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.
Pokušajte da izmerite krug. Sa prečnikom i poluprečnikom je lako, to su jednostavne prave linije koje možete izmeriti lenjirom. Ali da biste dobili obim kruga, treba vam metar ili uže, osim ako ne postoji bolji način. Dakle, jasno je da obim kruga postaje manji ili veći zajedno sa njegovim prečnikom, ali ta vezanost seže dalje. Zapravo, odnos ove dve mere je takav da se deljenjem obima kruga sa njegovim prečnikom uvek dobija isti broj, ma koliko krug bio mali ili veliki. Istoričari nisu sigurni kada niti kako je ovaj broj prvi put otkriven, ali je poznat u nekom obliku već 4.000 godina. Procene ovog broja javljaju se u delima antičkih Grka, Vavilonaca, Kineza, i indijskih matematičara. A veruje se čak i da je korišćen pri izgradnji egipatskih piramida. Matematičari su ga izračunavali ucrtavanjem mnogougla unutar kruga. A do godine 1400., proračunat je do desetog decimalnog broja. Dakle, kada su konačno otkrili njegovu tačnu vrednost umesto približne? Zapravo, nikad! Znate, odnos obima kruga i njegovog prečnika poznat je kao iracionalan broj, koji nikad ne može biti prikazan kao razlomak dva cela broja. Možete biti približno tačni, ali bez obzira koliko je precizan deo, uvek će nedostajati još samo malo. Te, da biste broj zapisali u decimalnom obliku, morate imati niz cifara koje počinju sa: 3,14159 a nastavlja se beskonačno! Stoga, umesto pokušavanja da zapišemo svaki put ovako beskrajan niz cifara, pribegavamo upotrebi grčkog slova pi. Danas, ispitujemo brzinu kompjutera tako što im zadajemo proračun broja pi, i izvesan broj kompjutera uspeva da izračuna i do dva kvadriliona decimala. Ljudi se takmiče u pamćenju što većeg broja cifara, a postavljen je rekord u pamćenju koji prelazi 67.000 cifara. U najvećem broju slučajeva za potrebe nauke, potrebno nam je prosečno oko 40 cifara. I za koje to naučne potrebe se koristi? Pa, za skoro sve proračune koji uključuju krugove, od računanja zapremine limenke soka, do putanje satelita. I to ne samo kada imamo krugove. Budući da se koristi i u izučavanju krivih linija, Pi nam pomaže da razumemo periodične ili oscilatorne sisteme kao što su satovi, elektromagnetni talasi, pa čak i muziku. U statistici, pi se upotrebljava u jednačini pri izračunavanju površine ispod krive linije sa normalnom raspodelom, što je zgodno pri utvrđivanju raspodele testova standardizovanih rezultata, finansijskih modula, ili graničnih grešaka u naučnim rezultatima. Kao da to nije bilo dovoljno, Pi se koristi u eksperimentima nad česticama u fizici, kao što je slučaj u korišćenju Velikog hadronskog akceleratora čestica, ne samo zbog okruglog oblika, već i iz suptilnijih razloga, zbog putanja kojima se te majušne čestice kreću. Naučnici pi koriste čak i za dokazivanje iluzorne pojave svetla koje funkcioniše i kao čestica i kao elektromagnetni talas, a, možda najimpresivnije je to što, pomoću njega proračunavaju gustinu čitavog univerzuma, koji je inače, i dalje sačinjen od beskrajno manje stvari u odnosu na ukupan niz cifara broja pi.