Try to measure a circle. The diameter and radius are easy, they're just straight lines you can measure with a ruler. But to get the circumference, you'd need measuring tape or a piece of string, unless there was a better way. Now, it's obvious that a circle's circumference would get smaller or larger along with its diameter, but the relationship goes further than that. In fact, the ratio between the two, the circumference divided by the diameter, will always be the same number, no matter how big or small the circle gets. Historians aren't sure when or how this number was first discovered, but it's been known in some form for almost 4,000 years. Estimates of it appear in the works of ancient Greek, Babylonian, Chinese, and Indian mathematicians. And it's even believed to have been used in building the Egyptian pyramids. Mathematicians estimated it by inscribing polygons in circles. And by the year 1400, it had been calculated to as far as ten decimal places. So, when did they finally figure out the exact value instead of just estimating? Actually, never! You see, the ratio of a circle's circumference to its diameter is what's known as an irrational number, one that can never be expressed as a ratio of two whole numbers. You can come close, but no matter how precise the fraction is, it will always be just a tiny bit off. 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! 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. Nowadays, we test the speed of computers by having them calculate pi, and quantum computers have been able to calculate it up to two quadrillion digits. People even compete to see how many digits they can memorize and have set records for remembering over 67,000 of them. But for most scientific uses, you only need the first forty or so. And what are these scientific uses? Well, just about any calculations involving circles, from the volume of a can of soda to the orbits of satellites. And it's not just circles, either. Because it's also useful in studying curves, pi helps us understand periodic or oscillating systems like clocks, electromagnetic waves, and even music. In statistics, pi is used in the equation to calculate the area under a normal distribution curve, which comes in handy for figuring out distributions of standardized test scores, financial models, or margins of error in scientific results. As if that weren't enough, pi is used in particle physics experiments, such as those using the Large Hadron Collider, not only due to its round shape, but more subtly, because of the orbits in which tiny particles move. Scientists have even used pi to prove the illusive notion that light functions as both a particle and an electromagnetic wave, and, perhaps most impressively, to calculate the density of our entire universe, which, by the way, still has infinitely less stuff in it than the total number of digits in pi.
如果要测量一个圆 直径和半径都容易解决 它们都是直线 可以用尺子测量 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 很显然的是 圆的周长会随着直径 变换长短 但它们之间的关系还不止如此 事实上 无论圆的大小如何 圆的周长除以直径 得出来的数值是恒定的 历史学家不确定这个数字 是何时出现 如何求得的 但它以某种形式 存在了近4000年 古希腊 巴比伦 中国 和印度的数学家都对它进行了估算 我们甚至认为它被运用到 埃及金字塔的建造中 数学家通过在圆内接多边形 来估算这个数值 到公元1400年 人们已经计算出小数点后第10位 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! 因为 圆周长和直径的比值 是一个无理数 它无法用两个整数的比值 来表示 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 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! 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 现在我们让电脑计算π 以测量其运算速度 量子计算机 可以计算出2000兆个数位 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 但一般的科学应用 只需要小数点后约40位就行了 那么 π能应用在什么地方呢? 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 但也不局限于圆的计算 因为学习曲线也需要用到π π帮助我们认识周期或振动系统 如钟摆 电磁波 甚至音乐 在统计学中,π可代入等式中 来计算正态分布曲线 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 不仅如此 π还用在粒子物理实验中 如大型强子对撞机有关的计算 不仅因为它是圆形的 更巧妙的是 这和微粒运行的轨道有关 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 更令人惊叹的是 π还能计算宇宙密度 不过 宇宙中的物质 还是比π的总数位少得多