Just then a noise was audible outside. Footsteps rang on the metal tiling.

这个时候，外面传来了声响。金属地板上发出脚步声。

Among the steps the interior ministry promised with a new unit dedicated to finding the missing in greater efforts to tiling national database of human remains in the country’s morgues with the DNA of disappeared people.

在所有措施中，内政部承诺设立新的机构，致力于利用失踪人口的DNA来对政府停尸房中的遗体建立据库。

You know, tiling, the process of putting tiles together so that they form a particular pattern.

所谓“铺砌”，就是铺上砖，形成某种图案。

But back in the 1970s, Roger Penrose made a contribution to the world of mathematics and that part of mathematics known as tiling.

但回到 20 世纪 70 年代，罗杰·彭罗斯也为界做出了一个贡献，所在域被称为“铺砌”。

In mathematics, this is a property known as aperiodicity and the notion of an aperiodic tile set using only two tiles was such a sensation, it was given the name Penrose tiling.

在中，该属性被称为“非周期性”，仅由两种砖组成的非周期性砖组合轰动一时，以至于被命名为“彭罗斯铺砌”。

Hill then interested himself in practical ways of ditching and tiling.

希对挖沟和平铺的实用方法产生了兴趣。

They're also a great use for things like cement, candles, tiling.

它们也非常适用于水泥、蜡烛、砖等物品。

Those were the first tilings she would invent.

这些是她发明的第一批砖。

Sort of yellow and pink flower tiling background.

JAD：有点黄色和粉红色的花朵平铺背景。

There was a deeply inset front door framed in a mosaic of multi-colored pieces of tiling and a small flower garden in front, behind a low stucco wall topped by an iron railing which the beach moisture had begun to corrode.

有一扇嵌得很深的前门，镶着五颜六色的马赛克砖，前面是一个小花园，面是一堵低矮的灰泥墙，上面是铁栏杆，海滩的水分已经开始腐蚀了。

It was in Ward 5, at the very top of the Royal Waterloo Hospital, people walking past Across Waterloo Bridge, you might recognize the building with the red terracotta tiling.

那是在皇家滑铁卢医院的五号病房， 位于医院的最顶层，人们走过滑铁卢桥时，可能会认出那座有着红色赤陶瓦片装饰的建筑。

What is the three-dimensional tiling pattern where a four-dimensional creature could stare at it, squint their eyes, and somehow see it as a stack of four-dimensional hypercubes?

什么样的三维密铺图案能让一个四维生物盯着看，眯起眼睛，以某种方式将其视为四维超立方体的堆栈？

It's this tiling—this way of piecing the world together—that makes representing the ocean so dang hard.

正是这种拼接——将世界拼合在一起的方式——使得描绘海洋如此困难。

So a natural question you might wonder is, is it possible to get from any one of these tiling patterns to another one just by using these little hexagonal rotation steps?

所以一个自然产生的问题是，是否可以通过这些小六边形旋转步骤从这些拼图模式中的任意一种变换到另一种？

Coins are used for all kinds of things—collecting, opulent floor tiling, throwing them at strangers on the street, and sometimes even buying stuff.

硬币可用于各种各样的事情——收集、华丽的地板砖、在街上向陌生人扔硬币，有时甚至可以用来买东西。

Before telling you 3, 4, and 5 though, let's circle back to talk about that first one, where we are tiling the hexagon.

在告诉你3、4和5之前，让我们先回到第一个问题，也就是我们用菱形铺满六边形的那个。

Any tiling of rhombuses necessarily has a corresponding stack of cubes.

任何菱形的拼图必然对应一叠立方体。

You and I can stare at this tiling of rhombuses, squint our eyes, and somehow think of it as a stack of cubes.

你和我可以盯着这幅由菱形组成的拼图，眯起眼睛， 然把它想象成一堆立方体。

And when you do that, you might notice that sometimes that creates a new hexagon that wasn't there before, that you could also rotate, taking a step to yet another one of these tilings.

当你这么做的时候， 你可能会注意到有时会形成一个新的六边形， 这个六边形之前并不存在，你也可以旋转它， 从而进入另一种这样的平面填充方式。

And then for the puzzle, you ask what is the maximum number of moves that it might take to get from one tiling to another.

然对于这个谜题，你问从一种拼法变换到另一种拼法最多可能需要多少步。