History of Pi By Julian Wolf

Babylonian Pi  The ratio of the circumference to the diameter of a circle is constant (namely, pi) has been recognized for as long as we have written records.  Ancient Babylonians calculated the area of a circle by taking 3 times the square of its radius (pi=3)  On one Babylonian tablet from ca 1680 bce gives pi a value of 3.125

Egyptian Pi  Ancient Egyptians calculated the area of a circle by using this formula. (d= diameter)  This means the value of pi is

Archimedes’ Pi  The first theoretical calculation of pi was done by Archimedes of Syracuse ( bce)  He figured that 223/71 <pi< 22/7. His results were based off based on the area of a regular polygon inscribed within the circle and the area of a regular polygon within which the circle was circumscribed.

Archimedes Cont.  By starting with a hexagon he was able go all the way up to a 96 sided polygon.  Called a :  Called a : Enneacontakaihexag on

European Pi  Early European mathematicians such as James Gregory ( ) developed new formulas.  His was pi/4 = 1 - 1/3 + 1/5 - 1/  The only problem with this formula is that you add millions of terms to find the value of pi/4 that extends to 6 or 7 decimal places

European Pi cont.  In 1706 John Machin improved Gregory’s formula, which is still used today to program pi on computers.  By using this formula William Shanks calculated pi to 707 places but only 527 places were right.

The Symbol Itself  Introduced by William Jones in 1706 he wrote : = pi = pi  This symbol was adopted by Euler in 1737 and is still the standard symbol today.