SOME CLASSES OF FIBONACCI NUMBERS
DOI:
https://doi.org/10.24867/10JV02MarkovicKeywords:
Fibonacci numbers, Lucas numbers, Gibonacci numbers, Binet’s formulaAbstract
The subject of research of this paper are Fibonacci numbers and similar ones such as: Lucas numbers, Gibonacci numbers and Tribonacci numbers. Emphasis is placed on their properties, as well as on their mutual relations, primarily the relations between Fibonacci and Lucas numbers. Also, this paper presents some interesting facts about Lucas and Fibonacci numbers and their presence in nature.
References
[1] Brousseau, A., “Fibonacci Numbers and Geometry, Fibonacci Quarterly”, Fibonacci Quarterly 10, pages 303-318, 1972.
[2] Devlin, K., ”The Man of Numbers: Fibonacci’s Number Arithmetic Revolution”, Walker Books, 2012.
[3] Dujella, A., “Uvod u teoriju brojeva; skripta”, Univerzitet u Zagrebu, Prirodoslovno - matematički fakultet, Zagreb 2003.
[4] Dujella, A., “Fibonačijevi brojevi”, Hrvatsko matematičko društvo, Zagreb, 2000.
[5] Goonatilake, S., “Toward a global Science”, Indiana University Press, Bloomington, Indiana, 1998.
[6] Kuhapatanakul, K., “The k-nacci triangle and applications”, Cogent Mathematics 4, page 14, 2017.
[7] Jeffery, T., Pereira, R., “Divisibility Properties of the Fibonacci, Lucas, and Related Sequences”, Hindawi Publishing Corporation ISRN Algebra 2014, page 5,
[8] Koshy, T., “Fibonacci and Lucas Numbers with Applications, Volume One”, John Wiley & Sons, Inc., Hoboken, New Jersey, 2018.
[9] Koshy, T., “Fibonacci and Lucas Numbers with Applications, Volume Two”, John Wiley & Sons, Inc., Hoboken, New Jersey, 2019.
[10] Scott, T.C., Marketos, P., “On the Origin of the Fibonacci Sequence”, MacTutor History of Mathematics, page 46, 2014.
[11] Stevanović, D., Ćirić, M., Simić, S., Baltić, V., “Diskretna matematika, Osnove kombinatorike i teorije grafova”, Univerzitet u Beogradu, Matematički fakultet, Beograd, mart 2007.
[12] https://www.mathstat.dal.ca/fibonacci
[13] https://www.wikipedia.org
[2] Devlin, K., ”The Man of Numbers: Fibonacci’s Number Arithmetic Revolution”, Walker Books, 2012.
[3] Dujella, A., “Uvod u teoriju brojeva; skripta”, Univerzitet u Zagrebu, Prirodoslovno - matematički fakultet, Zagreb 2003.
[4] Dujella, A., “Fibonačijevi brojevi”, Hrvatsko matematičko društvo, Zagreb, 2000.
[5] Goonatilake, S., “Toward a global Science”, Indiana University Press, Bloomington, Indiana, 1998.
[6] Kuhapatanakul, K., “The k-nacci triangle and applications”, Cogent Mathematics 4, page 14, 2017.
[7] Jeffery, T., Pereira, R., “Divisibility Properties of the Fibonacci, Lucas, and Related Sequences”, Hindawi Publishing Corporation ISRN Algebra 2014, page 5,
[8] Koshy, T., “Fibonacci and Lucas Numbers with Applications, Volume One”, John Wiley & Sons, Inc., Hoboken, New Jersey, 2018.
[9] Koshy, T., “Fibonacci and Lucas Numbers with Applications, Volume Two”, John Wiley & Sons, Inc., Hoboken, New Jersey, 2019.
[10] Scott, T.C., Marketos, P., “On the Origin of the Fibonacci Sequence”, MacTutor History of Mathematics, page 46, 2014.
[11] Stevanović, D., Ćirić, M., Simić, S., Baltić, V., “Diskretna matematika, Osnove kombinatorike i teorije grafova”, Univerzitet u Beogradu, Matematički fakultet, Beograd, mart 2007.
[12] https://www.mathstat.dal.ca/fibonacci
[13] https://www.wikipedia.org
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Published
2020-12-08
Issue
Section
Mathematics in Engineering
