 2) → V_{31}
  154. Intersect(OutlineA_1, OutlineB_1, 1) → W_{38}
  155. CircleArc(U_{62}, V_{31}, W_{38}) → RightWIntersection_1
  156. Circle(M_{103}, N_{103}) → A'_{17}
  157. Circle(O_{93}, P_{93}) → B'_{16}
  158. Circle(U_{63}, V_{34}) → OutlineA_2
  159. Circle(W_{41}, Z_{39}) → OutlineB_2
  160. Intersect(OutlineA_2, OutlineB_2, 2) → V_{35}
  161. Intersect(OutlineA_2, OutlineB_2, 1) → W_{42}
  162. CircleArc(U_{64}, V_{35}, W_{42}) → RightWIntersection_2
  163. Circle(M_{115}, N_{115}) → A'_{19}
  164. Circle(O_{104}, P_{104}) → B'_{18}
  165. Circle(M_{116}, N_{116}) → A'_{18}
  166. Circle(O_{105}, P_{105}) → B'_{17}
  167. Circle(U_{71}, V_{39}) → OutlineA_3
  168. Circle(W_{46}, Z_{43}) → OutlineB_3
  169. Intersect(OutlineA_3, OutlineB_3, 2) → V_{40}
  170. Intersect(OutlineA_3, OutlineB_3, 1) → W_{47}
  171. CircleArc(U_{72}, V_{40}, W_{47}) → RightWIntersection_3
  172. Polygon(E_{11}, F_{11}, G_{11}, H_{11}) → poly1, e_{11}, f_{11}, g_{11}, h_{11}
  173. Polygon(E_{12}, F_{12}, G_{12}, H_{12}) → poly2, e_{12}, f_{12}, g_{12}, h_{12}
  174. Polygon(G_{13}, H_{13}, E_{14}, F_{14}) → poly3, g_{13}, h_{13}, e_{14}, f_{14}
  175. Polygon(G_{15}, H_{15}, K_{15}, L_{15}) → poly4, g_{15}, h_{15}, k_{15}, l_{15}

AI Drawing Prompt Reference

Draw two polygons in different colors, then create three circles that intersect with the polygons, connecting the intersection points with arcs to illustrate set operations like intersections and unions, demonstrating geometric transformations including similarity and congruence, suitable for high school mathematics teaching to help students understand abstract set operations and geometric transformations.
The prompt above was compiled from the original drawing commands and is for reference only.