IT is now well known by all mathematicians that Euclid's theory of parallels is not indispensable for the construction of a self-consistent geometry, but that, on the contrary, there are three ...

IN a recent number of NATURE (June 30) there appeared a review of a book by G. Mannoury on the philosophy of mathematics, and the reviewer emphasised a statement of the author to the effect that the ...

Abstract This survey highlights some foundational history and some interesting recent discoveries in elementary geometry that deserve to be better known, such as the hierarchies of axiom systems, ...

Geometry may be one of the oldest branches of mathematics, but it’s much more than a theoretical subject. It’s part of our everyday lives, says Professor Jennifer Taback, and key to understanding many ...

Reintroduction : View from the twenty-first century -- Augmenting a 1983 history of the fourth dimension in culture and art (1900-1950) : X-rays and ether physics as the context for the "fourth ...

Bernhard Riemann was a man with a hypothesis. He was confident that it was true, probably. But he didn’t prove it. And attempts over the last century and a half by others to prove it have failed. A ...

A musical chord can be represented as a point in a geometrical space called an orbifold. Line segments represent mappings from the notes of one chord to those of another. Composers in a wide range of ...