二十棵树植树问题【转载】








二十棵树植树问题【转载】
20棵树植树问题，源于植树，升华在数学上的图谱学中，图谱构造的智、巧、美又广泛应用于社会的方方面面。20棵树植树问题，简单地说，就是：有20棵树，若每行四棵，问怎样种植（组排），才能使行数更多？

    20棵树植树问题，早在十六世纪，古希腊、古罗马、古埃及等都先后完成了十六行的排列并将美丽的图谱广泛应
用于高雅装饰建筑、华丽工艺美术（图1）。进入十八世纪，德国数学家高斯猜想20棵树植树问题应能达到十八行，但一直未能见其发表绘制出的十八行图谱。直
到十九世纪，此猜想才被美国的娱乐数学大师山姆.劳埃德完成并绘制出了精美的十八行图谱，而后还制成娱乐棋盛行于欧美，颇受人们喜爱（图1、2）。


 




    进入20世纪，电子计算机的高速发展方兴未艾，电子计算机的普及和应用在数学领域中也大显身手，电子计算机
绘制出的数学图谱更是广泛应用于工艺美术、建筑装饰和自然科学领域。数学上的20棵树植树问题也随之有了更新的进展。在二十世纪七十年代，两位数学爱好者
巧妙地运用电子计算机超越数学大师山姆.劳埃德保持的十八行纪录，成功地绘制出了精湛美丽的二十行图谱，创造了20棵树植树问题新世纪的新纪录并保持至今
（图3）。









引用地址： 南开大学组合数学中心
本文引用地址：
http://www.sciencenet.cn/m/user_content.aspx?id=219651

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