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Tiling the Plane – Activities 1 & 2

Tiling the Plane – Activities 1 & 2
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2020-08-26 22:15
PolygonCoordinate GeometryTransformationGeometric Construction
In collections Grade 6 Unit 1: Area and Surface Area
This GeoGebra example demonstrates the dynamic construction of plane tiling patterns, focusing on Activities 1 and 2, where parallelogram and polygon arrangements are explored. Core mathematical concepts include polygon properties, parallel line relationships, symmetry transformations, and the application of these ideas to create periodic tilings. The construction uses drawing tools Tool1, Tool2, Tool3 to generate polygon objects such as poly1, poly2, poly3, and employs sliders and loci to implement translations and rotations, resulting in a complete tiling structure. It is designed for high‑school geometry classes, mathematical modeling courses, and as a visual aid for teaching plane symmetry and periodic patterns, supporting classroom demonstrations, problem solving, and student inquiry.

GeoGebra Commands & Parameters

  1. Tool3(A_7) → B_4, poly1, f, g, h, i
  2. Tool3(C_7) → D_4, poly2, j, k, l, m
  3. Tool3(E) → F, poly3, n, p, q, r
  4. Tool2(K_3) → poly6, L_3, g_1, h_1, i_1, j_1
  5. Tool2(M) → poly7, N, k_1, l_1, m_1, n_1
  6. Tool1(O) → P, p_1, q_1, r_1, poly8
  7. Tool1(Q) → R, s_1, t_1, a_1, poly9
  8. Tool1(S) → T, b_1, c_1, d_1, poly10
  9. Tool1(U) → V, e_1, f_2, g_2, poly11
  10. Tool1(W) → Z, h_2, i_2, j_2, poly12
  11. Tool1(A_1) → B_1, k_2, l_2, m_2, poly13
  12. Tool1(C_1) → D_1, n_2, p_2, q_2, poly14
  13. Tool3(A_2) → B_2, poly1_1, f_3, g_3, h_3, i_3
  14. Tool3(C_2) → D_2, poly2_1, j_3, k_3, l_3, m_3
  15. Tool3(E_1) → F_1, poly3_1, n_3, p_3, q_3, r_2
  16. Tool2(G_1) → poly4_1, H_1, s_2, t_2, a_2, b_2
  17. Tool2(K_1) → poly6_1, L_1, g_4, h_4, i_4, j_4
  18. Tool2(M_1) → poly7_1, N_1, k_4, l_4, m_4, n_4
  19. Tool1(O_1) → P_1, p_4, q_4, r_3, poly8_1
  20. Tool1(Q_1) → R_1, s_3, t_3, a_3, poly9_1
  21. Tool1(S_1) → T_1, b_3, c_3, d_3, poly10_1
  22. Tool1(U_1) → V_1, e_3, f_5, g_5, poly11_1
  23. Tool1(W_1) → Z_1, h_5, i_5, j_5, poly12_1
  24. Tool1(A_3) → B_3, k_5, l_5, m_5, poly13_1
  25. Tool1(C_3) → D_3, n_5, p_5, q_5, poly14_1
  26. Tool2(G_2) → poly4_2, H_2, s_4, t_4, a_5, b_5
  27. Tool2(I_2) → poly5_2, J_2, c_4, d_4, e_4, f_6
  28. Tool2(K_2) → poly6_2, L_2, g_6, h_6, i_6, j_6

AI Drawing Prompt Reference

Draw a periodic plane tiling by first creating a parallelogram and two polygons as fundamental tiles, then applying translations and rotations controlled by sliders to replicate the tiles along two independent directions, producing a full lattice; the figure shows several families of parallel lines, symmetry axes, and many transformed copies of the polygons, illustrating polygon properties, parallelism, and symmetry transformations in tiling.
The prompt above was compiled from the original drawing commands and is for reference only.