Try to measure a circle. The diameter and radius are easy, they're just straight lines you can measure with a ruler.
试着测量一个圆。直径和半径都容易解决，它们都是直线，可以用尺子测量。
But to get the circumference, you'd need measuring tape or a piece of string, unless there was a better way.
但要测量圆的周长，你就得用卷尺或绳子，除非有更好的办法。
Now, it's obvious that a circle's circumference would get smaller or larger along with its diameter,
很显然的是，圆的周长会随着直径变换长短，
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, the circumference divided by the diameter,
事实上，圆的周长除以直径
will always be the same number, no matter how big or small the circle gets.
得出来的数值是恒定的，无论圆的大小如何。
Historians aren't sure when or how this number was first discovered,
历史学家不确定这个数字是何时出现、如何求得的。
but it's been known in some form for almost 4,000 years.
但它以某种形式存在了近4000年。
Estimates of it appear in the works of ancient Greek, Babylonian, Chinese, and Indian mathematicians.
古希腊、巴比伦、中国和印度的数学家都对它进行了估算。
And it's even believed to have been used in building the Egyptian pyramids.
我们甚至认为它被运用到埃及金字塔的建造中。
Mathematicians estimated it by inscribing polygons in circles.
数学家通过在圆内接多边形来估算这个数值。
And by the year 1400, it had been calculated to as far as ten decimal places.
到公元1400年，人们已经计算出小数点后第10位。
So, when did they finally figure out the exact value instead of just estimating? Actually, never!
那么，究竟什么时候能求出它的精确值而不再是一个估计值呢？其实，永远无法求出！
You see, the ratio of a circle's circumference to its diameter is what's known as an irrational number,
因为圆周长和直径的比值是一个无理数，
one that can never be expressed as a ratio of two whole numbers.
它无法用两个整数的比值来表示。
You can come close, but no matter how precise the fraction is, it will always be just a tiny bit off.
你的估值可以很接近，但无论这个数字多么精确，它总是差那么一点。

So, to write it out in its decimal form, you'd have an on-going series of digits starting with 3.14159 and continuing forever!
所以，如果用小数表示，需要一连串的数字，也就是说从3.14159开始后面跟着的数字没完没了！
That's why, instead of trying to write out an infinite number of digits every time, we just refer to it using the Greek letter pi.
所以我们用希腊字母π来表示，而不是写成小数形式，因为永远写不完。
Nowadays, we test the speed of computers by having them calculate pi,
现在我们让电脑计算π，以测量其运算速度，
and quantum computers have been able to calculate it up to two quadrillion digits.
量子计算机可以计算出2000兆个数位。
People even compete to see how many digits they can memorize and have set records for remembering over 67,000 of them.
人们也会比赛看谁能记住更多的数位，目前的世界纪录是最多能记住67000多个数位。
But for most scientific uses, you only need the first forty or so. And what are these scientific uses?
但一般的科学应用只需要小数点后约40位就行了。那么，这些科学应用是什么呢？
Well, just about any calculations involving circles, from the volume of a can of soda to the orbits of satellites.
所有和圆有关的计算都会用到，小到汽水罐的容积，大到卫星轨道。
And it's not just circles, either. Because it's also useful in studying curves,
但也不局限于圆的计算。因为研究曲线也需要用到π，
pi helps us understand periodic or oscillating systems like clocks, electromagnetic waves, and even music.
π帮助我们认识周期或振动系统，如钟摆，电磁波甚至音乐。
In statistics, pi is used in the equation to calculate the area under a normal distribution curve,
在统计学中，π可代入等式中来计算正态分布曲线，
which comes in handy for figuring out distributions of standardized test scores, financial models, or margins of error in scientific results.
求得数据分布情况，在计算标准化考试分数，财务模型或科学结果的误差范围时都会用到。
As if that weren't enough, pi is used in particle physics experiments,
不仅如此，π还用在粒子物理实验中，
such as those using the Large Hadron Collider, not only due to its round shape,
如大型强子对撞机有关的计算，不仅因为它是圆形的，
but more subtly, because of the orbits in which tiny particles move.
更巧妙的是，这和微粒运行的轨道有关。
Scientists have even used pi to prove the illusive notion that light functions as both a particle and an electromagnetic wave,
科学家还运用π证实了一个观点，光既是一种粒子，也是一种电磁波，
and, perhaps most impressively, to calculate the density of our entire universe,
更令人惊叹的是，π还能计算宇宙密度，
which, by the way, still has infinitely less stuff in it than the total number of digits in pi.
不过，宇宙中的物质还是比π的总数位少得多。