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Why Was Pi Invented?

Date: 04/10/2003 at 05:49:07
From: Katharine
Subject: Pi - why was it even invented??

Dr. Math,

I don't understand why pi was invented in the first place. I know the 
history of it but why did they even want to invent it?


Date: 04/10/2003 at 08:47:43
From: Doctor Peterson
Subject: Re: Pi - why was it even invented??

Hi, Katherine.

There are usually several ways to interpret a "why" question, so I'll 
suggest several answers.

First, pi simply represents an observation about circles. If you 
measure the circumference and diameter of a lot of circles, you will 
find that the ratio is always the same.  When something this 
significant is discovered, we want to be able to talk about it and 
make use of it.  Since that ratio is not some simple number like 1/2 
or 75, it's useful to name it, in order to be able to talk about it.  
For instance, this makes it easier to discuss the relation between the 
circumference and area of a circle - that both can be calculated using 
pi.

Second, pi is very useful.  It allows us to do calculations such as 
finding the diameter of a tree by measuring its circumference, or 
finding the surface area of the earth, by doing nothing more than 
multiplying or dividing by pi.

Third, we could get along just fine without pi, if we wanted to 
continue discussing math the way the ancient Greeks did.  We could say 
things like "the area of a circle is the same as that of a triangle 
whose base is the same as the circumference of the circle, and whose 
altitude is the radius of the circle."  (Bet you didn't know that!) 
But since the invention of algebra, we find it much easier to write 
the same thing as a formula:

    A = pi r^2

(which is the same as what I just put in words because the area of 
that triangle is 1/2 C r, or 1/2 * 2 pi r r, which is pi r^2).  This
makes calculations much easier, and is easier to write.

Finally, pi turns out to be important in many other ways. 
Trigonometry uses it constantly (pun not intended); it turns up in
probability, series, and physics, among other places.

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/ 
Associated Topics:
High School Euclidean/Plane Geometry

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