What is Pi?

Date: 4/1/96 at 7:14:46
From: Leigh Ausband
Subject: Pi

What is the significance of "pi"?

Ashley Milburn

Date: 4/2/96 at 4:51:41
From: Doctor Jodi
Subject: Re: questions for Dr. Math: pi and finding pi

Hi there! 

Pi is the ratio between the radius and circumference of a 
circle or between the radius and area of a circle.

Mathematicians love pi because it's a transcedental number - 
its digits never end and never repeat.

Archimedes had a neat way of approximating pi: To explain it 
you need to know a few words: inscribe, circumscribe, and 
polygon.

If you inscribe a figure in a circle (place it inside a circle
with only the vertices touching the circle) the figure will 
include some but not all of the area of the circle.

Now if you circumscribe a circle with a figure (place the figure 
outside a circle with the vertices just touching the circle), 
the figure will include all of the area of the circle, plus a bit 
more.
  
Archimedes used inscribed and circumscribed figures to 
approximate the area of the circle.  (It's easiest with regular 
polygons like the equilateral triangle, square, regular pentagon, etc.  
- regular polygons have equal sides and equal angles.  Do you 
know how to find their area? )

Then, knowing that the area of the circle is Pi*r ^2 (that's pi 
times radius squared), you can approximate pi. 

If you get a chance, try Archimedes' method and let us know 
what you find.

-Doctor Jodi,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/