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.
如果要測量圓 直徑、半徑都好解決 只是直線 用尺就行了 但量圓周時 就要動用到捲尺或線 除非有更好的辦法 很明顯地 圓周長短會變 直徑也是 但其實背後有更深的含意 事實上 圓周長除以直徑 數值永遠一樣 大圓小圓都一樣 史學家不確定這個數字 是何時出現、如何求得的 但它以某種形式 存在了 4000 年之久 各地數學家都有紀錄,包含希臘 巴比倫 中國 和印度 大家也相信 埃及金字塔和這數字有關 數學家用圓內接多邊形 來估算這個數字 西元 1400 年之前 已求出小數點後第 10 位 那究竟何時才有精確的數字 而不只是一個估值呢? 還沒求到! 其實 圓周長與直徑的比 是無理數 小數點後,位數無限 而且不會循環 雖然估值很接近 但不管換算的分數多精確 還是差了那麼一點 如果用小數表示 需要一連串的數字 也就是 3.14159 後面還有 沒完沒了! 所以通常不會真的這樣寫 因為永遠寫不完 就直接用希臘字 π 來表示 若想測量電腦的運算速度 就讓電腦計算 π 量子電腦很厲害 能算出 2000 兆個數字 大家也會辦比賽 看誰最會背 π 目前的世界紀錄 多達 67000 多位數 但一般科學應用 小數點後約 40 位就夠了 π 要怎麼應用呢? 基本上,圓的計算都會用上 小至汽水罐的容量 大到衛星軌道 但不僅限於圓的計算 曲線計算也很需要 π 能計算週期和振盪 像鐘擺 電磁波 甚至是音樂 統計上,π 可代入方程式 來計算常態分佈曲線 常用於數值分布的運算 像是標準化測驗 財務模型 或科學結果的誤差範圍 還不只如此 粒子物理實驗也會見到 像是瑞士的大強子對撞機 不只因為對撞機是圓形 還因為一個小細節 就是微小粒子環繞的軌道 科學家也利用 π 替「光」驗明正身 光可以是粒子 同時也是電磁波 更厲害的是 π 能計算宇宙的密度 不過 整個宇宙的密度 還是比 π 無限的數字還少