10809
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
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
Share:
Embed Interactive Demonstration
New!
Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site.
More details »
Download Demonstration as CDF »
Download Author Code »
(preview »)
Files require
Wolfram
CDF Player
or
Mathematica
.
Related Demonstrations
More by Author
Wagon Wheel Approximation of Pi
Robert L. Brown
Archimedes' Approximation of Pi
John Tucker
Approximating Pi with Continued Fractions
Andreas Lauschke
Approximating Pi with Inscribed Non-Regular Polygons
Izidor Hafner
Machin's Computation of Pi
Izidor Hafner
Euler's Estimate of Pi
Izidor Hafner
Vega's Second Calculation of Pi
Izidor Hafner
Computing Pi the Chudnovsky Way
Michael Stern
Approximating Pi by the Monte Carlo Method
Zubeyir Cinkir
Classical Approximations of Pi
Rob Morris
Related Topics
Algorithms
Approximation Methods
Pi
Recursion
Browse all topics
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to
Mathematica Player 7EX
I already have
Mathematica Player
or
Mathematica 7+