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 ...

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 ...

THIS work will be found really valuable by all students of geometry, especially by those who know little or nothing of the non-Euclidean theories. First of all we have a discussion of the elementary ...

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 ...

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 ...

in the diagram TR R is a diameter p r KT is a cyclic quad they talk about the chords and then they tell us that PK which is this entire length is the same as TK they have the same length and you can ...

There's a simple way to learn geometry over the summer. It is easy and fun. Imagine Euclidean geometry: the video game. If your experience in high school geometry was anything like mine, it probably ...

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 ...