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VERIŢNI RAZLOMCI I OPTIMIZACIJA HAJGENSOVOG MODELA PLANETARIJUMA
CONTINUED FRACTIONS AND OPTIMIZATION OF HUYGENS’ PLANETARIUM MODEL

Uĉenik : NIKOLINA MARKOVIĆ III razred Gimnazija u Lazarevcu
Mentori : prof. dr Nataša Ćirović i prof. dr Branko Malešević Elektrotehniĉki fakultet u
Beogradu
REZIME

Veriţni razlomci postali su predmet izuĉavanja u 17. veku, ali njihova upotreba u matematici postojala je i

ranje. Predstavljaju koristan naĉin aproksimiranja brojeva. Iracionalni brojevi u svojoj osnovi imaju
beskonaĉan broj cifara, da bismo mogli da ih koristimo potrebno je da ih predstavimo na konaĉan broj

decimala, a jedan od naĉina da to uradimo je uz pomoć veriţnih razlomaka. Mogu se koristiti i za problem
Hajgensovog modela planetarijuma, problem kalendara, problem muziĉke skale i mnogih drugih praktiĉnih

problema u matematici i prirodi.

U ovom radu ćemo se baviti definisanjem veriţnih razlomaka, kreiranjem algoritma koji pronalazi veriţne i
meĊuveriţne aproksimacije i optimizacijom Hajgensovog modela planetarijuma korišćenjem veriţnih i

meĊuveriţnih aproksimacija. Ključne reči: veriţni razlomci, meĊuveriţni razlomci, aproksimacije,
optimizacija i Hajgensov model planetarijuma.

SUMMARY

th
Continued fractions began subject of study in the 17 century, but the use of them in mathematics existed
long before. These fractions are useful way for approximating numbers. Irrational numbers in their base have

an infinite number of decimal places and if we want to use them we need to approximate them with the final
number of decimal places, and one of the ways for doing that is by using continued fractions. Also, we can

use continued fractions for problem of Huygens’ planetarium model, problem of calendar, problem of
musical scale and many other practical problems in mathematics and nature.

In this paper, we will deal with the defining of continued fractions, creating an algorithm which finds

continued and intermediate approximations and optimization of Huygens’ planetarium model by using
continued and intermediate fraction approximations.

Key words: continued fractions, intermediate fractions, approximations, optimization and Huygens’
planetarium model.