Machin's Computation of Pi
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Around 1706, John Machin found the arc tangent formula .
Contributed by: Izidor Hafner (May 2016)
Open content licensed under CC BY-NC-SA
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Details
Let ,
be an arc of radius 1, and
be perpendicular to
,
,
, and
. Construct points
and
on the arc
, and
and
on the straight line
, so that
and
.
Then and
,
.
So ,
.
See [1, pp. 8–9].
References
[1] V. F. Rickey. "Machin's Formula for Computing Pi." (Apr 28, 2016) fredrickey.info/talks/10-03-13-HPM-DC-Machin/10-03-13-HPM_DC_Machin.pdf.
[2] MacTutor. "John Machin." (Apr 28, 2016) www-history.mcs.st-andrews.ac.uk/Biographies/Machin.html.
[3] Wikipedia. "John Machin." (Apr 28, 2016) en.wikipedia.org/wiki/John_Machin.
[4] W. W. Rouse Ball, H. S. M. Coxeter, Mathematical Recreations and Essays, 13th ed., New York: Dover Publications, 1987 p. 356.
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