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Two physicists have come across infinitely many novel equations for pi while trying to develop a unifying theory of the fundamental forces

The number pi (π) appears in the most unlikely places. It can be found in circles, of course—as well as in pendulums, springs and river bends. This everyday number is linked to transcendental mysteries. It has inspired Shakespearean thought puzzles, baking challenges and even an original song. And pi keeps the surprises coming—most recently in January 2024, when physicists Arnab Priya Saha and Aninda Sinha of the Indian Institute of Science presented a completely new formula for calculating it, which they later published in Physical Review Letters.

Saha and Sinha are not mathematicians. They were not even looking for a novel pi equation. Rather, these two string theorists were working on a unifying theory of fundamental forces, one that could reconcile electromagnetism, gravity and the strong and weak nuclear forces. In string theory, the basic building blocks of the universe are not particles, such as electrons or photons, but rather tiny threads that vibrate like the strings of a guitar and in so doing cause all visible phenomena. In their work, Saha and Sinha have investigated how these strings could interact with each other—and accidentally discovered new formulas that are related to important mathematical quantities.

For millennia, mankind has been trying to determine the exact value of pi. This is not surprising, given the utility of calculating the circumference or area of a circle, which pi enables. Even ancient scholars developed geometric approaches to calculate this value. One famous example is Archimedes, who estimated pi with the help of polygons: by drawing an n-sided polygon inside and one outside a circle and calculating the perimeter of each, he was able to narrow down the value of pi.

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