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Gauss-Legendre Approximation of Pi
This Demonstration gives a Gauss–Legendre approximation of
. With the initial values
,
,
,
and using the recurrence relations
,
,
,
,
we can approximate
by
.
This converges very quickly as you can see by increasing
.
Contributed by:
Russ Johnson
THINGS TO TRY
Automatic Animation
SNAPSHOTS
RELATED LINKS
Pi
(
Wolfram
MathWorld
)
Pi Approximations
(
Wolfram
MathWorld
)
Pi Formulas
(
Wolfram
MathWorld
)
PERMANENT CITATION
Russ Johnson
"
Gauss-Legendre Approximation of Pi
"
http://demonstrations.wolfram.com/GaussLegendreApproximationOfPi/
Wolfram Demonstrations Project
Published: August 16, 2011
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