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第六百五十一章 莫泽的移动沙发转弯问题(结构)(2 / 2)

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在很长的的一段时间里,数学界的大部分人,包括Hammersley在内,都认为Hammersley沙发是完美的,是沙发问题的最终解。

但同样作为沙发问题的高玩的Gerver并不这么认为,他向Hammersley提出了质疑。

Hammersley不以为然,始终认为Hammersley沙发是最完美的。

直到1992年,Gerver在Hammersley沙发的基础上,通过旋转路径构建新的形状,提出了Gerver沙发。

尽管看起来和Hammersley沙发没什么区别,但从数学角度看,你会发现Gerver沙发更加复杂。

看看下面的图,刻度线描绘了边界上不同部分之间的过渡点——3条直线、15条曲线段。

其中 V, XIII和 XVIII三段是线段,

I, VI, XII,和 XVII是圆弧,

II, III, VII, XI, XV和 XVI是圆的渐开线,

IV和 XIV是圆的渐开线的渐开线。

每条曲线段由一个单独的解析表达式描述。

这个神似老式电话听筒的Gerver沙发,硬生生把沙发常数整整往上提升了足足 0.5%【沙发系数≈2.2195】,是目前单个走廊转角沙发移动问题中寻找到的最优解。

Gerver沙发是否就是最优的沙发曲线,他不得而知,但他表示最完美的沙发系数应该是在2.2195~2.37之间。

对于Gerver沙发的现世,数学家们纷纷拍手称好,除了加州大学戴维斯分校数学系教授Dan Romik。

据说Dan Romik刚拿驾照没多久,但却对沙发过弯问题有着极高的要求。

他并不满足于使用Gerver沙发漂移单个急弯,他认为能完美漂移过二连发急弯的男人才是真正的数学车神。

为了可以 0距离感受沙发,他甚至模仿葛优躺在沙发上思考如何优化。

躺在沙发上的Romik,一下子就想起了类似比基尼的形状。

喜欢数学心请大家收藏:数学心本站更新速度全网最快。

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