MHB What are some interesting approximations of pi?

[kaliprasad]

we know a couple of approximate values of $\pi$ mostly $\frac{22}{7}$ and $\frac{355}{133}$ but one I found (from the net )interesting was sum of 2 surds $\sqrt{2} + \sqrt{3}$.if anyone is aware of other of interesting observation kindly let me know.

 

[HOI]

Not an approximation but a mnemonic: "May I have a large container of coffee". The number of letters in each word: 3.1415926.

 

[Opalg]

There is a collection of weird and wonderful approximations for pi here. My favourite is the approximation $\frac{355}{113}$, which gives the first six decimal digits of $\pi$ correctly, even though the numerator and denominator of the fraction have only three digits. The reason for that is that the following term in the continued fraction expansion of $\pi$ is the large number 292.

 

[Wilmer]

pi - log(23.141) = .000013282...

 

[RLBrown]

My "Wagon Wheel Approximation of Pi" was featured at Wolfram on Pi day.

 

[kaliprasad]

My "Wagon Wheel Approximation of Pi" was featured at Wolfram on Pi day.

Congratulations for the same(Too late)