In this paper, we consider the usual Lucas numbers and the generalized order-k Fibonacci numbers. Then we give a new definition for generalization of the Lucas numbers. Therefore, we give the ...

Trying variants of a simple mathematical rule that yields interesting results can lead to additional discoveries and curiosities. The numbers 1, 1, 2, 3, 5, 8, 13, 21, 34, and 55 belong to a famous ...

https://doi.org/10.4169/college.math.j.48.2.97 https://www.jstor.org/stable/10.4169/college.math.j.48.2.97 Hong recently explored when the value of the generating ...

Dima Vonko is a software entrepreneur and writer for trade publications, including Trade2Win and Traders Tips. Gordon Scott has been an active investor and technical analyst or 20+ years. He is a ...

Here's a hypothetical and idealized question about rabbits, first posed by Leonardo di Pisa in 1202 (Leonardo is more commonly known as Fibonacci). There's a pair of rabbits in an enormous field. At ...

Pine cones. Stock-market quotations. Sunflowers. Classical architecture. Reproduction of bees. Roman poetry. What do they have in common? In one way or another, these and many more creations of nature ...

As their results began to crystallize, at first they didn’t notice the striking patterns emerging. But a colleague who reviewed their work spotted the famed Fibonacci numbers—a list whose entries have ...

Though generations of schoolchildren have cursed arithmetic, the world was a much more inconvenient place without it. Before the advent of modern arithmetic in the 13th century, basic calculations ...

To carry out their calculations, merchants in the early 13th century used an abacus or a system called finger reckoning. Commerce changed when Leonardo of Pisa — known today as Fibonacci — published ...

A series of whole numbers in which each number is the sum of the two preceding ones: 1, 1, 2, 3, 5, 8, 13, etc. Fibonacci numbers are used in a variety of algorithms, including stock market analysis.