WOLFRAM|DEMONSTRATIONS PROJECT

Three Calculations of Pi Before 1800

​
Sharp
de Lagny
unknown author
12
/power of 3
positive terms
negative terms
final calculations
S
1
354623317218212168216889121260170410813905765688882763014018068153459848090
S
2
40464051859232844370624782932220122394188825751372180916523608922678207456
π =
S
1
-
S
2
314159265358979323846264338327950288419716939937510582097494459230781640634
π to 74 dec.
314159265358979323846264338327950288419716939937510582097494459230781640628
This Demonstration shows three calculations of
π
using the Gregory–Leibniz series
arctan(x)=x-
3
x
/3+
5
x
/5-⋯
with
x=1
3
.
Then
π=
12
-
12
(3·3)+
12
(5·
2
3
)-
12
(7·
3
3
)+⋯
.
Let
S
1
and
S
2
be the subseries with positive and negative terms, respectively.