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一块披萨也能用物理学来解释!

Pizza physics (New York-style) - Colm Kelleher

很多人都喜欢吃披萨,
Pretty much everyone loves eating pizza,
但是它将成为一个复杂的行业。
but it can be a messy business.
披萨是又软又弯
Pizza is soft and bendable.
你如何能够阻止咬它的时候不掉落呢?
So how can you stop all that cheese from falling off?
你需要知道一些技巧:
You might know some tricks:
你有两种方法,并不是特别好,
you can use two hands — not so classy,
或许你可以用一个纸盘子
or you can use a paper plate
不让披萨掉出来
and allow only the tip of the pizza to peek out.
这儿还有别的小技巧 像这样
There’s one other trick, though:
握着它的外壳, 你可以像这样把它对折到中间
holding the crust, you can sort of fold the slice down the middle.
现在你就可以吃披萨不用担心掉出来啦
Now the tip of the pizza isn’t falling over,
你吃披萨的时候就不用担心番茄酱浅到满身都是。
and you can eat it without getting tomato sauce all over yourself
或是不小心咬到纸碟的边
or accidentally biting off some of that paper plate.
不过为什么只是把它卷起来就搞定了呢
But why should the tip stay up just because you bent the crust?
想明白原因,你需要知道这2件事:
To understand this, you need to know two things:
关于咬一小口的弯曲形状数学
a little bit about the math of curved shapes
和一点物理学上的薄片
and a little about the physics of thin sheets.
首先,关于数学
First, the math.
假设我有一张橡胶片儿,
Suppose I have a flat sheet made out of rubber.
这张橡胶片非常薄而且可弯曲的,所以很容易就把它卷成圆筒的样子
It’s really thin and bendable, so it’s easy to roll into a cylinder.
我都不用用力拉它就搞定了,只需要卷一下
I don’t need to stretch the sheet at all, just bend it.
这个性质让一个形状转变成另外一个形状
This property where one shape can be transformed into another
而不用通过拉伸或碾压,这叫等距
without stretching or crumpling, is called isometry.
数学家可能会说 这是一片等距柱面
A mathematician would say that a flat sheet is isometric to a cylinder.
不过不是所有形状都是等距的
But not all shapes are isometric.
如果我想要把这张片儿变成个球
If I try to turn my flat sheet into part of a sphere,
这是不可能我可以做到的
there’s no way I can do it.
你可以自己试一下
You can check this for yourself,
把一张平片纸变成一个足球
by trying to fit a flat sheet of paper onto a soccer ball
不通过使用拉伸或者挤压它
without stretching or crumpling the paper.
这不可能
It’s just not possible.
所以一位数学家会说
So a mathematician would say
这张平片和一个球体不是等体积的
that a flat sheet and a sphere aren’t isometric.
还有一个我们在已知的图形中
There’s one more familiar shape that isn’t isometric
更加熟悉的不等距图形—薯片
to any of the shapes we’ve seen so far: a potato chip.
薯片的形状不等距于平面图形
Potato chip shapes aren’t isometric to flat sheets.
如果你想把一个橡胶片变成薯片的形状
If you want to get a flat piece of rubber into the shape of a potato chip,
你需要拉伸它— 不仅仅是弯曲 还有拉伸
you need to stretch it — not just bend it, but stretch it as well.
这就是数学
So, that’s the math.
不难,对不对?
Not so hard, right?
现在到物理学了.
Now for the physics.
可以全部总结为一句话:
It can be summed up in one sentence:
这片儿很容易弯曲但很难伸张
Thin sheets are easy to bend but hard to stretch.
这是非常重要的一点
This is really important.
这片儿能很易折弯,但很难拉伸
Thin sheets are easy to bend but hard to stretch.
记得我们把那张橡皮片把它卷成圆筒吗?
Remember when we rolled our flat sheet of rubber into a cylinder?
那一点都不难,是不是?
That wasn’t hard, right?
但想一下多难,假如你拉那张橡胶片儿
But imagine how hard you’d have pull on the sheet
去增加它10%的面积
to increase its area by 10 percent.
这还挺困难的
It would be pretty difficult.
这重点就是 弯曲一张薄片儿
The point is that bending a thin sheet
只用相对较小的力量
takes a relatively small amount of force,
但拉伸或者压皱一张薄片会难很多
but stretching or crumbling a thin sheet is much harder.
现在,最后,我们来说一下披萨
Now, finally, we get to talk about pizza.
假设你去一家披萨店,并买了一片披萨
Suppose you go down to the pizzeria and buy yourself a slice.
你拿起披萨边,首先,先不把它卷起
You pick it up from the crust, first, without doing the fold.
因为重力,这片披萨是向下的
Because of gravity, the slice bends downwards.
毕竟披萨还是挺薄的
Pizza is pretty thin, after all,
并且我们知道薄片是更容易弯曲
and we know that thin sheets are easy to bend.
不能很好的吃到嘴里
You can’t get it in your mouth,
芝士和番茄酱掉到身上到处都是,这还真是挺麻烦的
cheese and tomato sauce dripping everywhere — it’s a big mess.
所以你把它折起来
So you fold the crust.
当你这样做的时候,你把披萨卷成像个鸡肉卷一样的形状
When you do, you force the pizza into something like a taco shape.
这并不难做,毕竟这形状是等距的
That’s not hard to do — after all, this shape is isometric
披萨原来的形状,是平坦的
to the original pizza, which was flat.
但试想一下,如果披萨往下掉会变成什么样呢
But imagine what would happen if the pizza were to droop down
当你把它卷起来的时候
while you’re bending it.
现在看起来就像个往下垂的鸡肉卷
Now it looks like a droopy taco.
那这个往下垂的鸡肉卷像什么?一个薯片!
And what does a droopy taco look like? A potato chip!
但我们知道薯片不是等距薄片或者橡胶
But we know that potato chips are not isometric to flat pieces of rubber
或平面披萨
or flat pizzas,
这意味着为了变成现在的形状
and that means that in order to get into the shape it’s in now,
这片薄披萨必须经过拉伸
the slice of pizza had to stretch.
虽然披萨很薄 但这需要很大的力量
Since the pizza is thin, this takes a lot of force,
相比它需要的力量
compared to the amount of force it takes
来弯曲披萨
to bend the pizza in the first place.
所以 结论是
So, what’s the conclusion?
当你从较脆的外壳面来弯曲披萨
When you fold the pizza at the crust,
你需要很大力量将它完全翻转
you make it into a shape where a lot of force is needed to bend the tip down.
通常 重力提供了足够力量
Often gravity isn’t strong enough to provide this force.
这包含了许多信息
That was kind of a lot of information,
让我们快速的做个回顾
so let’s do a quick backwards recap.
当披萨的外壳被弯曲时
When pizza is folded at the crust,
重力不足以对抗弯曲的尖端
gravity isn’t strong enough to bend the tip.
为什么呢?因为拉伸披萨是困难的
Why? Because stretching a pizza is hard.
弯那尖头会往下,要拉开披萨
And to bend the tip downwards, the pizza would have to stretch,
不然它会变成
because the shape the pizza would be in,
一个下垂的鸡肉卷形状,
the droopy taco shape,
这不是一个原来披萨的等距形状。
isn’t isometric to the original flat pizza.
为什么?因为数学。
Why? Because of math.
就像比萨所展示的,我们可以学到很多。
As the pizza example shows, we can learn a lot
通过观察不同形状的数学道具
by looking at the mathematical properties of different shapes.
而当这些形状是披萨块时 它尤其有趣
And it’s especially nice when those shapes happen to be pizza slices.

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