# Fibonometrija

Šoltić, Klara (2016) Fibonometrija. Diploma thesis, Faculty of Science > Department of Mathematics.

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Language: Croatian

Trigonometric functions are a good choice for deriving relations between Fibonacci and Lucas numbers. Since this is an elegant and simple approach to this issue, it deserves its own name, Fibonometry. One of the most interesting relations is \begin{eqnarray*} \sum_{n=1}^{\infty} \Tg^{-1} \frac{1}{F_{2k+1}}=\frac{\pi}{4}. \end{eqnarray*} which is one of many possible ways to write and aproximate number $\pi$. Beside various possibilities of creating fibonometric relations, trigonometric functions and Fibonacci and Lucas numbers enabled us to discover a story behind everyday phenomenon or things. One example is making weaves. Geometric aspect to this part of mathematics was also present. Using golden triangle properties we are able to calculate trigonometric values of the smallest integer angle of 3$^{\circ}$ which helps us calculate trigonometric values of many other angles without using a calculator. All this would not happen without the great Fibonacci and his original contributions which were only a base to all other findings.