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GeoGebra Geometric Construction and Function Graphing Example by Heather Pierce

GeoGebra Geometric Construction and Function Graphing Example by Heather Pierce
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2018-09-21 21:21
FunctionCoordinate GeometryGeometric Construction
This example demonstrates how to create geometric figures and function graphs using GeoGebra. Key mathematical concepts include geometric transformations, function graphs, and coordinate systems. Construction involves using commands like Circle, Segment, Sequence, and If to build shapes, with Random for dynamic adjustments. Suitable for middle school or high school students to learn basic geometry and function concepts, and understand principles of geometric transformations.

GeoGebra Commands & Parameters

  1. Circle(A, 0.125) → f
  2. Circle(B, 0.125) → g
  3. Circle(C, 0.125) → h
  4. Circle(D, 0.125) → k
  5. Circle(E, 0.125) → p
  6. Circle(F, 0.125) → q
  7. Circle(G, 0.125) → r
  8. Circle(H, 0.125) → s
  9. Circle(I, 0.125) → t
  10. Circle(J, 0.125) → c_1
  11. Circle(K, 0.125) → d_1
  12. Circle(L, 0.125) → e_1
  13. Circle(M, 0.125) → f_1
  14. Circle(N, 0.125) → g_1
  15. Circle(O, 0.125) → h_1
  16. Circle(P, 0.125) → k_1
  17. Circle(Q, 0.125) → p_1
  18. Circle(R, 0.125) → q_1
  19. Circle(S, 0.125) → r_1
  20. Circle(T, 0.125) → s_1
  21. Segment(U, G_1) → i
  22. Segment(V, H_1) → j
  23. Segment(W, I_1) → l
  24. Segment(Z, J_1) → m
  25. Segment(A_1, K_1) → n
  26. Segment(B_1, N_1) → i_1
  27. Segment(C_1, L_1) → j_1
  28. Segment(D_1, M_1) → l_1
  29. Segment(E_1, P_1) → m_1
  30. Segment(F_1, O_1) → n_1
  31. Segment(G_1, D_2) → t_1
  32. Segment(G_1, C_2) → a_1
  33. Segment(E_2, H_1) → b_1
  34. Segment(H_1, V_2) → f_2
  35. Segment(F_2, I_1) → g_2
  36. Segment(I_1, U_2) → h_2
  37. Segment(G_2, J_1) → i_2
  38. Segment(J_1, T_2) → j_2
  39. Segment(H_2, K_1) → k_2
  40. Segment(K_1, S_2) → l_2
  41. Segment(I_2, N_1) → m_2
  42. Segment(N_1, R_2) → n_2
  43. Segment(J_2, L_1) → p_2
  44. Segment(L_1, Q_2) → q_2
  45. Segment(K_2, M_1) → r_2
  46. Segment(M_1, P_2) → s_2
  47. Segment(L_2, P_1) → t_2
  48. Segment(P_1, O_2) → a_2
  49. Segment(M_2, O_1) → b_2
  50. Segment(O_1, N_2) → c_2
  51. Segment(R_3, Q_1) → d_2
  52. Segment(W_2, Q_1) → e_2
  53. Segment(Q_3, R_1) → f_3
  54. Segment(Z_2, R_1) → g_3
  55. Segment(P_3, S_1) → h_3
  56. Segment(A_3, S_1) → i_3
  57. Segment(O_3, T_1) → j_3
  58. Segment(B_3, T_1) → k_3
  59. Segment(N_3, U_1) → l_3
  60. Segment(C_3, U_1) → m_3
  61. Segment(M_3, V_1) → n_3
  62. Segment(D_3, V_1) → p_3
  63. Segment(L_3, W_1) → q_3
  64. Segment(E_3, W_1) → r_3
  65. Segment(K_3, Z_1) → s_3
  66. Segment(F_3, Z_1) → t_3
  67. Segment(J_3, A_2) → a_3
  68. Segment(G_3, A_2) → b_3
  69. Segment(H_3, B_2) → c_3
  70. Segment(I_3, B_2) → d_3
  71. Segment(U_5, K_5) → e_3
  72. Segment(Q_6, K_5) → f_4
  73. Segment(V_5, L_5) → g_4
  74. Segment(P_6, L_5) → h_4
  75. Segment(W_5, M_5) → i_4
  76. Segment(O_6, M_5) → j_4
  77. Segment(Z_5, N_5) → k_4
  78. Segment(N_6, N_5) → l_4
  79. Segment(A_6, O_5) → m_4
  80. Segment(M_6, O_5) → n_4
  81. Segment(B_6, P_5) → p_4
  82. Segment(L_6, P_5) → q_4
  83. Segment(C_6, Q_5) → r_4
  84. Segment(J_6, Q_5) → s_4
  85. Segment(D_6, R_5) → t_4
  86. Segment(I_6, R_5) → a_4
  87. Segment(E_6, S_5) → b_4
  88. Segment(H_6, S_5) → c_4
  89. Segment(F_6, T_5) → d_4
  90. Segment(G_6, T_5) → e_4
  91. Segment(D_4, N_4) → f_5
  92. Segment(M_4, C_4) → g_5
  93. Segment(B_4, L_4) → h_5
  94. Segment(K_4, A_4) → i_5
  95. Segment(Z_3, J_4) → j_5
  96. Segment(I_4, W_3) → k_5
  97. Segment(V_3, H_4) → l_5
  98. Segment(G_4, U_3) → m_5
  99. Segment(T_3, F_4) → n_5
  100. Segment(E_4, S_3) → p_5
  101. Segment(O_4, E_4) → q_5
  102. Segment(E_4, J_5) → r_5
  103. Segment(P_4, F_4) → s_5
  104. Segment(F_4, I_5) → t_5
  105. Segment(Q_4, G_4) → a_5
  106. Segment(G_4, H_5) → b_5
  107. Segment(R_4, H_4) → c_5
  108. Segment(H_4, G_5) → d_5
  109. Segment(S_4, I_4) → e_5
  110. Segment(I_4, F_5) → f_6
  111. Segment(T_4, J_4) → g_6
  112. Segment(J_4, E_5) → h_6
  113. Segment(U_4, K_4) → i_6
  114. Segment(K_4, D_5) → j_6
  115. Segment(V_4, L_4) → k_6
  116. Segment(L_4, C_5) → l_6
  117. Segment(W_4, M_4) → m_6
  118. Segment(M_4, B_5) → n_6
  119. Segment(Z_4, N_4) → p_6
  120. Segment(N_4, A_5) → q_6
  121. Sort(Sequence[(random(), Element[DataList, k]), k, 1, Length[DataList]]) → RandomDataPair
  122. Sequence(y(Element[RandomDataPair, k]), k, 1, e) → ChoosedList
  123. Polygon(R_6, D_7, E_7, O_7) → q1, r_6, d_7, e_7, o_7
  124. Polygon(D_7, S_6, N_7, E_7) → q2, s_6, t_6, n_7, a_6
  125. Polygon(S_6, C_7, F_7, N_7) → q3, b_6, c_7, f_7, c_6
  126. Polygon(C_7, T_6, M_7, F_7) → q4, d_6, e_6, m_7, g_7
  127. Polygon(T_6, B_7, G_7, M_7) → q5, h_7, b_7, i_7, j_7
  128. Polygon(B_7, U_6, L_7, G_7) → q6, k_7, u_6, l_7, p_7
  129. Polygon(U_6, A_7, H_7, L_7) → q7, q_7, a_7, r_7, s_7
  130. Polygon(A_7, V_6, K_7, H_7) → q8, t_7, v_6, f_8, g_8
  131. Polygon(V_6, Z_6, I_7, K_7) → q9, h_8, z_6, i_8, j_8
  132. Polygon(Z_6, W_6, J_7, I_7) → q10, k_8, w_6, l_8, m_8
  133. Polygon(E_7, O_7, P_7, B_8) → q11, n_8, p_8, q_8, b_8
  134. Polygon(E_7, N_7, Q_7, B_8) → q12, r_8, s_8, t_8, a_8
  135. Polygon(N_7, Q_7, A_8, F_7) → q13, c_8, d_8, e_8, f_9
  136. Polygon(F_7, A_8, R_7, M_7) → q14, g_9, h_9, i_9, j_9
  137. Polygon(M_7, G_7, Z_7, R_7) → q15, k_9, l_9, z_7, m_9
  138. Polygon(G_7, Z_7, S_7, L_7) → q16, n_9, p_9, q_9, r_9
  139. Polygon(L_7, S_7, W_7, H_7) → q17, s_9, t_9, w_7, a_9
  140. Polygon(H_7, K_7, T_7, W_7) → q18, b_9, c_9, d_9, e_9
  141. Polygon(K_7, I_7, V_7, T_7) → q19, f_{10}, g_{10}, v_7, h_{10}
  142. Polygon(I_7, J_7, U_7, V_7) → q20, i_{10}, j_{10}, u_7, k_{10}
  143. Segment(R_6, W_6) → l_{10}
  144. Segment(W_6, U_7) → m_{10}
  145. Segment(U_7, P_7) → n_{10}
  146. Segment(P_7, R_6) → p_{10}
  147. Segment(B_7, Z_7) → q_{10}
  148. Segment(O_7, J_7) → r_{10}
  149. Sort(Sequence[(random(), Element[DataList1, k]), k, 1, Length[DataList1]]) → RandomDataPair1
  150. Sequence(y(Element[RandomDataPair1, k]), k, 1, o) → Stratified1
  151. Sort(Sequence[(random(), Element[DataList1, k]), k, 1, Length[DataList1]]) → RandomDataPair2
  152. Sort(Sequence[(random(), Element[DataList1, k]), k, 1, Length[DataList1]]) → RandomDataPair3
  153. Sort(Sequence[(random(), Element[DataList1, k]), k, 1, Length[DataList1]]) → RandomDataPair4
  154. Sequence(y(Element[RandomDataPair2, k]), k, 1, o) → Stratified2
  155. Sequence(y(Element[RandomDataPair3, k]), k, 1, o) → Stratified3
  156. Sequence(y(Element[RandomDataPair4, k]), k, 1, o) → Stratified4
  157. Polygon(R_6, O_7, E_7, D_7) → q21, s_{10}, t_{10}, a_{10}, b_{10}
  158. Polygon(D_7, S_6, N_7, E_7) → q22, c_{10}, d_{10}, e_{10}, f_{11}
  159. Polygon(S_6, C_7, F_7, N_7) → q23, g_{11}, h_{11}, i_{11}, j_{11}
  160. Polygon(C_7, T_6, M_7, F_7) → q24, k_{11}, l_{11}, m_{11}, n_{11}
  161. Polygon(T_6, B_7, G_7, M_7) → q25, p_{11}, q_{11}, r_{11}, s_{11}
  162. Polygon(B_7, U_6, L_7, G_7) → q26, t_{11}, a_{11}, b_{11}, c_{11}
  163. Polygon(U_6, A_7, H_7, L_7) → q27, d_{11}, e_{11}, f_{12}, g_{12}
  164. Polygon(A_7, V_6, K_7, H_7) → q28, h_{12}, i_{12}, j_{12}, k_{12}
  165. Polygon(V_6, Z_6, I_7, K_7) → q29, l_{12}, m_{12}, n_{12}, p_{12}
  166. Polygon(Z_6, W_6, J_7, I_7) → q30, q_{12}, r_{12}, s_{12}, t_{12}
  167. Polygon(O_7, E_7, B_8, P_7) → q31, a_{12}, b_{12}, c_{12}, d_{12}
  168. Polygon(E_7, N_7, Q_7, B_8) → q32, e_{12}, f_{13}, g_{13}, h_{13}
  169. Polygon(N_7, F_7, A_8, Q_7) → q33, i_{13}, j_{13}, k_{13}, l_{13}
  170. Polygon(F_7, M_7, R_7, A_8) → q34, m_{13}, n_{13}, p_{13}, q_{13}
  171. Polygon(M_7, G_7, Z_7, R_7) → q35, r_{13}, s_{13}, t_{13}, a_{13}
  172. Polygon(G_7, L_7, S_7, Z_7) → q36, b_{13}, c_{13}, d_{13}, e_{13}
  173. Polygon(L_7, H_7, W_7, S_7) → q37, f_{14}, g_{14}, h_{14}, i_{14}
  174. Polygon(H_7, K_7, T_7, W_7) → q38, j_{14}, k_{14}, l_{14}, m_{14}
  175. Polygon(K_7, I_7, V_7, T_7) → q39, n_{14}, p_{14}, q_{14}, r_{14}
  176. Polygon(I_7, J_7, U_7, V_7) → q40, s_{14}, t_{14}, a_{14}, b_{14}
  177. If(o ≟ 4, strat1, o ≟ 8, Join[{strat1, strat2}], o ≟ 12, Join[{strat1, strat2, strat3}], o ≟ 16, Join[{strat1, strat2, strat3, strat4}]) → strat
  178. Sort(Sequence[(random(), Element[DataList2, k]), k, 1, Length[DataList2]]) → RandomDataPair5
  179. Sequence(y(Element[RandomDataPair5, k]), k, 1, u / 5) → cluster
  180. Polygon(R_6, B_7, G_7, O_7) → q41, c_{14}, d_{14}, e_{14}, f_{15}
  181. Polygon(B_7, W_6, J_7, G_7) → q42, g_{15}, h_{15}, i_{15}, j_{15}
  182. Polygon(O_7, P_7, Z_7, G_7) → q43, k_{15}, l_{15}, m_{15}, n_{15}
  183. Polygon(G_7, Z_7, U_7, J_7) → q44, p_{15}, q_{15}, r_{15}, s_{15}
  184. Random(1, floor(20 / v)) → w
  185. If(v ≟ 8, 2, round(20 / v)) → o_1
  186. Sequence(w + (k * o_1), k, 0, v - 1) → system
  187. Polygon(R_6, D_7, E_7, O_7) → q45, t_{15}, a_{15}, b_{15}, c_{15}
  188. Polygon(D_7, S_6, N_7, E_7) → q46, d_{15}, e_{15}, f_{16}, g_{16}
  189. Polygon(S_6, C_7, F_7, N_7) → q47, h_{16}, i_{16}, j_{16}, k_{16}
  190. Polygon(C_7, T_6, M_7, F_7) → q48, l_{16}, m_{16}, n_{16}, p_{16}
  191. Polygon(T_6, B_7, G_7, M_7) → q49, q_{16}, r_{16}, s_{16}, t_{16}
  192. Polygon(B_7, U_6, L_7, G_7) → q50, a_{16}, b_{16}, c_{16}, d_{16}
  193. Polygon(U_6, A_7, H_7, L_7) → q51, e_{16}, f_{17}, g_{17}, h_{17}
  194. Polygon(A_7, V_6, K_7, H_7) → q52, i_{17}, j_{17}, k_{17}, l_{17}
  195. Polygon(V_6, Z_6, I_7, K_7) → q53, m_{17}, n_{17}, p_{17}, q_{17}
  196. Polygon(Z_6, W_6, J_7, I_7) → q54, r_{17}, s_{17}, t_{17}, a_{17}
  197. Polygon(O_7, E_7, B_8, P_7) → q55, b_{17}, c_{17}, d_{17}, e_{17}
  198. Polygon(E_7, N_7, Q_7, B_8) → q56, f_{18}, g_{18}, h_{18}, i_{18}
  199. Polygon(N_7, F_7, A_8, Q_7) → q57, j_{18}, k_{18}, l_{18}, m_{18}
  200. Polygon(F_7, M_7, R_7, A_8) → q58, n_{18}, p_{18}, q_{18}, r_{18}
  201. Polygon(M_7, G_7, Z_7, R_7) → q59, s_{18}, t_{18}, a_{18}, b_{18}
  202. Polygon(G_7, L_7, S_7, Z_7) → q60, c_{18}, d_{18}, e_{18}, f_{19}
  203. Polygon(L_7, H_7, W_7, S_7) → q61, g_{19}, h_{19}, i_{19}, j_{19}
  204. Polygon(H_7, K_7, T_7, W_7) → q62, k_{19}, l_{19}, m_{19}, n_{19}
  205. Polygon(K_7, I_7, V_7, T_7) → q63, p_{19}, q_{19}, r_{19}, s_{19}
  206. Polygon(I_7, J_7, U_7, V_7) → q64, t_{19}, a_{19}, b_{19}, c_{19}

AI Drawing Prompt Reference

Create a geometric figure consisting of multiple concentric circles and segments connecting their centers. Start by drawing five concentric circles with a radius of 0.125, then connect their centers to form a star pattern. Continue by drawing more concentric circles and segments to create a complex geometric structure.
The prompt above was compiled from the original drawing commands and is for reference only.