Prudence ⚓ Fortitude

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The mathematical constant known as *π* is related to the properties of circles and spheres. For example, the circumference of a circle divided by its diameter gives us that irrational number that we call *π*. However because it is an irrational number, the best we can provide is an approximation of its value. It is believed that for most projects in antiquity, our ancestors used an approximation of 3. Even the Bible shows such approximation when describing the cast sea with a circumference of 30 cubits and a diameter of 10 cubits.^{[1]} Of course, over time we've simply gotten more exact renderings and with the advances in mathematics new formulas develops to calculate *π* with more accuracy.

There are only a few algorithms used to calculate *π*. In 1989, only 480 millions digits were known but thanks to modern computing, the constant *π* has now been calculated at over 202 trillions decimal places using the Chudnovsky formula.^{[2]} The vast majority of record breaking computations since 1989 were made with that formula and most of the remaining successful records were achieved using the Gauß-Legendre algorithm. Adding a new formula to the mix might not be of benefit in improving our modern approximation of *π*, especially considering efficient algorithms such as the Chudnovsky formula, but like anything new, it could be of interest.

Two physicists from the Indian Institute of Science have stumbled upon a new series representation for the irrational number *π*, which they say provides an easier way to extract *π* from calculations used to decipher the quantum scattering of high-energy particles flung about in particle accelerators. The physicists who discovered the new formula were not initially looking for one, it came by accident. They were attempting to better describe particle collisions; they were studying high-energy physics in quantum theory and trying to develop a model with fewer and more accurate parameters to understand how particles interact. What the team found was not only an efficient model that could explain particle interaction, but also a series representation of *π*:^{[3]}

The new formula under a certain limit closely reaches the representation of *π* suggested by Indian mathematician Sangamagrama Madhava in the 15^{th} century.

- 1 Kings 7:23 and 2 Chronicles 4:2.
- Jordan Ranous,
StorageReview Lab Breaks Pi Calculation World Record with Over 202 Trillion Digits,

*StorageReview*(https://www.storagereview.com/news/storagereview-lab-breaks-pi-calculation-world-record-with-over-202-trillion-digits : 28 June 2024). - Arnab Priya Saha and Aninda Sinha,
Field Theory Expansions of String Theory Amplitudes,

*Physical Review Letters*132, no. 22 (28 May 2024): 221601, doi:10.1103/PhysRevLett.132.221601.