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 ...

In two dimensions, it’s the Reuleaux triangle: an equilateral triangle with curved arcs connecting each corner, creating a shape with a constant width but a smaller area than a circle. Now, a team of ...

Mathematicians are creating their own version of the periodic table that will provide a vast directory of all the possible shapes in the universe across three, four and five dimensions, linking shapes ...

Ending a six-decade-old mathematical mystery with the help of computational methods, a trio of Chinese scientists have proven that manifolds of Kervaire invariant one do exist in dimension 126. The ...

Mathematicians have reinvented the wheel with the discovery of shapes that can roll smoothly when sandwiched between two surfaces, even in four, five or any higher number of spatial dimensions. The ...