Fibonacci sequenceinvolutionLet * denote the canonical involution of the group algebra KG induced by the map x u21a6 x-1 for x u2208 G. In case K is a real extension of u211a, we consider Cayley unitary elements built out of skew elements k = u03b1(x - x-1) in KG such that 1...
In this paper, we give the relationships between the orders of the cyclic groups obtained from the generating matrices of the Hadamard-type k -step Fibonacci sequences and the periods and the ranks of the Hadamard-type k -step Fibonacci sequences modulo m . We also extend the Hadamard-type...
Algebra Element cycles Interspersed repetitive sequences Number Theory Plant cell cycle Topological Groups and Lie Groups 1 Introduction Suppose that the (n+k)th term of a sequence is defined consecutively by a linear combination of the preceding k terms: an+k=c0an+c1an+1+⋯+ck−...
In Liber abaci (1202, 2d ed. 1228), for centuries a standard work on algebra and arithmetic, he advocated the adoption of Arabic notation. In Practica geometriae (1220) he organized and extended the material then known in geometry and trigonometry. The sequence of numbers 0, 1, 1, 2, 3...
How is the Fibonacci sequence used in art?Fibonacci :Fibonacci was born in Italy in 1170 and lived for 80 years; in he became a famous mathematician. He is also known as Leonardo Pisano or Leonardo Fibonacci. He came up with the Fibonacci numbers and rules that are used in mathematics to...
Next we investigate the Fibonacci sequence modulo p a prime and then generalize to prime powers. True to the objective the results we obtained were through the use of (but not limited to) important ideas from both Number Theory and Abstract Algebra including Fermat’s Little Theorem , Euler’...
known in Europe. Terms in the sequence were stated in a formula by the French-born mathematicianAlbert Girardin 1634:un + 2=un + 1+un, in whichurepresents the term and the subscript its rank in the sequence. The mathematicianRobert Simson at theUniversity of Glasgowin 1753 noted that, as...
"Liber Abaci" first introduced the sequence to the Western world. But after a few scant paragraphs on breeding rabbits, Leonardo of Pisa never mentioned the sequence again. In fact, it was mostly forgotten until the 19th century, when mathematicians worked out more about the sequence's mathemati...
In the literature one may encounter certain infinite tridiagonal matrices, the principal minors of which, constitute the Fibonacci or Lucas sequence. The major purpose of this article is to find new infinite matrices with this property. It is interesting to mention that the matrices found are not...
6) Fibonicci algebra 斐波那契代数补充资料:斐波那契数列 斐波那契数列Fibonacci sequence 递归数列的一种。意大利数学家L.斐波那契所著《算盘书 》中,有一个古代数学趣题 斐济维 提雷弗岛的红树之一——兔子问题:假定一对大兔每月能生出一对小兔,而小兔经过一个月就长成大兔,问从一对小兔开始,一年后共繁殖成多少...