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 ...

In our mind’s eye, the universe seems to go on forever. But using geometry we can explore a variety of three-dimensional shapes that offer alternatives to “ordinary” infinite space. When you gaze out ...

THE philosopher Kant declared that Euclidean geometry was inherent in the human mind and expressed the truth about space. We now recognize that non-Euclidean geometry is equally valid as an abstract ...

Materials were written for an entire year's course in geometry in which transformations were used to develop the concepts of congruence, similarity, and symmetry, as well as being a vehicle for proof.

Euclidean geometry is a mathematical well-known system attributed to the Greek mathematician Euclid of Alexandria. Euclid's text Elements was the first systematic discussion of geometry. It has been ...

Everyone learns the number one rule about triangles in high school: the angles of a triangle add up to 180 degrees. But did you know that sometimes they don't? Triangles are much more interesting than ...

In 1847, an eccentric British mathematician named Oliver Byrne released a new edition of Euclid’s famous mathematical treatise, The Elements of Geometry. Byrne added a rather longwinded but ultimately ...

Margaret Wertheim gave a talk for the Australian Mathematical Sciences Institute at their 2016 annual Summer School. We have built a world of largely straight lines – the houses we live in, the ...

Director, Australian International Gravitational Research Centre, The University of Western Australia I have spent almost 40 years trying to detect gravity waves. When I started there were just a few ...