11043
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
Newton's Pi Approximation
This Demonstration gives Newton's approximation of
based on calculating the area of a semicircle using an integral.
The area
under the arc
(light blue) is equal to the area of the sector
minus the area of triangle
(light green), that is,
.
On the other hand, the semicircle has equation
, so
. Set
and
.
Therefore,
.
Contributed by:
Izidor Hafner
THINGS TO TRY
Slider Zoom
Gamepad Controls
Automatic Animation
SNAPSHOTS
DETAILS
Newton presented
to 16 decimal places using 20 terms of the binomial series [1, p. 177].
Reference
[1] W. Dunham,
Journey through Genius
, New York: Penguin Books, 1990 pp. 174–177.
RELATED LINKS
Gauss-Legendre Approximation of Pi
(
Wolfram Demonstrations Project
)
Pi
(
Wolfram
MathWorld
)
Vega's Calculation of Pi
(
Wolfram Demonstrations Project
)
Vega's Second Calculation of Pi
(
Wolfram Demonstrations Project
)
Euler's Estimate of Pi
(
Wolfram Demonstrations Project
)
PERMANENT CITATION
Izidor Hafner
"
Newton's Pi Approximation
"
http://demonstrations.wolfram.com/NewtonsPiApproximation/
Wolfram Demonstrations Project
Published: August 22, 2013
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
Archimedes' Approximation of Pi
John Tucker
Wallis Sieve Pi Approximation
Michael Schreiber
Approximate Area and Circumference of a Circle Using Isosceles Triangles
Xiang Li
Area Approximation for Polar Plot
Michael Waters
Approximating Pi with Inscribed Non-Regular Polygons
Izidor Hafner
Euler's Estimate of Pi
Izidor Hafner
Vega's Calculation of Pi
Izidor Hafner
Machin's Computation of Pi
Izidor Hafner
Vega's Second Calculation of Pi
Izidor Hafner
Reconstruction of Vega's First Calculation of Pi
Izidor Hafner
Related Topics
Area
Integrals
Pi
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+