The field of two-dimensional (2D) materials has seen substantial growth with emerging options such as MXenes, transition metal dichalcogenides (TMDs), black ...

For 50 years, scientists believed that schools of fish would save the most energy by swimming in flat diamond formations.

Out of the entire infinitude of possible shapes in possible dimensions, the shapes in precisely one dimension still resisted classification. In the words of Douglas Ravenel, a mathematician at the ...

The shape of the Universe When you look around the Universe you live in, it looks like a 3D space, just like the surface of the Earth looks like a 2D space. However, just like the Earth, if you were ...

When you look at your surrounding environment, it might seem like you're living on a flat plane. After all, this is why you can navigate a new city using a map: a flat piece of paper that represents ...

For example, the surface of a giant doughnut is another 2D space. Through a field called geometric topology, mathematicians like me study all possible spaces in all dimensions.

For example, to find the vertex of a parabola f (x) = x2 + 3 x + 2, the function is derived from x and the result is set to zero: 0 = 2 x + 3. This means that the vertex can be found at x = –1.5.

Shapes capable of tiling a 2D space need a minimum of two corners, but in 3D the rules are different. A great example of a natural soft cell is found in the chambers of a nautilus shell, but this ...

Domokos replied that it was a nice example of 2D soft cells. Regős wrote back: no, they were 3D soft cells. “It doesn’t look soft at all,” Domokos thought. “I mean, it has corners.” ...