ZLATNI PRESEK I MAGIČAN BROJ Φ

Vesna Vujačić

doi:10.59417/nir.2014.5.57

Authors

Vesna Vujačić Osnovna škola“ Đura Jakšić“, Beograd, Republika Srbija

DOI:

https://doi.org/10.59417/nir.2014.5.57

Keywords:

: golden ratio, golden number Φ (Phi), Fibonacci sequence

Abstract

We can come across the golden ratio in everyday life without even being aware of it. The golden ratio has been well-known since the ancient times to the present day. It is commonly used in architecture, construction engi- neering, sculpture, art, painting, music, photography and design. The golden ratio or the divine proportion is the most perfect ratio in nature, simply perfect to the human eye. It is a harmony between extreme precision and chaotic imperfection. Fibonacci sequence has been the centre of study for mathematicians worldwide for over the centuries. It possesses various properties, algebraically and geometrically. They are closely connected with the golden ratio also known as number Φ (phi).

References

Basin, S. L. and Hoggatt, V. E. Jr. (1963). “A Primer on the Fibonacci Sequence”. Fib. Quart. 1. Brook, M. (1963). “Fibonacci Formulas." Fib. Quart. 1, 60. DOI: https://doi.org/10.1080/00150517.1963.12431605

D. E. JOYCE, Euclid’s Elements, Dept. Math. Comp. Sci.Clark University, http://aleph0.clarku.edu/˜djoyce/java/elements/-elements.html

Hoggatt, V. E. Jr. (1969). The Fibonacci and Lucas Numbers. Boston, MA: Houghton Mifflin. Halton, J. H. (1965). “On a General Fibonacci Identity”. Fib. Quart. 3, 31-43. DOI: https://doi.org/10.1080/00150517.1965.12431452

Kimberling, C. (2000). “A New Kind of Golden Triangle”. In Applications of Fibonacci Num- bers: Proceedings of the Fourth International Conference on Fibonacci Numbers and Their Applications,' Wake Forest.

Livio, M. (2002). The Golden Ratio: The Story of Phi, the World's Most Astonishing Number. New York: Broadway Books, pp. 78-79.

Pappas, T. (1989). “Fibonacci Sequence”, “Pascal's Triangle”, “The Pentagon, the Pentagram & the Golden Triangle”, The Joy of Mathematics. San Carlos, CA: Wide World Publ./Tetra, pp. 188-189.

Ram, R. “Fibonacci Formulae”, http://users.tellurian.net/hsejar/maths/fibonacci/.

http://milan.milanovic.org/math/srpski/nizovi/nizovi.html (01. 04. 2014.) DOI: https://doi.org/10.9790/3013-04020201-06

http://normala.hr/prezentacije/mkabic/zlatnirez/ZlatniRez.pdf ( 01. 04. 2014.)

http://en.wikipedia.org/wiki/Golden_ratio (03. 04. 2014.) http://mathworld.wolfram.com/GoldenRatio.html http://inspirationgreen.com/fibonacci-sequence-in-nature.html (03. 04. 2014.)

http://www.ted.com/talks/arthur_benjamin_the_magic_of_fibonacci_numbers/ Weisstein, E. W. “Books about Fibonacci Numbers”, http://www.ericweisstein.com/encyclopedias/books/FibonacciNumbers.html.