If you’ve watched Disney’s High School Musical, you might remember a scene where the female lead corrected the teacher “shouldn’t the second equation read sixteen over pi?”
What was written on the board looked vaguely familiar, and so it got me trawling over the world wide web looking for details to no avail. I later found out from one of the world’s renown expert on [tex]\frac{1}{\pi}[/tex] that indeed the equation is one of three series that appeared in Ramanujan’s work “Modular equations and approximations to [tex]\pi[/tex]” Naturally, I went back to the web and this time hit the jackpot. Two screencaps:
Ramanujan’s series
[tex]\displaystyle \frac{16}{\pi} = \sum_{n=0}^\infty \frac{ (42n+5)(\frac{1}{2})^3_n}{64^n (n!)^3}[/tex]
Now if you want to watch the video, here’s the link.
It happens in the first minute. So you don’t have to wait too long.
high school musical is the best move
i love maths & ramanujan i watnt to do some think in maths but no one support me plz give feed back to me i want to achive sometink in maths
Dear Manjula, I don’t know your background but I presume you are from India from your email. To achieve something in maths, you have to start learning it somewhere. A good place would be a university. Best wishes.
There’s a great article in a recent Scientific American by Jonathan Borwein and Peter Borwein on “Ramanujan and Pi.” The series is written in different form, as [tex] \frac{\sqrt{8}}{9801} \sum_{n=0}^{\infty} \frac{(4n)!(1103 26,390n)}{(n!)396^{4n}} = \frac{1}{\pi} [/tex]. Each new term betters [tex] \frac{1}{\pi} [/tex] by about eight digits. This development in 1914 was a HUGE improvement over Gergory’s (1671) arctangent-of-1-equals-pi-over-four series expansion, convergence to a any reasonable approximation requiring hundres of terms. Machin’s (1706) arctangent expansion was better, but nothing like Ramanujan’s.