  Three-dimensional protein structures usually contain regions of local order,
called secondary structure, such as $\alpha$-helices and $\beta$-sheets.
Secondary structure is characterized by the local rotational state of the
protein backbone, quantified by two dihedral angles called $\phi$ and $\psi$.
Particular types of secondary structure can generally be described by a single
(diffuse) location on a two-dimensional plot drawn in the space of the angles
$\phi$ and $\psi$, called a Ramachandran plot. By contrast, a
recently-discovered nanomaterial made from peptoids, structural isomers of
peptides, displays a secondary-structure motif corresponding to two regions on
the Ramachandran plot [Mannige et al., Nature 526, 415 (2015)]. In order to
describe such `higher-order' secondary structure in a compact way we introduce
here a means of describing regions on the Ramachandran plot in terms of a
single Ramachandran number, ${\mathcal{R}}$, which is a structurally meaningful
combination of $\phi$ and $\psi$. We show that the potential applications of
${\mathcal{R}}$ are numerous: it can be used to describe the geometric content
of protein structures, and can be used to draw diagrams that reveal, at a
glance, the frequency of occurrence of regular secondary structures and
disordered regions in large protein datasets. We propose that ${\mathcal{R}}$
might be used as an order parameter for protein geometry for a wide range of
applications.
