平移镶嵌 by jahatch8

几何画板及绘图内容加载中，请稍等……

2014-03-30 05:21

向量变换几何作图

所属专题 Tesselation by Translation Tesselation by Translation

这个范例演示了通过平移构造正方形镶嵌的过程。涉及的核心数学概念包括平移变换、角度和几何作图。通过使用GeoGebra命令如Polygon、AttachCopyToView、Point、Vector和Translate，可以动态地展示平移变换的性质。适合初中及以上学生学习几何变换和镶嵌图案。

GeoGebra 命令及参数

Polygon(A, B, 4) → poly1, a, b, c, d, C, D
AttachCopyToView(PolyLine[(2.1, -3.38), (2.02, -3.38), (1.94, -3.38), (1.8800000000000001, -3.4), (1.82, -3.42), (1.76, -3.46), (1.68, -3.5), (1.62, -3.54), (1.56, -3.56), (1.52, -3.62), (1.48, -3.68), (1.46, -3.7600000000000002), (1.46, -3.86), (1.46, -3.94), (1.48, -4.0200000000000005), (1.4000000000000001, -4.0200000000000005), (1.32, -4.0200000000000005), (1.26, -4.04), (1.18, -4.04), (1.12, -4.0600000000000005), (1.06, -4.08), (0.98, -4.12), (0.9, -4.14), (0.84, -4.16), (0.78, -4.2), (0.74, -4.26), (0.72, -4.32), (0.64, -4.32), (0.62, -4.38), (0.56, -4.44), (0.5, -4.5200000000000005), (0.44, -4.5600000000000005), (0.42, -4.64), (0.42, -4.72), (0.4, -4.8), (0.36, -4.74), (0.36, -4.66), (0.36, -4.58), (0.34, -4.64), (0.3, -4.7), (0.28, -4.76), (0.26, -4.82), (0.24, -4.76), (0.22, -4.7), (0.22, -4.62), (0.2, -4.68), (0.18, -4.76), (0.16, -4.82), (0.14, -4.76), (0.14, -4.66), (0.16, -4.6000000000000005), (0.22, -4.54), (0.24, -4.48), (0.3, -4.46), (0.34, -4.4), (0.38, -4.34), (0.4, -4.28), (0.42, -4.2), (0.44, -4.14), (0.46, -4.08), (0.5, -4.0200000000000005), (0.56, -3.96), (0.6, -3.9), (0.66, -3.88), (0.72, -3.84), (0.78, -3.8200000000000003), (0.86, -3.8200000000000003), (0.9, -3.7600000000000002), (0.86, -3.7), (0.8, -3.68), (0.74, -3.66), (0.68, -3.62), (0.64, -3.56), (0.58, -3.5), (0.54, -3.42), (0.52, -3.36), (0.5, -3.3000000000000003), (0.48, -3.24), (0.48, -3.16), (0.48, -3.08), (0.5, -2.98), (0.52, -2.9), (0.44, -2.88), (0.34, -2.88), (0.26, -2.88), (0.2, -2.84), (0.18, -2.7800000000000002), (0.14, -2.72), (0.1, -2.66), (0.08, -2.6), (0.06, -2.54), (0.06, -2.46), (0.04, -2.4), (-0.04, -2.4), (-0.1, -2.38), (-0.16, -2.32), (-0.22, -2.2800000000000002), (-0.28, -2.24), (-0.34, -2.2), (-0.4, -2.18), (-0.46, -2.16), (-0.54, -2.18), (-0.6, -2.2), (-0.66, -2.22), (-0.72, -2.24), (-0.8, -2.24), (-0.84, -2.3000000000000003), (-0.88, -2.36), (-0.92, -2.42), (-0.98, -2.46), (-1.06, -2.5), (-1.12, -2.54), (-1.18, -2.56), (-1.2, -2.62), (-1.24, -2.68), (-1.26, -2.74), (-1.28, -2.8000000000000003), (-1.34, -2.86), (-1.3800000000000001, -2.92), (-1.44, -2.96), (-1.46, -3.02), (-1.52, -3.08), (-1.54, -3.14), (-1.58, -3.2), (-1.6, -3.2600000000000002), (-1.56, -3.3200000000000003), (-1.5, -3.36), true], 1, (-4.3, -7.96), (23.38, 6.3), (0, 713), (1384, 0)) → stroke1
Point(a) → E
Point(c) → F
Vector(E, F) → u
Translate(stroke1, u) → stroke1'
AttachCopyToView(PolyLine[(-1.5, -3.38), (-1.58, -3.38), (-1.6600000000000001, -3.38), (-1.74, -3.38), (-1.82, -3.38), (-1.86, -3.44), (-1.9000000000000001, -3.5), (-1.92, -3.44), (-1.92, -3.36), (-1.9000000000000001, -3.3000000000000003), (-1.96, -3.2800000000000002), (-2.04, -3.2800000000000002), (-2.08, -3.34), (-2.1, -3.4), (-2.1, -3.3200000000000003), (-2.06, -3.2600000000000002), (-2, -3.2), (-1.94, -3.16), (-1.8800000000000001, -3.14), (-1.82, -3.1), (-1.76, -3.08), (-1.7, -3.04), (-1.68, -2.96), (-1.6400000000000001, -2.9), (-1.6400000000000001, -2.82), (-1.62, -2.7600000000000002), (-1.6, -2.7), (-1.58, -2.64), (-1.54, -2.58), (-1.48, -2.52), (-1.46, -2.46), (-1.44, -2.4), (-1.42, -2.32), (-1.4000000000000001, -2.2600000000000002), (-1.36, -2.18), (-1.32, -2.12), (-1.26, -2.08), (-1.2, -2.04), (-1.1400000000000001, -2.02), (-1.08, -2), (-1.02, -1.98), (-0.96, -1.94), (-0.92, -1.8800000000000001), (-0.88, -1.82), (-0.8200000000000001, -1.78), (-0.78, -1.72), (-0.78, -1.6400000000000001), (-0.78, -1.56), (-0.78, -1.48), (-0.8, -1.42), (-0.86, -1.4000000000000001), (-0.92, -1.3800000000000001), (-0.98, -1.36), (-1.08, -1.36), (-1.18, -1.36), (-1.24, -1.3800000000000001), (-1.32, -1.4000000000000001), (-1.42, -1.42), (-1.52, -1.42), (-1.58, -1.44), (-1.6400000000000001, -1.46), (-1.7, -1.48), (-1.76, -1.5), (-1.82, -1.52), (-1.86, -1.6), (-1.8800000000000001, -1.6600000000000001), (-1.9000000000000001, -1.72), (-1.92, -1.78), (-1.92, -1.86), (-1.92, -1.94), (-1.84, -1.94), (-1.76, -1.94), (-1.68, -1.94), (-1.6, -1.94), (-1.54, -1.92), (-1.48, -1.8800000000000001), (-1.5, -1.94), (-1.54, -2), (-1.56, -2.06), (-1.58, -2.12), (-1.62, -2.18), (-1.6600000000000001, -2.24), (-1.68, -2.32), (-1.74, -2.34), (-1.8, -2.38), (-1.84, -2.32), (-1.84, -2.24), (-1.86, -2.18), (-1.9000000000000001, -2.24), (-1.94, -2.3000000000000003), (-1.96, -2.36), (-1.98, -2.3000000000000003), (-2, -2.22), (-2.04, -2.16), (-2.06, -2.1), (-2.08, -2.04), (-2.1, -1.98), (-2.1, -1.9000000000000001), (-2.1, -1.82), (-2.1, -1.74), (-2.12, -1.68), (-2.12, -1.58), (-2.12, -1.5), (-2.12, -1.42), (-2.12, -1.34), (-2.12, -1.24), (-2.1, -1.18), (-2.04, -1.1400000000000001), (-1.96, -1.12), (-1.9000000000000001, -1.1), (-1.82, -1.1), (-1.72, -1.1), (-1.6600000000000001, -1.08), (-1.58, -1.08), (-1.5, -1.08), (-1.44, -1.04), (-1.3800000000000001, -1.02), (-1.32, -0.96), (-1.3, -0.9), (-1.24, -0.86), (-1.18, -0.8200000000000001), (-1.1400000000000001, -0.76), (-1.06, -0.76), (-0.98, -0.76), (-0.9, -0.76), (-0.84, -0.74), (-0.78, -0.72), (-0.72, -0.7000000000000001), (-0.68, -0.64), (-0.62, -0.6), (-0.6, -0.54), (-0.58, -0.48), (-0.54, -0.42), (-0.52, -0.36), (-0.48, -0.3), (-0.42, -0.26), (-0.38, -0.2), (-0.34, -0.14), (-0.32, -0.08), (-0.3, 0), (-0.26, 0.08), (-0.24, 0.16), (-0.24, 0.24), (-0.24, 0.32), (-0.24, 0.4), (-0.24, 0.48), (-0.24, 0.56), (-0.3, 0.58), (-0.36, 0.62), (-0.42, 0.64), (-0.5, 0.64), (-0.56, 0.68), (-0.62, 0.7000000000000001), (-0.68, 0.66), (-0.74, 0.64), (-0.78, 0.58), (-0.8200000000000001, 0.52), (-0.88, 0.5), (-0.92, 0.44), (-0.98, 0.4), (-1.04, 0.36), (-1.12, 0.26), (-1.18, 0.22), (-1.24, 0.18), (-1.3, 0.16), (-1.3800000000000001, 0.16), (-1.44, 0.2), (-1.44, 0.28), true], 1, (-4.3, -7.96), (23.38, 6.3), (0, 713), (1384, 0)) → stroke2

AI 绘图提示语参考

绘制一个由多个正方形通过平移变换形成的平铺图案。首先绘制一个正方形，然后通过平移该正方形的边得到一个新的正方形，重复此过程，直到形成一个完整的平铺图案。

以上提示语为根据原始绘图命令整理而来，仅供参考。