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 ,

			(2)
			(3)
			(4)
			(5)
			(6)
			(7)

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.