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Math Class

Sam Parkhurst

on 21 January 2013

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Transcript of Pi

Egypt (1650 bc)

"Cut off 1/9 of a diameter and construct
a square upon the remainder; this has the same area as the circle.

Pi=4(8/9)2= 3.16049calculated the perimeters of inscribed polygons with 12, 24, 48, and 96 sides as (9.65, (9.81, (9.86, and (9.87 respectively China (hundereds of years later)

1 Kings 7:23;
"Also he made a molten sea of ten cubits from brim to brim, round in compass, and five cubits the height thereof; and a line of thirty cubits did compass it round about"
This implies that pi = 3
Antiphon and Bryson of Heraclea
inscribing a polygon inside a circle, finding its area, and doubling the sides over and over
their work only resulted in a few digits Greece
Archimedes of Syracuse
polygons' perimeters as opposed to their areas
approximated the circle's circumference instead of the area
Tsu Ch'ung-chih and his
son Tsu Keng-chih

calculated 3.1415926 < pi < 3.1415927 India
gave the 'accurate' value
62,832/20,000 = 3.1416
but he apparently
never used it, nor
did anyone else for
several centuries India
calculated the perimeters
of inscribed polygons
with 12, 24, 48, and 96
sides as (9.65, (9.81, (9.86,
and (9.87 respectively
therefore pi, would approach
the square root of 10 =3.162...
Saudi Arabia
Mohammed ibn Musa
3 1/ 7, the square root of 10, and 62,832/20,000 France
16th century
Françle;ois Viéte
used Archimedes' method,
starting with two hexagons
and doubling the number of
sides sixteen times
3.1415926535 < pi < 3.1415926537
Adrianus Romanus
circumscribed polygon with
230 sides to compute pi to
17 digits after the decimal,
of which 15 were correct
Ludolph Van Ceulen
20 digits, using the Archimedes
an method with polygons with
over 500 million sides
accurately found 35 digits England
John Wallis
approximated the
area of a quarter
circle using infinitely
small rectangles,
and arrived at the
formula 4/pi =

James Gregory
arctan (t) = t - t3/3 + t5/5 -t7/7 + t9/9.... Germany
Gottfried Leibniz
(/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9....
300 terms of the series are required to get only 2 decimal places, and 10,000 terms are required for 4 decimal places New Jersey Rutgers http://www.math.rutgers.edu/~cherlin/History/Papers2000/wilson.html By:
Full transcript