A young students inspiring journey of discovery to uncover the secrets of Pi.

Sindhia, now a Y11 student at St Helen’s School is one of a select few individuals who have discovered and proved an expression for Pi with her findings being published in the Young Global Scientists Journal.


Pi is an enigmatic and endlessly fascinating number which has captivated the minds of mathematicians for centuries. Known as the unchangeable ratio of the circumference to the diameter of any circle, Pi is an irrational number that cannot be expressed as a sum of finite fractions, yet its digits are fixed, and this has led some to wonder if there is a pattern hidden within them.

As a young mathematician, Sindhia too was intrigued by Pi’s infinite yet structured nature and this inspired her to navigate this journey of discovery – a journey she started while still in year 9. It all began while seated at her desk doing her homework, Sindhia was inspired to explore the numerical values of Pi.


“Sometimes when I’m doing my maths homework, I get distracted. While I suspect this is not uncommon, one of my distractions sparked a journey which resulted in me discovering and proving an expression for Pi as an infinite series of fractions.” – Sindhia


While both her and her maths teacher, Dr Dolby, initially thought the result was new, upon further research they discovered that it had originally been published over 500 years ago, by Nilakantha Somayaji.

While the theorem made sense, it would require proof that it worked, and importantly, that it worked every time. This proved to be far more time-consuming for Sindhia than making her initial discovery. Dr Dolby provided support in providing her with a roadmap to develop and prove her discovery.?After countless hours spent experimenting, she was able to prove that this theorem worked, and this journey is outlined in her now published paper. Her tenacity and commitment to seeing it through is highly commendable with her name now being associated to the discovery.


“Remembering Edison’s quote, I told myself ‘I have not failed 10,000 times—I’ve successfully found 10,000 ways that will not work.’ Failure lies in not trying. I did not give up. I kept going, hoping that there was some sort of cubic sequence or polynomial I could find.” – Sindhia


We are incredibly proud of Sindhia and have no doubt that her discovery and subsequent proof will inspire many more young mathematicians.

Her paper is available to read online: https://www.ygsjournal.com/_files/ugd/389a2b_3d75e05e29ec46dc9179ee48b954e657.pdf