Revolutionizing the Representation of Pi

Scientists at the Indian Institute of Science (IISc) have made a groundbreaking discovery while exploring the applications of string theory in explaining physical phenomena. Their research has led to the unveiling of a new series representation for the irrational number pi, which could revolutionize calculations related to processes like quantum scattering of high-energy particles.

The newly uncovered formula, when analyzed within a specific limit, closely aligns with the representation of pi proposed by Indian mathematician Sangamagrama Madhava in the 15th century. Madhava's series for pi was the first of its kind recorded in history. The study, conducted by Arnab Saha, a post-doc, and Aninda Sinha, a Professor at the Centre for High Energy Physics (CHEP), has been published in Physical Review Letters.

According to Sinha, the initial goal of their research was not to discover a new perspective on pi. Instead, they were focused on studying high-energy physics in quantum theory and developing a model with fewer and more precise parameters to enhance the understanding of particle interactions. The team was pleasantly surprised when their work led them to a fresh interpretation of pi.

Sinha's group specializes in string theory, a theoretical framework positing that all quantum processes in nature involve various modes of vibrations on a string. Their research delves into the interactions of high-energy particles, such as those observed when protons collide in the Large Hadron Collider. The team aims to simplify the analysis of these interactions by minimizing the number of factors involved, a concept akin to solving "optimization problems."

By combining the Euler-Beta Function and the Feynman Diagram, Saha and Sinha devised an efficient model to represent particle interactions. The Euler-Beta Function is a mathematical tool widely used in physics and engineering problem-solving, while the Feynman Diagram illustrates the energy exchange during particle interactions. Through their collaboration, the team not only developed a model to explain particle interactions but also stumbled upon a series representation of pi.