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 ...

AbstractIn this note we consider two sequences of polynomials, which are denoted by { U n,m (k) } and { V n,m (k) } , where 𝑘, 𝑚, 𝑛 are nonnegative integers, and 𝑚 ≥ 2. These sequences represent ...

The Monthly publishes articles, as well as notes and other features, about mathematics and the profession. Its readers span a broad spectrum of mathematical interests, and include professional ...

First mapped by a merchant's son in 13th-century Italy, the Fibonacci sequence has become one of the most influential patterns in science, design, and technology. When you think of math, you might ...

It’s wild to think that a math puzzle from the 1200s is now helping power AI, encryption, and the digital world we live in. Every November 23, math lovers celebrate Fibonacci Day, a nod to the ...

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 ...