Questions from middle schoolers I: Pi

I travel a lot to work with middle school math teachers. In one classroom recently, I was oversold as a visiting mathematician. Visiting I was. Mathematician I am not. I do think about mathematics for a living, but I do not create original mathematics.

Nonetheless, students in the class generated a number of questions they wanted to ask a mathematician. So this series is for Ms. Otto’s eighth-grade students at KMS…

Who discovered Pi?

Can you believe that an entire book has been written about this subject? It’s called A History of Pi by Petr Beckmann.

Here’s the very short version…

In order to discover pi, people needed to understand ratios. That is, they needed to not just be able to count objects, they needed to be able to see relationships between quantities. That took a long time, until about 2000 B.C.

At that time, there were two major societies doing serious mathematics-the Babylonians and the Egyptians. Each of these societies appears to have noticed that there is a relationship between the diameter of a circle and its circumference, and both societies had decent estimates for pi (although neither called it that).

The next several thousand years involved people getting better estimates of the value of pi. There are lots of interesting mathematical advances that came about as people tried to do this.

In the 1700’s, at least two mathematicians demonstrated that pi was irrational (Lambert and Legendre). In 1882, Lindemann proved that pi is not just irrational; it has an even more profound property-it is transcendental. This means that it is not the square root (nor cube root, nor…) of any rational number. It is an even more special number than the square root of 2.

So who discovered pi? That’s a bit like asking who built the Empire State Building. Pi is an achievement of human intellect more than of a single person.


2 responses to “Questions from middle schoolers I: Pi

  1. Your blog is fascinating. I think I’m going to start clicking on random categories more often to see blog posts from 4 years ago!!

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s