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 ...

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 ...

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 ...

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 ...

What do pine cones and paintings have in common? A 13th-century Italian mathematician named Leonardo of Pisa. Better known by his pen name, Fibonacci, he came up with a number sequence that keeps ...

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 ...

What do pine cones and paintings have in common? A 13th century Italian mathematician named Leonardo of Pisa. Better known by his pen name, Fibonacci, he came up with a number sequence that keeps ...