Continued fraction for 
John Wallis expanded it as the following infinite products
We can convert it into continued fraction by the following formula
(regular expression)
in special form
of 0220
in special form
William Brouncker did the same kind of thing as
in special form
or
in special form
An Indian scholar expanded it as
that is
arctan(1)
and also
We can convert the latter into continued fraction by the following formula
(regular
expression)
in
special form
Since
we have
in special form
after applying the rules of signs(up->front, down->front&next in every two terms).