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。

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

所谓“铺砌”，就是铺上瓷，形成某种图案。

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

希尔随后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、瓷品。

Those were the first tilings she would invent.

这些是她发明的第一批瓷。

Sort of yellow and pink flower tiling background.

JAD：有点黄色和粉红色的花朵平铺背景。

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——使得描绘海洋如此困难。

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·彭罗斯也为数学界做出了一个贡献，所在数学领域被称为“铺砌”。

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

何菱形的拼图必然对应一叠立方体。

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、在街上向陌生人扔硬币，有时甚至可以用来买东西。

And after some analysis, concluded that this was, in fact, Penrose tiling 500 years before Penrose.

经过一些分析后，发现这其实是早于彭罗斯 500 年的彭罗斯铺砌。

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， 然后把它想象成一堆立方体。

Moore saw that kind Mrs Wood had brought many good tilings from her own kitchen.

摩尔看到伍德太太从她自己的厨房里带来了许多好的瓷。

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。

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.

然后对于这个谜题，你问从一种拼法变换到另一种拼法最多可能需要多少步。

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盯着看，眯起眼睛后，以某种方将其视为四维超立方体的堆栈？

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.

在数学中，该属性被称为“非周期性”，仅由两种瓷组成的非周期性瓷组合轰动一时，以至于被命名为“彭罗斯铺砌”。

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。

The game is that every time inside this big tiling you find a small 1x1x1 rhombic dodecahedron, you make this move where each piece can slide through the middle.

游戏规则是每次在大拼接中找到一个边长为1x1x1的菱形十二面体时，你可以进行这样的操作：每个部分都可以从中间滑动。

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中的意一种变换到另一种？