11–20 of 113 posts
Ok, I'm confused, what exactly is the point here? If you don't care, 3.14 is sufficient, if you do care then you use π, and if you really care you use τ[1]. [1]( http://tauday.com/tau-manifesto ) (And if you really really really care, you use a different font then the one HN defaults too.)
I think the reason for this is Thue–Siegel–Roth theorem that says there are only finitely many "good" rational approximations of pi (or any other irrational number).
Ok, I'm confused, what exactly is the point here? If you don't care, 3.14 is sufficient, if you do care then you use π, and if you really care you use τ[1]. [1]( http://tauday.com/tau-manifesto ) (And if you really really really care, you use a different font then the one HN defaults too.)
3.1415927 is really just a shorthand for 31415927/10000000, so shouldn't it count as 17 characters rather than 9?
No it isn't. It isn't "a shorthand". It is a notation. Of those two notations, no one is "a shorthand" of another.
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PS. The author is offering a prize to the reader who finds the rational number which gets the most decimals of Pi right for every digit of such rational number that has to be memorized. (Note that only rational numbers are allowed -- that is, fractions with integers in the numerator and denominator. Using formulas or numbers that are not rational is not allowed in the competition.)
If log and square root are allowed, then the obvious solution is log(-1)/(sqrt(-1)*log(e)) which is accurate to an infinite number of digits.
Very neat: naive attempts to memorize Pi with rational-number shortcuts (i.e., fractions with integers in the nominator and denominator, such as 22/7 and 355/113) seem pointless, because getting more decimal digits of Pi right requires that one memorize a correspondingly larger number of digits in the numerator and/or denominator, defeating the purpose of these native attempts. -- PS. The author is offering a prize t…
113355
We know we want a fraction, not a single number, so split down the middle:
113/355
And we know pi won't be less than 1, so flip it: 355/113. Knowing that the digits sequences are doubled lets you do some cheap, mental run length encoding. In a case where you need a hand calculation, spending 3 seconds to re-derive the sequence seems tolerable.
Earlier quoted context omitted.
No it isn't. It isn't "a shorthand". It is a notation. Of those two notations, no one is "a shorthand" of another.
I think the point is that McLoone is using two different notations and measuring an artifact of this. There's nothing special about base-10 denominators.