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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