Pizza physics (New York-style) - Colm Kelleher

比萨物理学（纽约风味） - 科尔姆·凯莱赫

Transcriber: Andrea McDonough Reviewer: Bedirhan Cinar

翻译人员: Geoff Chen 校对人员: Zhiting Chen

Pretty much everyone loves eating pizza,

几乎所有人都爱吃比萨

but it can be a messy business.

但这可能是个糟糕的生意

Pizza is soft and bendable.

比萨很柔软、易弯 你该如何避免奶酪掉到地上呢？

So how can you stop all that cheese from falling off?

You might know some tricks:

你也许知道一些技巧：

你可以使用两只手

you can use two hands -- not so classy,

这不怎么文明

or you can use a paper plate

你也可以使用纸盘

and allow only the tip of the pizza to peek out.

让一小段比萨不掉落

There's one other trick, though:

还有另一个法子，那就是：

握着饼皮边，你可以将比萨折到中间

holding the crust, you can sort of fold the slice down the middle.

Now the tip of the pizza isn't falling over,

这样饼尖就不会往下弯

and you can eat it without getting tomato sauce all over yourself

你可以吃着它，同时不担心 番茄酱会洒落在身上

或不小心吃到那纸盘的边缘

or accidentally biting off some of that paper plate.

但为什么当你折叠饼皮边时 比萨饼尖会保持它原先的位置而不弯曲？

But why should the tip stay up just because you bent the crust?

为了理解这个现象 你必须知道两件事：

To understand this, you need to know two things:

a little bit about the math of curved shapes

一点儿关于弯曲形状的数学

and a little about the physics of thin sheets.

和一点儿关于薄片的物理学

First, the math.

首先是数学

Suppose I have a flat sheet made out of rubber.

假设我有一个橡皮薄片

It's really thin and bendable, so it's easy to roll into a cylinder.

它非常薄，可以弯折 所以它非常容易卷成筒状

I don't need to stretch the sheet at all, just bend it.

我不须要拉长薄片，就只是折弯它

This property where one shape can be transformed into another

这使一个形状 可以转变为另一个形状

without stretching or crumpling, is called isometry.

却不会拉伸或弄皱其原本的特性 称为等距

A mathematician would say that a flat sheet is isometric to a cylinder.

数学家可能会说 薄片就是个等距的圆筒

But not all shapes are isometric.

但并不是每一种形状都是等距的

If I try to turn my flat sheet into part of a sphere,

如果我试着将我的薄片弄成球面

there's no way I can do it.

这完全不可行

You can check this for yourself,

你可以自己试着将

by trying to fit a flat sheet of paper onto a soccer ball

一张薄纸片弄成一个足球

而不拉伸或弯折那张纸

without stretching or crumpling the paper.

这完全不可能

It's just not possible.

So a mathematician would say

因此数学家会说

that a flat sheet and a sphere aren't isometric.

薄片和球体不是等距的

There's one more familiar shape that isn't isometric

有另一种类似的形状

to any of the shapes we've seen so far: a potato chip.

和任何我们看到的形状相比 都不是等距的

薯片

Potato chip shapes aren't isometric to flat sheets.

薯片的形状对平板来说不是等距的

If you want to get a flat piece of rubber into the shape of a potato chip,

如果你想要将一个橡皮平板 变成一个薯片

你需要拉伸它

you need to stretch it -- not just bend it, but stretch it as well.

而不是折弯它或是延展它

So, that's the math.

因此，那是数学

Not so hard, right?

不难吧，不是吗？

Now for the physics.

现在我们看看物理学

It can be summed up in one sentence:

它可以总结为一句话：

Thin sheets are easy to bend but hard to stretch.

纸张容易折弯但难以拉伸

This is really important.

这很重要

Thin sheets are easy to bend but hard to stretch.

薄的纸片容易折弯，但难以延展

Remember when we rolled our flat sheet of rubber into a cylinder?

还记得我们将 橡胶薄片卷成圆筒的时刻吗？

That wasn't hard, right?

那不难，是吧？

But imagine how hard you'd have pull on the sheet

但想象一下你得多用力 才能将那薄片

增加百分之十的面积

to increase its area by 10 percent.

It would be pretty difficult.

那会很困难的

The point is that bending a thin sheet

重点是将一张薄片折弯 只需要花很少的力气

takes a relatively small amount of force,

but stretching or crumbling a thin sheet is much harder.

但是要拉长或揉捏 一张薄片是比较困难的

Now, finally, we get to talk about pizza.

现在，最后，我们来谈谈比萨

Suppose you go down to the pizzeria and buy yourself a slice.

假设你去比萨店买一片比萨

You pick it up from the crust, first, without doing the fold.

你首先拾起它的硬皮边 试着不让它弯折下落

Because of gravity, the slice bends downwards.

由于重力的原因 这片饼皮会往下弯曲

Pizza is pretty thin, after all,

比萨挺薄的

and we know that thin sheets are easy to bend.

我们知道薄片容易弯曲

You can't get it in your mouth,

你没法儿将它放进嘴里

cheese and tomato sauce dripping everywhere -- it's a big mess.

起司和番茄酱会掉满地

弄得一团糟

So you fold the crust.

所以你将饼皮折叠在一起

When you do, you force the pizza into something like a taco shape.

当你这么做时 你使比萨形成某种钟型形状

这并不难

That's not hard to do -- after all, this shape is isometric

毕竟这种形状是原来比萨饼的等距 它是平的

to the original pizza, which was flat.

But imagine what would happen if the pizza were to droop down

但想象一下，如果比萨掉到地上的话 然而你折弯它时

这会怎样呢？

while you're bending it.

Now it looks like a droopy taco.

现在，它看起来像一个 下垂的玉米面豆卷

And what does a droopy taco look like? A potato chip!

一个下垂的玉米面豆卷 看起来像什么呢？

一片薯片！

But we know that potato chips are not isometric to flat pieces of rubber

但我们知道薯片和橡胶薄片不是等距的

or flat pizzas,

或是扁平的比萨

and that means that in order to get into the shape it's in now,

这意味着为了把它弄成现在的形状

我们需要延展比萨饼皮

the slice of pizza had to stretch.

Since the pizza is thin, this takes a lot of force,

由于比萨饼很薄，这需要很多力气

compared to the amount of force it takes

相较于一开始折叠

to bend the pizza in the first place.

比萨饼时所需的力气

所以结论是什么呢？

So, what's the conclusion?

When you fold the pizza at the crust,

当你在饼皮尖折比萨的时候

you make it into a shape where a lot of force is needed to bend the tip down.

你必须花上许多力气来折弯那尖端

Often gravity isn't strong enough to provide this force.

通常地心引力没有提供那么强烈的力量

That was kind of a lot of information,

这堂课包含了许多信息

so let's do a quick backwards recap.

所以让我们来回顾一下吧

When pizza is folded at the crust,

当比萨饼从饼皮端对折时

gravity isn't strong enough to bend the tip.

地心引力并不强达到足以折弯那顶尖

Why? Because stretching a pizza is hard.

为什么？

因为要延展比萨饼是很困难的

And to bend the tip downwards, the pizza would have to stretch,

为了要折弯顶端

比萨必须延展

because the shape the pizza would be in,

为什么？

因为当比萨饼

the droopy taco shape,

那章鱼的下垂造型

isn't isometric to the original flat pizza.

和原来扁平比萨饼相比，并不是等距的

Why? Because of math.

为什么呢？

因为数学

As the pizza example shows, we can learn a lot

就像那比萨饼的例子所显示的

我们可以借由观察 不同的形状的数学属性来学习

by looking at the mathematical properties of different shapes.

And it's especially nice when those shapes happen to be pizza slices.

特别正好是那些形状刚好类似比萨时