The infinite life of pi - Reynaldo Lopes

无穷无尽的圆周率 - Reynaldo Lopes

翻译人员: Xuan Hong 校对人员: Cissy Yun

Try to measure a circle.

如果要测量一个圆

The diameter and radius are easy,

直径和半径都容易解决

they're just straight lines

它们都是直线

you can measure with a ruler.

可以用尺子测量

But to get the circumference,

但要测量圆的周长

you'd need measuring tape or a piece of string,

你就得用卷尺或绳子

unless there was a better way.

除非有更好的办法

Now, it's obvious

很显然的是

that a circle's circumference would get smaller or larger

圆的周长会随着直径

along with its diameter,

变换长短

but the relationship goes further than that.

但它们之间的关系还不止如此

In fact, the ratio between the two,

事实上

the circumference divided by the diameter,

无论圆的大小如何

will always be the same number,

圆的周长除以直径

no matter how big or small the circle gets.

得出来的数值是恒定的

Historians aren't sure when or how

历史学家不确定这个数字

this number was first discovered,

是何时出现 如何求得的

but it's been known in some form

但它以某种形式

for almost 4,000 years.

存在了近4000年

Estimates of it appear in the works of ancient Greek,

古希腊

Babylonian,

巴比伦

Chinese,

中国

and Indian mathematicians.

和印度的数学家都对它进行了估算

And it's even believed to have been used

我们甚至认为它被运用到

埃及金字塔的建造中

in building the Egyptian pyramids.

Mathematicians estimated it

数学家通过在圆内接多边形

by inscribing polygons in circles.

来估算这个数值

And by the year 1400,

到公元1400年

it had been calculated to as far as ten decimal places.

人们已经计算出小数点后第10位

So, when did they finally figure out the exact value

那么 究竟什么时候能求出它的精确值

instead of just estimating?

而不再是一个估计值呢？

Actually, never!

其实 永远无法求出！

You see, the ratio

因为

of a circle's circumference to its diameter

圆周长和直径的比值

is what's known as an irrational number,

是一个无理数

one that can never be expressed

它无法用两个整数的比值

as a ratio of two whole numbers.

来表示

You can come close,

你的估值可以很接近

but no matter how precise the fraction is,

但无论这个数字多么精确

it will always be just a tiny bit off.

它总是差那么一点

So, to write it out in its decimal form,

所以，如果用小数表示

you'd have an on-going series of digits

需要一连串的数字

starting with

也就是说

3.14159

从3.14159开始

and continuing

后面跟着的数字

forever!

没完没了！

That's why, instead of trying to write out

所以我们用希腊字母π来表示

an infinite number of digits every time,

而不是写成小数形式

we just refer to it using the Greek letter pi.

因为永远写不完

Nowadays, we test the speed of computers

现在我们让电脑计算π

by having them calculate pi,

以测量其运算速度

and quantum computers have been able

量子计算机

to calculate it up to two quadrillion digits.

可以计算出2000兆个数位

People even compete to see

人们也会比赛

how many digits they can memorize

看谁能记住更多的数位

and have set records for remembering

目前的世界纪录是

over 67,000 of them.

最多能记住67000多个数位

But for most scientific uses,

但一般的科学应用

you only need the first forty or so.

只需要小数点后约40位就行了

And what are these scientific uses?

那么 π能应用在什么地方呢？

Well, just about any calculations involving circles,

所有和圆有关的计算都会用到

from the volume of a can of soda

小到汽水罐的容积

to the orbits of satellites.

大到卫星轨道

And it's not just circles, either.

但也不局限于圆的计算

Because it's also useful in studying curves,

因为学习曲线也需要用到π

pi helps us understand periodic or oscillating systems

π帮助我们认识周期或振动系统

like clocks,

如钟摆

electromagnetic waves,

电磁波

and even music.

甚至音乐

In statistics, pi is used in the equation

在统计学中，π可代入等式中

to calculate the area under a normal distribution curve,

来计算正态分布曲线

which comes in handy for figuring out distributions

求得数据分布情况

of standardized test scores,

在计算标准化考试分数

financial models,

财务模型

or margins of error in scientific results.

或科学结果的误差范围时都会用到

As if that weren't enough,

不仅如此

pi is used in particle physics experiments,

π还用在粒子物理实验中

such as those using the Large Hadron Collider,

如大型强子对撞机有关的计算

not only due to its round shape,

不仅因为它是圆形的

but more subtly,

更巧妙的是

because of the orbits in which tiny particles move.

这和微粒运行的轨道有关

Scientists have even used pi

科学家还运用π

to prove the illusive notion

证实了一个观点

that light functions as both a particle

光既是一种粒子

and an electromagnetic wave,

也是一种电磁波

and, perhaps most impressively,

更令人惊叹的是

to calculate the density of our entire universe,

π还能计算宇宙密度

which, by the way,

不过

still has infinitely less stuff in it

宇宙中的物质

than the total number of digits in pi.

还是比π的总数位少得多