Egypt (1650 bc)

Ahmes

"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)

Pi=3

Isreal

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

Greece

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

China

Tsu Ch'ung-chih and his

son Tsu Keng-chih

calculated 3.1415926 < pi < 3.1415927 India

Aryabhata

gave the 'accurate' value

62,832/20,000 = 3.1416

but he apparently

never used it, nor

did anyone else for

several centuries India

Brahmagupta

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

al'Khwarizmi

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

Belgium

Adrianus Romanus

circumscribed polygon with

230 sides to compute pi to

17 digits after the decimal,

of which 15 were correct

Germany

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 =

(3(3(5(5(7(7(9...)/(2(4(4(6(6(8(8...)

Scotland

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:

Sam

Parkhurst

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