The infinite life of pi - Reynaldo Lopes

Beskonačan život broja pi - Rejnaldo Lopez (Reynaldo Lopes)

Prevodilac: Jasna Andjelkovic Lektor: Mile Živković

Try to measure a circle.

Pokušajte da izmerite krug.

The diameter and radius are easy,

Sa prečnikom i poluprečnikom je lako,

they're just straight lines

to su jednostavne prave linije

you can measure with a ruler.

koje možete izmeriti lenjirom.

But to get the circumference,

Ali da biste dobili obim kruga,

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

treba vam metar ili uže,

unless there was a better way.

osim ako ne postoji bolji način.

Now, it's obvious

Dakle, jasno je

that a circle's circumference would get smaller or larger

da obim kruga postaje manji ili veći

along with its diameter,

zajedno sa njegovim prečnikom,

but the relationship goes further than that.

ali ta vezanost seže dalje.

In fact, the ratio between the two,

Zapravo, odnos ove dve mere

the circumference divided by the diameter,

je takav da se deljenjem obima kruga sa njegovim prečnikom

will always be the same number,

uvek dobija isti broj,

no matter how big or small the circle gets.

ma koliko krug bio mali ili veliki.

Historians aren't sure when or how

Istoričari nisu sigurni kada niti kako

this number was first discovered,

je ovaj broj prvi put otkriven,

but it's been known in some form

ali je poznat u nekom obliku

for almost 4,000 years.

već 4.000 godina.

Estimates of it appear in the works of ancient Greek,

Procene ovog broja javljaju se u delima antičkih Grka,

Babylonian,

Vavilonaca,

Chinese,

Kineza,

and Indian mathematicians.

i indijskih matematičara.

And it's even believed to have been used

A veruje se čak i da je korišćen

pri izgradnji egipatskih piramida.

in building the Egyptian pyramids.

Mathematicians estimated it

Matematičari su ga izračunavali

by inscribing polygons in circles.

ucrtavanjem mnogougla unutar kruga.

And by the year 1400,

A do godine 1400.,

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

proračunat je do desetog decimalnog broja.

So, when did they finally figure out the exact value

Dakle, kada su konačno otkrili njegovu tačnu vrednost

instead of just estimating?

umesto približne?

Actually, never!

Zapravo, nikad!

You see, the ratio

Znate, odnos

of a circle's circumference to its diameter

obima kruga i njegovog prečnika

is what's known as an irrational number,

poznat je kao iracionalan broj,

one that can never be expressed

koji nikad ne može biti prikazan

as a ratio of two whole numbers.

kao razlomak dva cela broja.

You can come close,

Možete biti približno tačni,

but no matter how precise the fraction is,

ali bez obzira koliko je precizan deo,

it will always be just a tiny bit off.

uvek će nedostajati još samo malo.

So, to write it out in its decimal form,

Te, da biste broj zapisali u decimalnom obliku,

you'd have an on-going series of digits

morate imati niz cifara

starting with

koje počinju sa:

3.14159

3,14159

and continuing

a nastavlja se

forever!

beskonačno!

That's why, instead of trying to write out

Stoga, umesto pokušavanja da zapišemo

an infinite number of digits every time,

svaki put ovako beskrajan niz cifara,

we just refer to it using the Greek letter pi.

pribegavamo upotrebi grčkog slova pi.

Nowadays, we test the speed of computers

Danas, ispitujemo brzinu kompjutera

by having them calculate pi,

tako što im zadajemo proračun broja pi,

and quantum computers have been able

i izvesan broj kompjutera uspeva

to calculate it up to two quadrillion digits.

da izračuna i do dva kvadriliona decimala.

People even compete to see

Ljudi se takmiče

how many digits they can memorize

u pamćenju što većeg broja cifara,

and have set records for remembering

a postavljen je rekord u pamćenju

over 67,000 of them.

koji prelazi 67.000 cifara.

But for most scientific uses,

U najvećem broju slučajeva za potrebe nauke,

you only need the first forty or so.

potrebno nam je prosečno oko 40 cifara.

And what are these scientific uses?

I za koje to naučne potrebe se koristi?

Well, just about any calculations involving circles,

Pa, za skoro sve proračune koji uključuju krugove,

from the volume of a can of soda

od računanja zapremine limenke soka,

to the orbits of satellites.

do putanje satelita.

And it's not just circles, either.

I to ne samo kada imamo krugove.

Because it's also useful in studying curves,

Budući da se koristi i u izučavanju krivih linija,

pi helps us understand periodic or oscillating systems

Pi nam pomaže da razumemo periodične ili oscilatorne sisteme

like clocks,

kao što su satovi,

electromagnetic waves,

elektromagnetni talasi,

and even music.

pa čak i muziku.

In statistics, pi is used in the equation

U statistici, pi se upotrebljava u jednačini

to calculate the area under a normal distribution curve,

pri izračunavanju površine ispod krive linije sa normalnom raspodelom,

which comes in handy for figuring out distributions

što je zgodno pri utvrđivanju raspodele

of standardized test scores,

testova standardizovanih rezultata,

financial models,

finansijskih modula,

or margins of error in scientific results.

ili graničnih grešaka u naučnim rezultatima.

As if that weren't enough,

Kao da to nije bilo dovoljno,

pi is used in particle physics experiments,

Pi se koristi u eksperimentima nad česticama u fizici,

such as those using the Large Hadron Collider,

kao što je slučaj u korišćenju Velikog hadronskog akceleratora čestica,

not only due to its round shape,

ne samo zbog okruglog oblika,

but more subtly,

već i iz suptilnijih razloga,

because of the orbits in which tiny particles move.

zbog putanja kojima se te majušne čestice kreću.

Scientists have even used pi

Naučnici pi koriste čak i

to prove the illusive notion

za dokazivanje iluzorne pojave

that light functions as both a particle

svetla koje funkcioniše i kao čestica

and an electromagnetic wave,

i kao elektromagnetni talas,

and, perhaps most impressively,

a, možda najimpresivnije je to što,

to calculate the density of our entire universe,

pomoću njega proračunavaju gustinu čitavog univerzuma,

which, by the way,

koji je inače,

still has infinitely less stuff in it

i dalje sačinjen od beskrajno manje stvari

than the total number of digits in pi.

u odnosu na ukupan niz cifara broja pi.