When most people think of shapes, they imagine a triangle, a rectangle, or maybe even a fancier-sounding rhombus or trapezoid. But to mathematicians, shapes encompass a vast universe of surprising ...

It can be tempting to assume that your intuitions about three-dimensional space carry over to higher-dimensional realms. After all, adding another dimension simply creates a new direction to move ...

Mathematicians have long wondered how “shapes of constant width” behave in higher dimensions. A surprisingly simple construction has given them an answer. In 1986, after the space shuttle Challenger ...

Mathematicians are “reinventing the wheel” by giving it a new shape. Their newly imagined wheel looks like a many-dimensional guitar pick, and it could theoretically roll in ways beyond our ...

Hydrogen is considered an environmentally friendly alternative to conventional fossil fuels. Until now, expensive and rare substances such as platinum have been needed for its catalytic production, ...

The book Flatland: A Romance of Many Dimensions by Edwin A. Abbott explores the concept of physical dimensions through characters who encounter higher-dimensional beings. The protagonist, “A. Square,” ...

A research team has discovered how catalysts and many other nanoplatelets can be produced in an environmentally friendly way from readily available materials and in sufficient quantities. Hydrogen is ...