THE two books under notice together constitute an excellent introduction to non-Euclidean geometry in all its aspects. The lectures of F. Klein now appear in print for the first time under the ...

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 ...

Virtual reality can take you to some far-out places — mountaintops, distant cities and even fantastical game worlds. A team of artists and mathematicians is now adding to that list: universes where ...

Grid cells, space-mapping neurons of the entorhinal cortex of rodents, could also work for hyperbolic surfaces. A new study tests a model (a computer simulation) based on mathematical principles, that ...

We’ve all learned “parallel lines never intersect” in high school geometry. But what your teachers failed to explain is that “parallel lines never intersect” is only true in Euclidean geometry, which ...

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 ...

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 ...