Researchers from the Indian Institute of Science (IISc) and the University of Calgary have made a groundbreaking discovery in the field of mathematics. While working on applying quantum field theory (QFT) principles to string theory amplitudes, scientists stumbled upon a new way to represent the mathematical constant pi (π).
Pi, which is the ratio of the circumference of a circle to its diameter, has been calculated in various ways over the centuries. From integrals to continued fractions and infinite series, mathematicians have explored different methods to express this irrational number. However, the new formula discovered by researchers Arnab Priya Saha and Aninda Sinha offers a fresh perspective on representing pi.
The accidental discovery of this novel mathematical series has the potential to revolutionize how we calculate pi. Unlike traditional series representations that require millions of terms for high precision, the new formula developed by Saha and Sinha converges much more rapidly. With just 40 terms, the series can achieve 15 decimal places of accuracy by setting a parameter to 41.5, whereas the traditional series may need 50 million terms for a similar level of precision.
This rapid convergence is attributed to the use of the Euler-Beta function and tree-level string theory amplitudes. By adjusting parameters and employing the crossing symmetric dispersion relation, researchers were able to derive a series that quickly converges to pi. This new approach not only simplifies the calculation of pi but also has significant implications for fields like high-energy particle physics, numerical simulations, cryptographic algorithms, and computational geometry.
The study published in the Physical Review Letters highlights how ideas from high-energy physics can lead to practical advancements in pure mathematics. The researchers’ work demonstrates the importance of interdisciplinary collaboration and the potential for using physics principles to enhance our computational toolkit. Moreover, this discovery could pave the way for exploring other mathematical constants and functions using similar techniques in the future.
Sinha emphasizes that previous attempts to explore this line of research were abandoned due to its complexity, but with the right tools and collaborative efforts, this new method for calculating pi has emerged. The researchers hope that their findings will inspire further exploration of mathematical constants like e or the natural logarithm, ultimately contributing to the development of new computational tools and techniques.
In conclusion, the unexpected breakthrough in representing pi by Saha and Sinha showcases the power of interdisciplinary research and the potential for cross-pollination of ideas between different fields of study. This discovery not only offers a faster and more efficient method for calculating pi but also opens up new possibilities for advancing mathematical knowledge and computational capabilities.
