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Symmetry in Native American Art: Geometric Constructions

Symmetry in Native American Art: Geometric Constructions
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2017-12-03 03:11
PolygonGeometric Construction
This example demonstrates the construction of symmetric patterns inspired by Native American art using GeoGebra. It involves core mathematical concepts such as symmetry, geometric constructions, polygon formation, probability & statistics, quadrilaterals, and similar triangles. The construction utilizes commands like Point, Intersect, Segment, Polygon, and objects including AY, YT, PA, TO, ON, NP, A, B, C, D, E, F, G, H, I, CA, J, K, AB, L, BR, M, N, O, P, Q, R, RI, S, T, U, IA, V, W, Z, f, g, h, i, j. It is suitable for high school mathematics education, showcasing the intersection of geometric symmetry and artistic design.

GeoGebra Commands & Parameters

  1. Point(yAxis) → AY
  2. Point(xAxis) → PA
  3. Point(xAxis) → B
  4. Point(yAxis) → E
  5. Point(xAxis) → CA
  6. Point(xAxis) → J
  7. Intersect(xAxis, yAxis) → K
  8. Point(yAxis) → AB
  9. Point(yAxis) → L
  10. Point(xAxis) → IA
  11. Point(xAxis) → V
  12. Segment(D, W) → f
  13. Segment(RI, T) → g
  14. Segment(P, R) → h
  15. Segment(YT, Q) → i
  16. Segment(S, U) → j
  17. Segment(TO, Z) → k
  18. Segment(O, N) → l
  19. Segment(BR, M) → m
  20. Segment(A, H) → n
  21. Segment(ON, G) → p
  22. Segment(AY, E) → q
  23. Segment(RI, S) → r
  24. Segment(D, TO) → s
  25. Segment(W, Z) → t
  26. Segment(T, U) → a
  27. Segment(N, M) → b
  28. Segment(I, F) → c
  29. Segment(H, G) → d
  30. Segment(V, IA) → e
  31. Segment(A, ON) → f_1
  32. Segment(C, NP) → g_1
  33. Segment(O, BR) → h_1
  34. Point(h) → A_1
  35. Intersect(g, s) → B_1
  36. Polygon(RI, P, A_1, B_1) → q1, ri, p_1, a_1, b_1
  37. Intersect(j, s) → C_1
  38. Intersect(i, s) → D_1
  39. Polygon(YT, S, C_1, D_1) → q2, yt, s_1, c_1, d_1
  40. Intersect(m, g_1) → E_1
  41. Intersect(l, g_1) → F_1
  42. Polygon(O, BR, E_1, F_1) → q3, o, br, e_1, f_2
  43. Intersect(g, t) → G_1
  44. Intersect(h, t) → H_1
  45. Polygon(G_1, H_1, R, T) → q4, g_2, h_2, r_1, t_1
  46. Intersect(i, t) → I_1
  47. Intersect(j, t) → J_1
  48. Polygon(I_1, J_1, U, Q) → q5, i_1, j_1, u, q_1
  49. Intersect(l, c) → K_1
  50. Intersect(m, c) → L_1
  51. Polygon(K_1, L_1, M, N) → q6, k_1, l_1, m_1, n_1
  52. Intersect(l, t) → M_1
  53. Intersect(m, t) → N_1
  54. Polygon(M_1, N_1, L_1, K_1) → q7, m_2, n_2, l_2, k_2
  55. Intersect(m, s) → O_1
  56. Intersect(l, s) → P_1
  57. Polygon(F_1, E_1, O_1, P_1) → q8, f_3, e_2, o_1, p_2
  58. Polygon(I, K_1, N, M, L_1, F, Q, R) → poly1, i_2, k_3, n_3, m_3, l_3, f_4, q_2, r_2
  59. Polygon(C, F_1, O, BR, E_1, NP, YT, P) → poly2, c_2, f_5, o_2, br_1, e_3, np, yt_1, p_3
  60. Polygon(N_1, I_1, F, L_1) → q9, n_4, i_3, f_6, l_4
  61. Segment(H_1, M_1) → j_2
  62. Polygon(H_1, M_1, K_1, I) → q10, h_3, m_4, k_4, i_4
  63. Intersect(l, d) → Q_1
  64. Intersect(m, d) → R_1
  65. Polygon(Q_1, R_1, N_1, M_1) → q11, q_3, r_3, n_5, m_5
  66. Polygon(C, F_1, P_1, A_1) → q12, c_3, f_7, p_4, a_2
  67. Polygon(E_1, NP, D_1, O_1) → q13, e_4, np_1, d_2, o_3
  68. Intersect(m, f_1) → S_1
  69. Intersect(l, f_1) → T_1
  70. Polygon(P_1, O_1, S_1, T_1) → q14, p_5, o_4, s_2, t_2
  71. Intersect(h, f_1) → U_1
  72. Polygon(A_1, P_1, T_1, U_1) → q15, a_3, p_6, t_3, u_1
  73. Intersect(i, f_1) → V_1
  74. Polygon(O_1, D_1, V_1, S_1) → q16, o_5, d_3, v_1, s_3
  75. Intersect(h, d) → W_1
  76. Polygon(W_1, Q_1, M_1, H_1) → q17, w_1, q_4, m_6, h_4
  77. Intersect(i, d) → Z_1
  78. Polygon(R_1, Z_1, I_1, N_1) → q18, r_4, z_1, i_5, n_6
  79. Intersect(g, e) → A_2
  80. Intersect(n, e) → B_2
  81. Polygon(A_2, B_2, H, W_1, H_1, G_1) → poly3, a_4, b_2, h_5, w_2, h_6, g_3
  82. Intersect(j, e) → C_2
  83. Intersect(p, e) → D_2
  84. Polygon(Z_1, I_1, J_1, C_2, D_2, G) → poly4, z_2, i_6, j_3, c_4, d_4, g_4
  85. Intersect(l, e) → E_2
  86. Polygon(E_2, K, E, Q_1) → q19, e_5, k_5, e_6, q_5
  87. Polygon(J, E_2, Q_1, W_1) → q20, j_4, e_7, q_6, w_3
  88. Polygon(B_2, J, W_1, H) → q21, b_3, j_5, w_4, h_7
  89. Intersect(m, e) → F_2
  90. Polygon(K, F_2, R_1, E) → q22, k_6, f_8, r_5, e_8
  91. Polygon(F_2, CA, Z_1, R_1) → q23, f_9, ca, z_3, r_6
  92. Polygon(CA, D_2, G, Z_1) → q24, ca_1, d_5, g_5, z_4
  93. Polygon(A, U_1, J, B_2) → q25, a_5, u_2, j_6, b_4
  94. Polygon(U_1, T_1, E_2, J) → q26, u_3, t_4, e_9, j_7
  95. Polygon(T_1, AY, K, E_2) → q27, t_5, ay, k_7, e_{10}
  96. Polygon(AY, S_1, F_2, K) → q28, ay_1, s_4, f_{10}, k_8
  97. Polygon(S_1, V_1, CA, F_2) → q29, s_5, v_2, ca_2, f_{11}
  98. Polygon(V_1, ON, D_2, CA) → q30, v_3, on, d_6, ca_3
  99. Polygon(B_1, A_1, U_1, A, B_2, A_2) → poly5, b_5, a_6, u_4, a_7, b_6, a_8
  100. Polygon(D, B_1, A_2, V) → q31, d_7, b_7, a_9, v
  101. Polygon(V, A_2, G_1, W) → q32, v_4, a_{10}, g_6, w
  102. Polygon(D_1, C_1, C_2, D_2, ON, V_1) → poly6, d_8, c_5, c_6, d_9, on_1, v_5
  103. Polygon(C_1, TO, IA, C_2) → q33, c_7, to, ia, c_8
  104. Polygon(C_2, IA, Z, J_1) → q34, c_9, ia_1, z_5, j_8

AI Drawing Prompt Reference

Create a symmetric pattern inspired by Native American art. Start by creating points on the x-axis (B, CA, J) and y-axis (AY, AB, L, IA, V). Then construct multiple segments to form triangles and quadrilaterals, ultimately creating a complex symmetric pattern. Ensure symmetry by mirroring each part across the axes.
The prompt above was compiled from the original drawing commands and is for reference only.