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正方形铺砖谜题

正方形铺砖谜题
几何画板及绘图内容加载中，请稍等……
2018-01-06 05:33
多边形向量三角函数解析几何几何作图
①本范例演示如何通过正方形网格构建复杂的铺砖图案；②涉及的核心数学概念包括平面几何、向量运算、三角函数关系以及二维坐标几何；③作图要点：运用了Point（点）、Polygon（多边形）、Sort（排序）、Sequence（序列）、Join（连接）、If（条件判断）、Rotate（旋转）等GeoGebra命令；④适合高中数学教学，用于探索二维图形的变换与组合规律。

GeoGebra 命令及参数

  1. Point(Circle[H1, 1]) → H2
  2. Point(Circle[I31, 1]) → I32
  3. Point(Circle[S1, 1]) → S2
  4. Point(Circle[L1, 1]) → L2
  5. Point(Circle[I21, 1]) → I22
  6. Point(Circle[I41, 1]) → I42
  7. Point(Circle[L21, 1]) → L22
  8. Point(Circle[V221, 1]) → V222
  9. Point(Circle[V211, 1]) → V212
  10. Polygon(A1, A2, A5, A3, A4, A1, A5, A6, A7, A8, A9) → Rahmen, f, p, q, g, h, i, j, k, l, m, n
  11. Sort({V11, V12, V13, V14, V211, V212, V221, V222}) → Schwarz
  12. Sort(Union[Union[Union[Union[Union[Union[Union[{S1, S2, S4, S3}, {L1, L2, L3}], {I21, I22}], {I31, I32, I33}], {I41, I42, I43, I44}], {Q1, Q2, Q3, Q4}], {L21, L22, L23, L24}], {H1, H2, H4, H3}]) → Weiss
  13. Sequence(Segment[(0.5, i), (6.5, i)], i, 1.5, 5.5, 1) → XStrecken
  14. Sequence(Segment[(i, 0.5), (i, 6.5)], i, 1.5, 5.5, 1) → YStrecken
  15. Join(Sequence[Sequence[(i, j), j, 1, 6], i, 1, 6]) → Alles
  16. Sort(Union[Weiss, Schwarz]) → Zusammen
  17. If(Zusammen ≟ Alles, 1, 0) → korrekt
  18. Polygon(V12 + (0.5, 0.5), V12 + (-0.5, 0.5), V12 + (-0.5, -0.5), V12 + (0.5, -0.5)) → VielV12, r, s, t, a
  19. Polygon(V11 + (0.5, 0.5), V11 + (-0.5, 0.5), V11 + (-0.5, -0.5), V11 + (0.5, -0.5)) → VielV11, b, c, d, e
  20. Polygon(V13 + (0.5, 0.5), V13 + (-0.5, 0.5), V13 + (-0.5, -0.5), V13 + (0.5, -0.5)) → VielV13, f_1, g_1, h_1, i_1
  21. Rotate(Polygon[V211 + (-0.5, -0.5), V211 + (1.5, -0.5), V211 + (1.5, 0.5), V211 + (-0.5, 0.5)], Angle[V212 - V211], V211) → VielV21
  22. Polygon(V14 + (0.5, 0.5), V14 + (-0.5, 0.5), V14 + (-0.5, -0.5), V14 + (0.5, -0.5)) → VielV14, j_1, k_1, l_1, m_1
  23. Rotate(Polygon[V221 + (-0.5, -0.5), V221 + (1.5, -0.5), V221 + (1.5, 0.5), V221 + (-0.5, 0.5)], Angle[V222 - V221], V221) → VielV22
  24. Rotate(Polygon[I21 + (-0.5, -0.5), I21 + (1.5, -0.5), I21 + (1.5, 0.5), I21 + (-0.5, 0.5)], Angle[I22 - I21], I21) → VielI2
  25. Rotate(Polygon[I31 + (-1.5, -0.5), I31 + (1.5, -0.5), I31 + (1.5, 0.5), I31 + (-1.5, 0.5)], Angle[I32 - I31], I31) → VielI3
  26. Rotate(Polygon[I41 + (-1.5, -0.5), I41 + (2.5, -0.5), I41 + (2.5, 0.5), I41 + (-1.5, 0.5)], Angle[I42 - I41], I41) → VielI4
  27. Polygon(Q1 + (-0.5, -0.5), Q1 + (1.5, -0.5), Q1 + (1.5, 1.5), Q1 + (-0.5, 1.5)) → VielQ, n_1, p_1, q_1, r_1
  28. Rotate(Polygon[L21 + (-0.5, (-0.5 * L2x)), L21 + (1.5, (-0.5 * L2x)), L21 + (1.5, (0.5 * L2x)), L21 + (0.5, (0.5 * L2x)), L21 + (0.5, (2.5 * L2x)), L21 + (-0.5, (2.5 * L2x)), L21 + (-0.5, (0.5 * L2x))], Angle[L22 - L21], L21) → VielL2
  29. Rotate(Polygon[L1 + (-0.5, (-0.5 * Lx)), L1 + (1.5, (-0.5 * Lx)), L1 + (1.5, (0.5 * Lx)), L1 + (0.5, (0.5 * Lx)), L1 + (0.5, (1.5 * Lx)), L1 + (-0.5, (1.5 * Lx)), L1 + (-0.5, (0.5 * Lx))], Angle[L2 - L1], L1) → VielL1
  30. Rotate(Polygon[S1 + (-0.5, (-0.5 * Sx)), S1 + (0.5, (-0.5 * Sx)), S1 + (0.5, (-1.5 * Sx)), S1 + (1.5, (-1.5 * Sx)), S1 + (1.5, (-0.5 * Sx)), S1 + (1.5, (0.5 * Sx)), S1 + (0.5, (0.5 * Sx)), S1 + (0.5, (1.5 * Sx)), S1 + (-0.5, (1.5 * Sx)), S1 + (-0.5, (0.5 * Sx))], Angle[S2 - S1], S1) → VielS
  31. Rotate(Polygon[H1 + (-1.5, (-0.5 * Hx)), H1 + (1.5, (-0.5 * Hx)), H1 + (1.5, (0.5 * Hx)), H1 + (0.5, (0.5 * Hx)), H1 + (0.5, (1.5 * Hx)), H1 + (-0.5, (1.5 * Hx)), H1 + (-0.5, (0.5 * Hx)), H1 + (-1.5, (0.5 * Hx))], Angle[H2 - H1], H1) → VielH