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 ...

It has long been observed that many plants produce leaves, shoots, or flowers in spiral patterns. Cauliflower provides a unique example of this phenomenon, because those spirals repeat at several ...

Learn about the origins of the Fibonacci sequence, its relationship with the golden ratio and common misconceptions about its significance in nature and architecture. When you purchase through links ...

An unusual arrangement of leaves in a 407-million-year-old fossilized plant is complicating scientists’ understanding of plant evolution. Most land plants living today have spiral patterns involving ...