Our favorite mathematical constant, pi (Ï€), describing the ratio between a circle's circumference and its diameter, has taken on new meaning.

The new representation was borne out of the twists and turns
of string theory, and two physicists' attempts to better describe particle
collisions.

"Our efforts, initially, were never to find a way to
look at pi," says Aninda Sinha of the Indian Institute of Science (IISc)
who co-authored the new work with fellow IISc theoretical physicist Arnab Priya
Saha.

"All we were doing was studying high-energy physics in quantum theory and trying to develop a model with fewer and more accurate parameters to understand how particles interact. We were excited when we got a new way to look at pi."

Being a mathematical constant, the value of pi hasn't
changed, however irrational a number it is; over time we've simply gotten more
exact renderings of its precise value, achieving 105 trillion figures at the
latest count.

This new work from Saha and Sinha posits a new series
representation of pi, which they say provides an easier way to extract pi from
calculations used to decipher the quantum scattering of high-energy particles
flung about in particle accelerators. But some mathematicians disagree.

In mathematics, a series lays out the components of a
parameter like pi such that mathematicians can quickly arrive at the value of
pi, from its component parts. It's like following a recipe, adding each
ingredient in the correct amount and order, to produce a tasty dish.

Except if you don't have the recipe, then you don't know
which ingredients make up a meal or how much to add and when.

Finding the correct number and combination of components to
represent pi has stumped researchers since the early 1970s, when they first
tried to represent pi in this way, "but quickly abandoned it since it was
too complicated," Sinha explains.

Sinha's group was looking at something else entirely: ways
to mathematically represent subatomic particle interactions using as few and as
simple factors as possible.

Saha, a postdoctoral researcher in the group, was tackling
this so-called 'optimization problem' by trying to describe these interactions
– which give off all sorts of strange and hard-to-glimpse particles – based on
various combinations of the particles' mass, vibrations, and the wide spectrum
of their erratic movements, among other things.

What helped to unlock the problem was a tool called a
Feynman diagram, which represents the mathematical expressions describing the
energy exchanged between two particles that interact and scatter.

Not only did this yield an efficient model of particle
interactions that captured "all the key stringy features up to some
energy," but it also produced a new formula for pi that closely resembles
the first-ever series representation for pi in recorded history, put forward by
Indian mathematician Sangamagrama Madhava in the 15th century.

The findings are purely theoretical at this stage, but could
have some practical uses.

"One of the most exciting prospects of the new representations in this paper is to use suitable modifications of them to reexamine experimental data for hadron scattering," Saha and Sinha write in their

published paper.

"Our new representation will also be useful in
connecting with celestial holography," the pair adds, referring to an
intriguing but still-hypothetical paradigm seeking to reconcile quantum
mechanics with general relativity through holographic projections of spacetime.

For the rest of us, we can be satisfied knowing researchers
can more accurately describe what exactly makes up the famed irrational number.