In his new book Creating Symmetry, Frank Farris uses ideas from advanced mathematics, such as complex analysis and abstract algebra, to transform snapshots of landscapes, flowers, or even his dinner ...

For more than 50 years, mathematicians have been searching for a rigorous way to prove that an unusually strong symmetry is universal across physical systems at the mysterious juncture where they’re ...

We are fond of saying things are symmetric, but what does that really mean? Intuitively we have a sense of symmetry as a kind of mirroring. Suppose we draw a vertical line through the middle of a ...

Reflective symmetry is when a shape can be folded in half, with either side of the fold being a mirror image of the other. Rotational symmetry is when a shape can be rotated and it still looks the ...

To begin to understand what mathematicians and physicists see in the abstract structures of symmetries, let’s start with a familiar shape. We are fond of saying things are symmetric, but what does ...

A group of mathematicians has shown that at critical moments, a symmetry called rotational invariance is a universal property across many physical systems. For more than 50 years, mathematicians have ...