Abstraction lies at the heart of mathematics. It makes math powerful, but at the same time, it can make math hard to understand. Abstraction makes math simultaneously beautiful and austere, useful and ...

Some properties of the ordinary two-parameter Cauchy family, the circular or wrapped Cauchy family, and their connection via Möbius transformation are discussed. A key simplification is achieved by ...

Imaginary numbers are a solution to a very real problem, according to a new study published in Scientific Reports. Two physicists at Argonne National Laboratory offered a way to mathematically ...

In this paper, we propose a new transformation of circular random variables based on circular distribution functions, which we shall call inverse distribution function (idf) transformation. We show ...