Where did Pi come from?

Date: Fri, 2 Dec 1994 10:20:16 EST
From: 904
Subject: question

Good day, Dr. Math:

We are an adult high school and we were wondering if you could answer
our question.  Where did the word pi come from, and how did someone 
determine it was equal to 3.14?

Thank you,
Margie at TCLFLA5.

Date: Mon, 5 Dec 1994 15:09:11 -0500 (EST)
From: Dr. Sydney
Subject: Re: question

Dear Margie:

     Thanks for writing Dr. Math!  We are more than happy to answer 
your questions.  

     Pi is defined to be the ratio of the circumference of a circle to the 
diameter of a circle.  Say you have a circle of radius 1.  Then the 
circumference of the circle is 2Pi(1) and the diameter is 2(1), so the 
ratio of the circumference to the diameter is Pi.  Anyway, Pi is an 
infinite decimal that is approximately equal to 3.14.  

     People have worked on approximating Pi for thousands of years.  
For instance, Archimedes approximated Pi by inscribing polygons in 
the circle and taking the ratio of the circumference of the polygon to the 
radius of the circle (which is also the "radius" of the polygon).  The more 
sides on the polygon, the more accurate the approximation.  So, if you 
inscribe a dodecagon (12-sided polygon) and compute the ratio of the 
circumference to the radius, you will get a better approximation than if 
you do the same for a hexagon (6 sides).  

     This makes sense if you draw it out.  The polygons with the greater 
number of sides more closely resemble circles.  It is important to 
remember Pi does not equal 3.14; instead, 3.14 is an approximation for Pi.  
Really Pi = 3.141592653... (it is an infinite decimal).  

Mathematicians began notating this ratio with the Greek letter Pi around 
1706.  Perhaps the letter Pi was chosen to represent "periphery" (Pi is the 
ratio of the circumference (periphery) to the diameter).

     I hope this helps.  If not or if you have any other questions, please feel
free to write back.  Thanks!

--Sydney, Dr. "Math Rocks"