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 ...

It’s hard to explain Möbius transformations with a flat illustration in a textbook. But two professors at the University of Minnesota found that a 3-D animation lets them show the mathematical concept ...

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 ...

The Nature Index 2024 Research Leaders — previously known as Annual Tables — reveal the leading institutions and countries/territories in the natural and health sciences, according to their output in ...

Read article at Massey Research Online: Hyperbolic spaces have constant negative curvature and the study of discrete groups of transformations on these spaces allows their geometry to be investigated ...