FIBONACCI NUMBERS AND SEMISIMPLE CONTINUED FRACTION

DOI QR Code

The ratios of any two Fibonacci numbers are expressed by means of semisimple continued fraction.

D. Burton, Elementary Number Theory, 3rd ed. WCB, Oxford, England, 1994.
M. Drmota, Fibonacci numbers and continued fraction expansions, in G. E. Vergum et. al (eds.) Applications of Fibonacci numbers, vol 5, 2nd ed. Kluwer Academic Publishers, Netherlands, 1993.
S. Kalia, Fibonacci numbers and continued fractions, MIT PRIMES, 2011. (retrived from web.mit.edu/primes/materials/2011/2011-conf-booklet.pdf)
S. Katok, Continued fractions, hyperbolic geometry, quadratic froms, in MASS Selecta, Teaching and learning advanced undergraduate mathematics (S. Katok, A. Sossinsky, S. Tabachnikov eds.) American Math. Soc. 2003.
F. Koken and D. Bozkurt, On Lucas numbers by the matrix method, Hacet. J. Math. Stat. 39 (2010), no. 4, 471-475.
T. E. Phipps, Fibonacci and continued fractions, Aperion 15 (2008), no. 4, 534-550.