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 ...

Time for some simple mathematics that span across the scientific world. This week, we’re exploring just some examples of the “golden ratio”. * Enough of getting bogged down in the numbers, here’s ...

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 ...

The stable or robust transfer of matter, information, or energy, from one point in space to another is a crucial scientific and technological challenge. In 1983, Nobel laureate D. J. Thouless proposed ...

Casey Murphy has fanned his passion for finance through years of writing about active trading, technical analysis, market commentary, exchange-traded funds (ETFs), commodities, futures, options, and ...

A century ago, the strange behavior of atoms and elementary particles led physicists to formulate a new theory of nature. That theory, quantum mechanics, found immediate success, proving its worth ...

In this paper, we derive some new symmetric properties of 𝑘-Fibonacci numbers by making use of symmetrizing operator. We also give some new generating functions for the products of some special ...