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Maths and Textiles: Jacquard Pattern Construction

Maths and Textiles: Jacquard Pattern Construction
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2020-02-16 20:17
PolygonVectorSequenceGraphing
This example demonstrates how geometric transformations and function graphs are used to construct complex patterns for jacquard textiles. Core math concepts include vectors, sequences, polygon construction, transformations, and graphing functions. GeoGebra commands like Motif1, Vector, Sequence, Line, and Polygon are employed to create and combine geometric shapes. Suitable for high school and above students learning geometric constructions, function graphing, and transformation applications.

GeoGebra Commands & Parameters

  1. Motif1(B_1, C_1) → poly15, poly16, poly25, poly26, poly27, poly17, poly18, poly19, poly20, poly21, poly22, poly23, poly24
  2. Vector(A, A + (1, 0)) → e
  3. Vector(A, A + (0, 1)) → f
  4. Sequence(Sequence[Translate[liste1, Vector[(s * e) + (t * f)]], s, 0, n], t, 0, n) → liste2
  5. Outil2(D_1, E_1) → poly14, poly28, poly37, poly38, poly29, poly30, poly31, poly32, poly33, poly34, poly35, poly36
  6. Sequence(Sequence[Translate[liste3, Vector[(s * e) + (t * f)]], s, 0, n], t, 0, n) → liste4
  7. Outil3(F_1, G_1) → poly39, poly40, poly49, poly50, poly41, poly42, poly43, poly44, poly45, poly46, poly47, poly48
  8. Outil3(H_1, I_1) → poly51, poly52, poly61, poly62, poly53, poly54, poly55, poly56, poly57, poly58, poly59, poly60
  9. Sequence(Sequence[Translate[liste5, Vector[(s * e) + (t * f)]], s, 0, n], t, 0, n) → liste6
  10. Outil3(C, D) → poly1, poly2, poly11, poly12, poly3, poly4, poly5, poly6, poly7, poly8, poly9, poly10
  11. Outil2(E, F) → poly13, poly63, poly72, poly73, poly64, poly65, poly66, poly67, poly68, poly69, poly70, poly71
  12. Motif1(G, H) → poly74, poly75, poly84, poly85, poly86, poly76, poly77, poly78, poly79, poly80, poly81, poly82, poly83
  13. Outil4(Q_1, R_1) → poly96, poly97, poly98, poly99, poly100, poly101, poly102, poly103
  14. Sequence(Sequence[Translate[liste7, Vector[(s * e) + (t * f)]], s, 0, n], t, 0, n) → liste8
  15. Outil4(S_1, T_1) → poly88, poly89, poly90, poly91, poly92, poly93, poly94, poly95
  16. Outil5(W_1, Z_1) → poly116, poly117, poly126, poly127, poly118, poly119, poly120, poly121, poly122, poly123, poly124, poly125
  17. Sequence(Sequence[Translate[liste9, Vector[(s * e) + (t * f)]], s, 0, n], t, 0, n) → liste10
  18. Outil5(A_2, B_2) → poly128, poly129, poly138, poly139, poly130, poly131, poly132, poly133, poly134, poly135, poly136, poly137
  19. Outil6(C_2, D_2) → poly112, poly113, poly114, poly115, poly140, poly141, poly142, poly143
  20. Sequence(Sequence[Translate[liste11, Vector[(s * e) + (t * f)]], s, 0, n], t, 0, n) → liste12
  21. Outil7(B, I) → poly87, poly104, poly105, poly106, poly107, poly108, poly109, poly110
  22. Sequence(Sequence[Translate[liste13, Vector[(s * e) + (t * f)]], s, 0, n], t, 0, n) → liste14
  23. Outil6(J, K) → poly111, poly144, poly145, poly146, poly147, poly148, poly149, poly150
  24. Outil7(L, M) → poly151, poly152, poly153, poly154, poly155, poly156, poly157, poly158
  25. Line(N, O) → j
  26. Polygon(G, H, 4) → poly159, k, l, m, p, P, Q
  27. Polygon(E, F, 4) → poly160, q, r, s, t, R, S
  28. Polygon(C, D, 4) → poly161, a_1, b_1, c_1, d_1, T, U
  29. Polygon(S_1, T_1, 4) → poly162, e_1, f_1, g_1, h_1, V, W
  30. Polygon(J, K, 4) → poly163, i_1, j_1, k_1, l_1, Z, A_1
  31. Polygon(A_2, B_2, 4) → poly164, m_1, n_1, p_1, q_1, J_1, K_1
  32. Polygon(L, M, 4) → poly165, r_1, s_1, t_1, a_2, L_1, M_1

AI Drawing Prompt Reference

Create a complex geometric pattern demonstrating the use of geometric transformations and function graphs in jacquard textiles. Begin by constructing multiple quadrilaterals, then use vector transformations and sequence operations to translate and combine these shapes, forming layered patterns. The design features repeated geometric units that are rotated and translated to create a continuous texture, showcasing the application of function graphs and vectors.
The prompt above was compiled from the original drawing commands and is for reference only.