e Approximations
المؤلف:
Castellanos, D.
المصدر:
"The Ubiquitous Pi. Part I." Math. Mag. 61
الجزء والصفحة:
...
2-2-2020
1107
e Approximations
An amazing pandigital approximation to 
that is correct to 18457734525360901453873570 decimal digits is given by
 |
(1)
|
found by R. Sabey in 2004 (Friedman 2004).
Castellanos (1988ab) gives several curious approximations to 
,
which are good to 6, 7, 9, 10, 12, and 15 digits respectively.
E. Pegg Jr. (pers. comm., Mar. 2, 2002), found
 |
(8)
|
which is good to 7 digits.
J. Lafont (pers. comm., MAy 16, 2008) found
 |
(9)
|
where 
is a harmonic number, which is good to 7 digits.
N. Davidson (pers. comm., Sept. 7, 2004) found
 |
(10)
|
which is good to 6 digits.
D. Barron noticed the curious approximation
 |
(11)
|
where 
is Catalan's constant and 
is the Euler-Mascheroni constant, which however, is only good to 3 digits.
REFERENCES:
Castellanos, D. "The Ubiquitous Pi. Part I." Math. Mag. 61, 67-98, 1988.
Friedman, E. "Problem of the Month (August 2004)." http://www.stetson.edu/~efriedma/mathmagic/0804.html.
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