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Davidbau.com The Mystery Of 355/113
Mar 14, 2010 ... We all know that 22/7 is a very good approximation to pi. But this well-known fraction is is actually 1/791 larger than a slightly less-well- ... [ReadMore..]
Not All Best Rational Approximations Are The Convergents Of The ...
[For more background on continued fractions and why they are so wonderful at approximations (and wonderful generally) — eventually I may edit this post to mention that. For now I just want to quick… Jan 10, 2011 ... Among all fractions with denominator at most 113, the fraction 355/113 is closest to π. And so on. Every convergent is a best rational ... [ReadMore..]
All Rational Approximations Of Pi Are Useless—Wolfram Blog
Investigation to find a better rational approximation for pi. Can we get out more digits than we put in? Chance to win a prize if you can do bette Jun 30, 2011 ... Investigation to find a better rational approximation for pi. Can we get out more digits than we put in? Chance to win a prize if you can do ... [ReadMore..]
What's So Great About Continued Fractions?
Continued fractions are objectively the best in approximation technology Mar 17, 2015 ... There's no such thing as a closest rational approximation to an ... a list of all the best rational approximations (of the first kind) of pi ... [ReadMore..]
Pi Approximations -- From Wolfram MathWorld
Convergents of the pi continued fractions are the simplest approximants to pi. The first few are given by 3, 22/7, 333/106, 355/113, 103993/33102, 104348/33215, ... (OEIS A002485 and A002486), which are good to 0, 2, 4, 6, 9, 9, 9, 10, 11, 11, 12, 13, ... (OEIS A114526) decimal digits, respectively. Two approximations follow from the near-identity function 3sinx/(2+cosx) evaluated at x=pi/4 and pi/8, giving pi approx (12)/7(2sqrt(2)-1) (1) approx ... . The first few are given by 3, 22/7, 333/106, 355/113, 103993/33102, 104348/33215, ... (OEIS A002485 and A002486), which are good to 0, 2, 4, 6, 9, 9, 9, 10, ... [ReadMore..]
Best Rational Approximations For Pi
It's easy to create rational approximations for π. Every time you write down π to a few decimal places, that's a rational approximation. For example, 3.14 = 314/100. But that's not the best approximation. Think of the denominator of your fraction as something you have to buy. If you have enough budget to buy a three-digit May 22, 2018 ... If you have enough budget to buy a three-digit denominator, then you're better off buying 355/113 rather than 314/100 because the former is more ... [ReadMore..]
C++ - What Is The Best Rational Approximation To Pi Using A 64-bit ...
Jul 15, 2020 ... You can use continued fractions to get excellent approximations of an irrational number. If you haven't encountered continued fractions ... [ReadMore..]
Rational Approximations Of Irrational Numbers.
give a sequence of better and better approximations to pi . We can measure the quality of these approximations by noticing that pi ... [ReadMore..]
What Is The Best Fractional Representation Of Pi? | WIRED
Yes. Pi Day is over. Well, at least it is over for those of us that write the date as mm/dd/yy (called middle endian). However, there is another way to represent the date. Some people (ok, most people) use the dd/mm/yy format (called little endian). Really, I can see where they are coming from. This […] Mar 18, 2011 ... You know, like 22 divided by 7 as an approximation for Pi? This would be in July - a nice month for a holiday. What about 14/3. [ReadMore..]
Approximations Of E And π: An Exploration
If x is a real number, an irreducible fraction p q with q > 0 is said to be a best rational approximation for x if, for any integer q with 0 < q. [ReadMore..]
Nt.number Theory - A "better" Rational Approximation Of Pi ...
355/113 is a good fractional approximation of π, because we use six digits to produce seven correct digits of π. 355113=3.1415929 ... [ReadMore..]