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 ...

Piano Keys: In an octave, there are a total of 13 keys (8 white and 5 black, arranged as 2 and 3).

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 ...

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 ...

Fibonacci cubes represent a fascinating class of graphs that emerge as subgraphs of the n-dimensional hypercube. Defined by the restriction to binary strings that avoid consecutive 1s, these graphs ...