Page 372 - PowerPoint Presentation

FIBONAĈIJEVI BROJEVI I NEPREKIDNA PODELA. FIBONACCI NUMBERS AND CONTINUOUS
DIVIDING

AUTOR : LUKA ŽIVKOVIĆ , VIII6 , O.Š. "Branko Ćopid" Beograd

NASTAVNIK : SLAĐANA KOSAČEVIĆ ,nast.mat. O.Š. "Branko Ćopid" Beograd

MENTOR : VESNA RAJŠIĆ , prof. matematike, E.T.Š "Nikola Tesla" Beograd

REZIME

Upoznavanje sa ovim neobiĉnim poretkom brojeva uvodi nas u mnoštvo zanimljivih ma-tematiĉkih pojava u svetu oko

nas, pa i u nama samima. Fibonačijevi brojevi predstavlja-ju niz koji poĉinje brojevima 0 i 1 i ĉiji je svaki sledeći ĉlan
zapravo zbir svoja dva pret-hodnika. U prirodi ga moţemo uoĉiti u ţivom ali i u neţivom svetu. Odnos izmeĊu dva su-

sedna broja ovog niza daje vrednost Zlatnog preseka koji je poznat i kao boţanska proporcija .Korišćen je u arhitekturi

od davnina , ali je takoĊe prisutan i u graĊi ţivih or-ganizama. Zlatni presek se dobija ako se jedna duţ podeli na takav
naĉin da je odnos ve-ćeg dela prema celini isti kao i odnos manjeg dela prema većem . Fibonaĉijevi brojevi su blisko

povezani sa Lukasovim brojevima koji meĊusobno stoje u skoro identiĉnom od-nosu, osim što su prva dva broja ovog
niza 1 i 3. Pomoću Fibonaĉijevih brojeva se mogu izraĉunati i Pitagorine trojke. Ovi nizovi su sadrţani u Paskalovom

trouglu koji predstavlja jedan od osnovnih brojnih obrazaca u prirodi.

Ključne reči: Fibonaĉijev niz, Lukasovi brojevi, rekurzija ,konvergencija, graniĉna vred-nost, Zlatni presek, broj Phi ,
Pitagorine trojke, Paskalov trougao, binomni koeficijenti.

SUMMARY

Introduction to the unusual order of these numbers brings us a lot of interesting mathema-tic phenomena in the world

around us and in us. Fibonacci numbers represent a series of numbers that begins with 0 and 1 and whose every member
of the following is actually the sum of its two-pret the corridor. In nature it can be seen in a live, but also in the inani-

mate world. The relationship between the two adjacent numbers of this series gives the value of the Golden section,
which is also known as the divine proportion . Used in archi-tecture from antiquity, but is also present in material of the

living organism. Golden Sec-tion gets one along the division in such a way that the ratio of the greater whole the same

as the ratio of small to larger. Fibonacci numbers are more closely related to Lukas num-bers to each other are almost
identical comparison, except that the first two of this series 1 and 3.Using Fibonacci numbers can be calculated

Pythagorean triples. These sequen-ces are contained in the Pascal triangle, which is one of a number basic forms in
nature.

Key words: Fibonacci number, Lucas numbers, recursion, convergence, limit, Golden Section, the number of

Phi , Pythagorean triples, Pascal triangle, binomial coefficients.