Where do math symbols come from? - John David Walters

Prevodilac: Ema Maričić Lektor: Tijana Mihajlović

U 16. veku, matematičar Robert Rekord

In the 16th century, the mathematician Robert Recorde

wrote a book called "The Whetstone of Witte"

napisao je knjigu „Brušenje oštroumlja“

to teach English students algebra.

da bi podučavao engleske studente algebri.

But he was getting tired of writing the words "is equal to" over and over.

Ali, dosadilo mu je da piše reči „jednako je“ iznova i iznova.

Njegovo rešenje?

His solution?

He replaced those words with two parallel horizontal line segments

Te reči je zamenio sa dve paralelene horizontalne duži

because the way he saw it, no two things can be more equal.

jer je smatrao da ne postoje dve stvari koje su više jednake.

Could he have used four line segments instead of two?

Da li je mogao da koristi četiri umesto dve linije?

Of course.

Naravno.

Da li je mogao da koristi vertikalne duži?

Could he have used vertical line segments?

In fact, some people did.

Zapravo, neki su to i radili.

There's no reason why the equals sign had to look the way it does today.

Ne postoji razlog zašto znak jednakosti izgleda onako kako izgleda danas.

At some point, it just caught on, sort of like a meme.

U nekom trenutku je jednostavno prihvaćen, pomalo kao mem.

More and more mathematicians began to use it,

Sve više matematičara je krenulo da ga koristi

and eventually, it became a standard symbol for equality.

i na kraju je postao standardni simbol za jednakost.

Math is full of symbols.

Matematika je puna simbola.

Lines,

Linije,

dots,

tačke,

arrows,

strelice,

English letters,

latinična slova,

Greek letters,

grčka slova,

superscripts,

eksponenti,

subscripts.

indeksi.

It can look like an illegible jumble.

Može da izgleda kao nečitka žvrljotina.

It's normal to find this wealth of symbols a little intimidating

Normalno je da nam je ovo obilje simbola pomalo zastrašujuće

and to wonder where they all came from.

i da se pitamo odakle su svi oni potekli.

Ponekad, kako je i sam Rekord pisao o svom znaku jednakosti,

Sometimes, as Recorde himself noted about his equals sign,

there's an apt conformity between the symbol and what it represents.

simbol je u pogodnoj saglasnosti sa onom što predstavlja.

Another example of that is the plus sign for addition,

Još jedan primer je znak plus za sabiranje,

which originated from a condensing of the Latin word et meaning and.

koji potiče od sabijanja latinske reči „et“ koja ima značenje veznika „i“.

Sometimes, however, the choice of symbol is more arbitrary,

Ponekad je, međutim, izvor simbola proizvoljniji,

such as when a mathematician named Christian Kramp

kao kad je matematičar pod imenom Kristijan Kramp

introduced the exclamation mark for factorials

uveo znak uzvika za faktorijele

samo zato što mu je trebao znak koji se brzo piše za ovakve izraze.

just because he needed a shorthand for expressions like this.

In fact, all of these symbols were invented or adopted

Zapravo, svi ovi simboli su izumljeni ili prisvojeni

by mathematicians who wanted to avoid repeating themselves

od strane matematičara koji su hteli da izbegnu ponavljanje

or having to use a lot of words to write out mathematical ideas.

ili da koriste mnogo reči za pisanje matematičkih ideja.

Mnogi simboli koji se koriste u matematici su slova,

Many of the symbols used in mathematics are letters,

usually from the Latin alphabet or Greek.

obično iz latiničnog ili grčkog alfabeta.

Characters are often found representing quantities that are unknown,

Slova obično predstavljaju nepoznate vrednosti

i veze između varijabli.

and the relationships between variables.

They also stand in for specific numbers that show up frequently

Takođe označavaju specifične brojeve koji se često javljaju,

a čiji bi potpuni decimalni zapis bio zamoran ili nemoguć.

but would be cumbersome or impossible to fully write out in decimal form.

Sets of numbers and whole equations can be represented with letters, too.

Nizovi brojeva i cele jednačine se mogu predstaviti i slovima.

Other symbols are used to represent operations.

Drugi simboli se koriste za predstavljanje operacija.

Some of these are especially valuable as shorthand

Neki od njih su posebno važni kao prečica

because they condense repeated operations into a single expression.

jer sažimaju ponovljene operacije u jedan izraz.

The repeated addition of the same number is abbreviated with a multiplication sign

Ponovljeno sabiranje istog broja se skraćuje znakom puta,

so it doesn't take up more space than it has to.

pa ne zauzima više prostora nego što je potrebno.

A number multiplied by itself is indicated with an exponent

Broj koji se množi samim sobom se označava eksponentom

that tells you how many times to repeat the operation.

koji vam govori koliko puta se ponavlja operacija.

And a long string of sequential terms added together

A dugi niz sekvenci koje su pridodate jedna drugoj

is collapsed into a capital sigma.

se skuplja u veliko slovo, sigmu.

These symbols shorten lengthy calculations to smaller terms

Ovi simboli skraćuju dugačke kalkulacije u manje termine

that are much easier to manipulate.

kojima se lakše koristimo.

Symbols can also provide succinct instructions

Simboli nam daju i sažeta upustva

about how to perform calculations.

kako da računamo.

Consider the following set of operations on a number.

Razmislite o datom nizu operacija sa brojevima.

Take some number that you're thinking of,

Uzmite proizvoljan broj,

multiply it by two,

pomnožite ga brojem dva,

subtract one from the result,

oduzmite jedan od rezultata,

multiply the result of that by itself,

pomnožite rezultat toga samim sobom,

divide the result of that by three,

podelite taj rezultat brojem tri

and then add one to get the final output.

i onda dodajte jedan da dobijete krajnji rezultat.

Without our symbols and conventions, we'd be faced with this block of text.

Bez simbola i konvencija imali bismo samo ovaj tekst.

With them, we have a compact, elegant expression.

Sa njima imamo kompaktan, elegantan izraz.

Sometimes, as with equals,

Ponekad, kao kod znaka jednakosti,

these symbols communicate meaning through form.

ovi simboli prenose značenje putem forme.

Many, however, are arbitrary.

Mnogi su, međutim, proizvoljni.

Understanding them is a matter of memorizing what they mean

Njihovo razumevanje znači memorisanje njihovih značenja

and applying them in different contexts until they stick, as with any language.

i njihovo primenjivanje u različitim kontekstima do prihvatanja,

kao kod bilo kog jezika.

Ako bismo se susreli sa vanzemaljskom civilizacijom,

If we were to encounter an alien civilization,

they'd probably have a totally different set of symbols.

oni bi verovatno imali drugačiju grupu simbola.

But if they think anything like us, they'd probably have symbols.

Ali, ako bi razmišljali bar malo kao mi, verovatno bi imali simbole.

And their symbols may even correspond directly to ours.

A njihovi simboli bi možda čak i direktno odgovarali našim.

They'd have their own multiplication sign,

Imali bi svoj znak za množenje,

symbol for pi,

simbol za pi

i, naravno, znak jednakosti.

and, of course, equals.