Certain inequalities connected with the golden ratio and the Fibonacci numbers

• Autorzy: Adam M. , Piątek B. , Pleszczyński M. , Smoleń B. , Wituła R.

Identyfikatory

DOI

10.17512/jamcm.2016.1.01

• Języki publikacji: EN

Abstrakty

EN

In the present paper we give some condensation type inequalities connected with Fibonacci numbers. Certain analytic type inequalities related to the golden ratio are also presented. All results are new and seem to be an original and attractive subject also for future research.

Słowa kluczowe

EN

Fibonacci numbers; golden ratio; Perrin constant

PL

liczby Fibonacciego; złota proporcja; stała Perrin’a

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2016
• Tom: Vol. 15, nr 1
• Strony: 5--15
• Opis fizyczny: BiIbliogr. 11 poz., rys.

Twórcy

autor

Adam M.

• Institute of Mathematics, Silesian University of Technology Gliwice, Poland

autor

Piątek B.

• Institute of Mathematics, Silesian University of Technology Gliwice, Poland

autor

Pleszczyński M.

• Institute of Mathematics, Silesian University of Technology Gliwice, Poland

autor

Smoleń B.

autor

Wituła R.

• Institute of Mathematics, Silesian University of Technology Gliwice, Poland

Bibliografia

• [1] Dunlop R., The Golden Ratio and Fibonacci Numbers, World Scientific, Singapore 2006.
• [2] Vajda S., Fibonacci and Lucas Numbers, and the Golden Section Theory and Applications, Dover Publications Inc., New York 2008.
• [3] Hoggatt V.E., Fibonacci and Lucas Numbers, The Fibonacci Association, Santa Clara 1979.
• [4] Mongoven C., Sonification of multiple Fibonacci-related sequences, Annales Mathematicae et Informaticae 2013, 41, 175-192.
• [5] Wituła R., Słota D., Hetmaniok E., Bridges between different known integer sequences, Annales Mathematicae et Informaticae 2013, 41, 255-263.
• [6] Słanina P., Generalizations of Fibonacci polynomials and free linear groups, Linear and Multilinear Algebra, DOI: 10.1080/03081087.2015.1031073.
• [7] Herz-Fischler R., A “very pleasant” theorem, College Mathematics Journal 1993, 24, 4, 318-324.
• [8] Chern S., Cui A., Fibonacci numbers close to a power of 2, The Fibonacci Quarterly 2014, 52, 4, 344-348.
• [9] Hetmaniok E., Wituła R., Lorenc P., Pleszczyński M., On an improvement of the numerical application for Cardano’s formulae in Mathematica software (in review).
• [10] Wituła R., Lorenc P., Różański M., Szweda M., Sums of the rational powers of roots of cubic polynomials, Zeszyty Naukowe Politechniki Śląskiej, Seria Matematyka Stosowana 2014, 4, 17-34.
• [11] Dubickas A., Hare K.G., Jankauskas J., There are no two nonreal conjugates of a Pisot number with the same imaginary part, arXiv:1410.1600v1 [math.NT].

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.