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 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 ...

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 ...

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 ...

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 paper is concerned with a striking visual experience: that of seeing geometric visual hallucinations. Hallucinatory images were classified by Klüver into four groups called form constants ...

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 ...

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 ...

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 ...