Here is a long article on other pi approximations: http://mathworld.wolfram.com/PiApproximations.html It turns out that 355/113 does a great job compared to most of the expressions given there! But none seem to be better than just remembering 3.14159.
Not hard to memorize either part. Slow to calculate, but the accuracy is only limited by how far you expand the Taylor series.
If you remember it with denominator first, then it's 113-355, which is relatively easy to remember. :)
> and it is just a little bit more accurate than directly remembering 6 digits of pi.
It's accurate up to one digit more than that, which is why I called it surprisingly accurate.
But I agree that there is hardly a practical purpose to such numerology.
To find a better approximation to pi as a rational you will need a denominator of 16604 (52163/16604)
See https://en.m.wikipedia.org/wiki/Continued_fraction#Best_rati... for an intro to the theory. Reason for that large jump is the 292 in the continued fraction of pi.
Decimal notation is just a concsise way of writing down expressions for certain numbers. Fractions are another.
Of course, the real reason to prefer 355/113 is that it's cool.