"It has come to my attention that various and sundry folk have done far better approximations of the ratio of a circle's circumference to its diameter than had been possible with my excellent 96-sided regular polygon method.
"Î¼Ï€ÏÎ¬Î²Î¿," I say (or would if this calculating engine of yours could properly handle "Unicode"). It pleases me to no end to know that the great work has continued, lo these many years since that obstreperous Italic fellow with the red cloak so rudely interrupted my research.
However, with an eternity in Hades on my hands, I have endeavored to stay busy by continuing to produce more accurate approximations. (That rake Sisyphus tells me it's a waste of time, but he is not one to talk in that regard.)
What follows is the closest approximation I have made in my posthumous calcutatory diversions. "Pi," to use your modern shorthand, is about...
I guess until then we can, for objects a tad smaller than the entire universe, go with just 6 digits of precision. If you ever get stuck having to use a vanilla calculator that does not have Pi built-in, just remember "113355". Split that in the middle into 113 and 355. 355 / 113 = 3.1415292 .. close enough for many applications.Practically though, if you memorize or use Pi to 31 places where the first zero appears - past that it really cannot mater all that much. We aren't all Daniel Tammet's who can recite Pi to 20,000 places.
Could you explain why it makes sense to remember six digits in order to get an approximation of pi that's only valid to 4 digits?
The 5-digit approximation 3.1416 is more accurate and easier to remember; or you can memorize it to six digits as 3.14159. (The latter is both a correct rounding and a correct truncation, which is nice so if you ever want to learn more digits, you don't have to unlearn the final one.)
You really don't see the structure in "113355"? If you have to remember that as an arbitrary sequence of six digits, I honestly feel sorry for you.
Don't know how, but I totally missed that. Thanks for pointing it out.
The incredible bit was that I realized it was a non-strictly monotonous sequence, but didn't think the implication of that (w/r/t recovery from transposing adjacent digits) was worth mentioning, because that doesn't make it much easier to remember. (I assumed this property was why the AC concatenated it in denominator:numerator order instead of the usual.) And yet I missed the two elements (odd numbers in sequence, and each number repeated) that were obviously the real point.
I agree with you that it seems easier to just remember the digits.
However, I believe the AC made a mistake in the arithmetic. The given fraction agrees with pi to more than 4 decimal places. I suggest you check it yourself, but I believe the first few digits of 355/113 are 3.1415929. This is a better approximation than the AC indicated.
355/113 is 7 digits of accuracy in only 6 digits. It's also more convenient if your calculator doesn't do floating point.
It also seems to get you accuracy within 1/1000th of a millimeter per meter - which scales to about 1 millimeter of inaccuracy per kilometer.