Some of the greatest scientific discoveries of all time happened by chance – or at least were made while scientists were looking for something else.
I’m not sure if this discovery will be remembered in this category, but it’s still pretty interesting to find a new way to write Pi.
The evolution of Pi goes on indefinitely and there is no way to predict what number will come next; even NASA only bothers to learn about 15 digits.
However, if you are clever, there are ways to express the constant exactly – and that is exactly what a team of physicists at the Indian Institute of Science has done.
In fact, they have found a way to express pi that had previously gone completely unnoticed by mathematicians and scientists – and this happened purely by chance, says Aninda Sinha, one of the study’s co-authors.
“Our initial efforts were not aimed at finding a way to look at pi. We were simply studying high-energy physics in quantum theory and trying to develop a model with fewer and more precise parameters to understand how particles interact. We were excited when we found a new way to look at pi.”
The idea of an infinite series boils down to the sum (or product) of the terms of an infinite sequence. They can be extremely useful in calculating the digits of pi and are also very nice to look at, says mathematician John Joseph O’Connor.
“One of the earliest infinite series for pi was that of Wallis, and one of the best known seems to have been first discovered by James Gregory. These are both dramatic and astonishing formulas, for the expressions on the right-hand side are purely arithmetic in nature, while pi comes primarily from geometry. They demonstrate the surprising results that infinite processes can produce, and point the way to the wonderful riches of modern mathematics.”
However, the search was not yet over.
“However, from the point of view of calculating pi, neither is useful at all. In Gregory’s series, for example, we need about 10,000 terms of the series to get 4 decimal places correct.”
However, this new formula is fast. It is related to Gregory’s series, but was developed in a different way. That is, they were able to vary a certain constraint to maximize efficiency.
“While the Madhava series requires five billion terms to converge to ten decimal places, the new representation with 𝜆 between 10 and 100 requires 30 terms.”
They also think they know why no one has noticed before.
“Physicists and mathematicians have overlooked this until now because they lacked the right tools. We only made this discovery through the work we have done together with our colleagues over the last three years or so.”
Science is constantly progressing.
And more and more answers are coming to light.
If you liked this story, check out what happened when a guy gave ChatGPT $100 to make as much money as possible and it turned out exactly as you expected.
