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Pi (π), the mathematical constant that connects circles to other objects such as river bends and pendulums, never ceases to amaze us. While researching on string theory in the beginning of 2024, Indian Institute of Science physicists Arnab Priya Saha and Aninda Sinha discovered a brand-new formula for pi. Their research, which was published in Physical Review Letters, advances the long tradition of pi mystery-solving by humans.
Saha and Sinha looked into the interactions between these vibrating strings in light of the string theory, which holds that the fundamental building blocks of the cosmos are strings rather than particles. Creating a cohesive theory of fundamental forces was their aim. They discovered new mathematical relationships along the way, one of which gives an infinite series for calculating pi.
Mathematicians have been searching for effective ways to calculate pi for centuries; Archimedes is credited with one of the first such methods. Pi’s value was reduced by his technique of sketching polygons within and outside of circles, but it was not practicable for an exact computation. The Indian scholar Madhava found a more straightforward series in the fifteenth century that made it possible to calculate pi with a growing degree of precision by adding fractions with odd denominators.
Madhava’s work was expanded upon by Saha and Sinha’s discovery, which showed that his series was merely an extreme example of a much wider equation. They present a parameter, λ, in their formula that has an unlimited range of values that can lead to pi. For example, their formula simplifies to Madhava’s original series when λ is infinite.
Their formula’s effectiveness is what sets it apart. Saha and Sinha’s formula for a small λ only needs 30 terms to obtain the same precision as Madhava’s series, which needs billions of terms to approximate pi to ten decimal places.
Their formula for pi adds a fascinating chapter to the long history of pi, even if it was an unanticipated by-product of their string theory research. “”We didn’t set out to discover a new pi formula,” Sinha clarified in a statement. “”Pi was only an incidental result.”
Their findings may even have wider ramifications since they may provide light on the Riemann zeta function, which remains one of mathematics’ greatest puzzles. For the time being, however, their new formula for pi stands as an astounding mathematical finding resulting from the hunt for the universe’s fundamental components.
