Fibonacci sequence

English Fibonacci number Alternative forms en Fibonacci's sequence Etymology Named after the Italian mathematician later known as en Fibonacci (c.1175 – c.1250), who introduced the sequence to a European readership in his 1202 book Liber Abaci. Noun en mathematics The sequence of integers, each of which is the sum of the preceding two, the first and second numbers both being 1. en 1999 Walter Steurer; Torsten Heibach 3. Crystallography of Quasicrystals Zbigniew M. Stadnik Physical Properties of Quasicrystals Springer https://books.google.com.au/books?id=fBB0a56uS5MC&pg=PA60&dq=%22Fibonacci+sequence%22%7C%22Fibonacci+sequences%22&hl=en&sa=X&ved=0ahUKEwjOo9G_2tnbAhXEfrwKHbEvAXUQ6AEIhQQwVQ#v=onepage&q=%22Fibonacci%20sequence%22%7C%22Fibonacci%20sequences%22&f=false 60 If the Fibonacci sequence is chosen for the quasiperiodic direction of a 1D QC,[quasicrystal] it may simply be called a Fibonacci phase. en 2000 Martin Nowak; Robert M. May Virus Dynamics: Mathematical Principles of Immunology and Virology https://books.google.com.au/books?id=Kixhc3IiCy4C&pg=PA6&dq=%22Fibonacci+sequence%22%7C%22Fibonacci+sequences%22&hl=en&sa=X&ved=0ahUKEwjOo9G_2tnbAhXEfrwKHbEvAXUQ6AEIxQEwHw#v=onepage&q=%22Fibonacci%20sequence%22%7C%22Fibonacci%20sequences%22&f=false 6 w:Oxford University Press The number of adult rabbit pairs being present in consecutive months is then given by the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, ... (every term is the sum of its two predecessors). This work can be seen as the very beginning of mathematical biology, though one has to admit that the Fibonacci sequence exerts a greater fascination for number theorists than for reproductive biologists. en 2009 Roger V. Jean Phyllotaxis: A Systemic Study in Plant Morphogenesis https://books.google.com.au/books?id=9pCn3W0gfFAC&pg=PA1&dq=%22Fibonacci+sequence%22%7C%22Fibonacci+sequences%22&hl=en&sa=X&ved=0ahUKEwjOo9G_2tnbAhXEfrwKHbEvAXUQ6AEIzQIwNg#v=onepage&q=%22Fibonacci%20sequence%22%7C%22Fibonacci%20sequences%22&f=false 1 w:Cambridge University Press In a well-known chapter on phyllotaxis, Coxeter (1969) calls the appearance of the Fibonacci sequence in botany a "fascinatingly prevalent tendency," called by Cook (1914) the "Law of Wiesner." The prevalence of the Fibonacci sequence in phyllotactic patterns is often referred to as “the mystery of phyllotaxis,” and “the bugbear of botanists.” en 2019-06-24 Juan Triana Negafibonacci Numbers via Matrices Introduction Bulletin of TICMI https://www.viam.science.tsu.ge/others/ticmi/blt/vol23_1/3_triana.pdf https://web.archive.org/web/20190713012641/https://www.viam.science.tsu.ge/others/ticmi/blt/vol23_1/3_triana.pdf 23 1 1 The Fibonacci sequence {fn} is defined by the following recurrence relation 1512-0082 en 2026 Gordon Korman Hypergifted 139 "Fibonacci was the most famous mathematician of his time," Noah explained. "He created the Fibonacci Sequence, where every number is the sum of the two numbers before it—one, two, three, five, eight, and so on. [...]" en mathematics Any sequence of numbers such that each is the sum of the preceding two. en 1977 w:Scientific American 236 https://books.google.com.au/books?id=bkU7AAAAMAAJ&q=%22a+fibonacci+sequence%22&dq=%22a+fibonacci+sequence%22&hl=en&sa=X&ved=0ahUKEwjOqI-hqdrbAhWCHHwKHb9RC6EQ6AEIqAIwLQ 137 Indeed, these pairs belong to a Fibonacci sequence of what are called Lucas numbers that begins 2, 1, 3, 4, 7, 11,... 2007, Anthony Nicolaides, Make The Grade At GCSE Mathematics, Higher Tier, P.A.S.S. Publications, 3rd Edition, page 169, 19. The first two terms of a Fibonacci sequence are a and b. Write out a few terms. Usage notes In modern usage, the sequence is often defined by specifying 0 as the zeroth number and 1 as the first. The notation is often used for the nth number in the sequence. Related terms en Fibonacci number en Fibonacci spiral Translations sequence of numbers Bulgarian: bg числа́ на Фибона́чи n-p Chinese: Mandarin: cmn 斐波那契數列 Fěibōnàqì shùliè Czech: cs Fibonacciho posloupnost f Estonian: et Fibonacci rida Finnish: fi Fibonaccin lukujono French: fr suite de Fibonacci f German: de Fibonaccifolge f Hungarian: hu Fibonacci-sorozat Italian: it successione di Fibonacci f Japanese: ja フィボナッチ数列 Fibonatchi-sūretsu Portuguese: pt sucessão de Fibonacci, pt sequência de Fibonacci Russian: ru после́довательность Фибона́ччи f Turkish: tr Fibonacci dizisi See also en Lucas sequence en Tribonacci Further reading Golden ratio Generalizations of Fibonacci numbers Lucas number Padovan sequence Fibonacci polynomials Fibonacci retracement en eponyms