正六边形三边形密铺
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①本范例演示了正六边形以三边形方式进行的正则密铺图形;②涉及的核心数学概念包括多边形构造、向量运算、几何变换等;③作图要点提炼自构造摘要,使用了Point、Polygon、Vector、Translate等GeoGebra命令与对象;④适合高中数学教学,用于展示平面图形的密铺特性与变换规律。
GeoGebra 命令及参数
Point(xAxis) → BPolygon(A, B, 6) → poly1, f, F, g, h, i, j, k, C, D, EPolygon(D, C, 6) → poly2, l, J, m, n, p, q, r, G, H, IPolygon(I, H, 6) → poly3, s, N, t, a, b, c, d, K, L, MPoint(xAxis) → OVector(B, O) → uTranslate(poly1, u) → poly1'Point(yAxis) → PVector(A, P) → vTranslate(poly2, v) → poly2'Translate(poly2, u) → poly2'_{1}Translate(poly1', u) → poly1''Translate(poly2', u) → poly2''Translate(poly3, u) → poly3'Translate(poly1', v) → poly1''_{1}Translate(poly1'', v) → poly1'''Translate(poly1, v) → poly1'_{1}Translate(poly2', v) → poly2''_{1}Translate(poly2'_{1}, u) → poly4Translate(poly2'', u) → poly2'''Translate(poly2''_{1}, u) → poly5Translate(poly5, u) → poly5'Translate(poly1''', u) → poly6Translate(poly1'', u) → poly1'''_{1}Translate(poly4, u) → poly4'Translate(poly3', u) → poly3''Translate(poly2''', u) → poly7Translate(poly1'''_{1}, u) → poly8Translate(poly6, u) → poly6'Translate(poly1'_{1}, v) → poly9Translate(poly2''_{1}, v) → poly10Translate(poly1''_{1}, v) → poly11Translate(poly1''', v) → poly12Translate(poly5, v) → poly5'_{1}Translate(poly9, v) → poly9'Translate(poly10, v) → poly10'Translate(poly11, v) → poly11'Translate(poly5'_{1}, v) → poly13Translate(poly12, v) → poly12'Translate(poly5', v) → poly5''Translate(poly6, v) → poly6'_{1}Translate(poly7, v) → poly7'Translate(poly7', v) → poly7''Translate(poly6'_{1}, v) → poly14Translate(poly5'', v) → poly5'''Translate(poly6', v) → poly6''Translate(poly7'', v) → poly7'''Translate(poly6'', v) → poly6'''Translate(poly6''', v) → poly15Translate(poly9', v) → poly9''Translate(poly10', v) → poly10''Translate(poly11', v) → poly11''Translate(poly13, v) → poly13'Translate(poly12', v) → poly12''Translate(poly5''', v) → poly16Translate(poly14, v) → poly14'Translate(poly7''', v) → poly17Translate(poly4', u) → poly4''Translate(poly7, u) → poly7'_{1}Translate(poly6', u) → poly6''_{1}Translate(poly7', u) → poly7''_{1}Translate(poly6'', u) → poly6'''_{1}Translate(poly7''_{1}, v) → poly18Translate(poly18, v) → poly18'Translate(poly6'''_{1}, v) → poly19Translate(poly19, v) → poly19'Translate(poly18', v) → poly18''Translate(poly8, u) → poly8'Translate(poly9'', v) → poly9'''Translate(poly11'', v) → poly11'''Translate(poly12'', v) → poly12'''Translate(poly14', v) → poly14''Translate(poly15, v) → poly15'Translate(poly19', v) → poly19''Translate(poly7'_{1}, u) → poly20Translate(poly7''_{1}, u) → poly21Translate(poly18, u) → poly18'_{1}Translate(poly4'', u) → poly4'''Translate(poly18'_{1}, v) → poly22Translate(poly22, v) → poly22'Translate(poly8', u) → poly8''Translate(poly8'', v) → poly8'''Translate(poly8''', v) → poly23Translate(poly23, v) → poly23'Translate(poly23', v) → poly23''Translate(poly23'', v) → poly23'''Translate(poly3'', u) → poly3'''Translate(poly3''', u) → poly24
AI 绘图提示语参考
画一个正则平铺{6,3}的六边形网格:先在平面上取两条参考轴确定基准点A,并以A和另一点B为起点构造一个以6边为边数的正六边形。再用六边形的对应顶点关系构造相邻的第二、第三个六边形,使它们在同一平面上连成带状布局。然后在两组平移方向上定义平移向量:一组由B指向参考轴上的O,另一组由A指向参考轴上的P。按这两个向量对第1、2、3个六边形进行重复平移,形成多行多列的规则六边形镶嵌,并让各平移后的六边形与原图保持边对边贴合。
以上提示语为根据原始绘图命令整理而来,仅供参考。