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数学与纺织：提花图案的几何构造

数学与纺织：提花图案的几何构造
几何画板及绘图内容加载中，请稍等……
2020-02-16 20:17
多边形向量数列函数图像
①本范例演示了如何利用几何变换和函数图像构造提花织物的复杂图案；②涉及的核心数学概念包括向量、数列、多边形构造、变换与函数图像；③作图要点提炼自GeoGebra命令：Motif1, Vector, Sequence, Line, Polygon等命令用于创建和组合几何图形；④适合高中及以上学生学习几何作图、函数图像与变换应用。

GeoGebra 命令及参数

  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 绘图提示语参考

绘制一个复杂的几何图案，展示几何变换和函数图形在织锦图案中的应用。首先构建多个四边形，然后通过向量变换和序列操作，将这些四边形平移并组合，形成层叠的图案。图案中包含多个重复的几何单元，通过旋转和平移操作，形成连续的纹理效果，体现函数图形和向量的应用。
以上提示语为根据原始绘图命令整理而来，仅供参考。