Circle squaring is the problem of constructing a square equal in area to a circle using
only a straightedge and compass.
This was one of the three geometric
problems of antiquity, and was perhaps first attempted by Anaxagoras. It was
finally proved to be an impossible problem when pi was proven
to be transcendental by Lindemann in 1882.
The Indiana pi bill of 1897 was a legislative attempt to endorse an erroneous circle-squaring method; among its incompatible consequences
were the values
and
(Edington 1935).
However, approximations to circle squaring are given by constructing lengths close to .
Ramanujan (1913-1914), Olds (1963), Gardner (1966, pp. 92-93), and (Bold 1982,
p. 45) give geometric constructions for . Dixon (1991) gives constructions for and (Kochanski's
approximation).
and 
(Edington 1935).
.
Ramanujan (1913-1914), Olds (1963), Gardner (1966, pp. 92-93), and (Bold 1982,
p. 45) give geometric constructions for 
. Dixon (1991) gives constructions for 
and 
(Kochanski's
approximation).
." Quart. J. Pure. Appl. Math. 45, 350-372,
1913-1914.Wells, D.