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Tessellation Creator V.Square01

Tessellation Creator V.Square01
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2012-10-12 20:48
PolygonVectorTransformationGeometric Construction
In collections Geo&Alg:Area Volume Pythagorean Th.
This example demonstrates how to create a square‑based tile for tessellation by dragging points. It involves core concepts such as polygon geometry, vector operations, and translation transformations. The construction uses GeoGebra commands Polygon, Vector, Point, and Translate with objects like A, B, poly1, a, b, c, d, etc. It is suitable for high‑school geometry classes or interdisciplinary projects that explore the mathematics of tiling.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, a, b, c, d, C, D
  2. Vector(D, A) → u
  3. Vector(D, C) → v
  4. Point(d) → E
  5. Point(d) → N
  6. Polygon(E, F, G, H, I, J, K, L, M, N) → poly2, e, n, f, g, h, i, j, k, l, m
  7. Point(c) → O
  8. Point(c) → B_1
  9. Polygon(O, P, A_1, B_1, Q, R, S, T, U, V, W, Z) → poly3, o, z, a_1, b_1, p, q, r, s, t, u_1, v_1, w
  10. Translate(E, v) → E'
  11. Translate(F, v) → F'
  12. Translate(G, v) → G'
  13. Translate(H, v) → H'
  14. Translate(I, v) → I'
  15. Translate(J, v) → J'
  16. Translate(K, v) → K'
  17. Translate(L, v) → L'
  18. Translate(M, v) → M'
  19. Translate(N, v) → N'
  20. Polygon(E', F', G', H', I', J', K', L', M', N') → poly2', e', n', f', g', h', i', j', k', l', m'
  21. Translate(O, u) → O'
  22. Translate(P, u) → P'
  23. Translate(Q, u) → Q'
  24. Translate(R, u) → R'
  25. Translate(S, u) → S'
  26. Translate(T, u) → T'
  27. Translate(U, u) → U'
  28. Translate(V, u) → V'
  29. Translate(W, u) → W'
  30. Translate(Z, u) → Z'
  31. Translate(A_1, u) → C_1
  32. Translate(B_1, u) → D_1
  33. Polygon(O', P', C_1, D_1, Q', R', S', T', U', V', W', Z') → poly3', o', z', c_1, d_1, p', q', r', s', t', u', v', w'
  34. Polygon(D, O, Z, A_1, B_1, C, E', F', G', H', I', J', P, K', L', M', N', B, D_1, C_1, Z', W', V', Q, U', T', S', R', Q', P', O', A, N, M, R, L, K, J, I, H, G, F, E, S, T, U, V, W) → poly4, d_2, w_1, z_1, a_2, b_2, c_2, e'_1, f'_1, g'_1, h'_1, i'_1, o_1, j'_1, k'_1, l'_1, m'_1, n'_1, b_3, d_3, c_3, z'_1, w'_1, p_1, v'_1, u'_1, t'_1, s'_1, r'_1, q'_1, p'_1, o'_1, a_3, n_1, q_1, m_1, l_1, k_1, j_1, i_1, h_1, g_1, f_1, e_1, r_1, s_1, t_1, u_2, v_2