I sometimes think we are spoiled by modern computational accuracy. If you draw a circle using 355/113 instead of pi, and the circumference is 1 inch off, the circle is over 59 miles in diameter. I suspect New York City would easily fit inside that circle.
-----Original Message----- From: math-fun [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Allan Wechsler Sent: Saturday, February 17, 2018 5:30 PM To: math-fun Subject: Re: [math-fun] a numerical approximation close to 7 digit pi
Just as a rule of thumb, the number of digits in the arbitrary constants on the left side ought to be smaller than the negative of the log10 of the relative error. So Eugene Salamin's example is more interesting than James Buddenhagen's, because 8 < 9.494, but 10 > 9.78. By this rule, 355/113 is barely interesting, because 6 < 6.57.
On Sat, Feb 17, 2018 at 4:03 PM, James Buddenhagen <jbuddenh@gmail.com> wrote:
There is also (77729/254)^(1/5) = 3.1415926541114871, with log10 of relative error -9.78
On Sat, Feb 17, 2018 at 11:14 AM, Eugene Salamin via math-fun < math-fun@mailman.xmission.com> wrote:
My favorite is (2143/22)^(1/4) = 3.1415926525826463. Log10 of relative error is -9.494.
-- Gene
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