home | courses | topics | theorems | starters | worksheets | timeline | KS3 | KS4 | KS5

   
 
           
                   

Some things are irrational, some are not measurable - Pi (which is written the same way as at the top of this page) is one of those things - in fact not only is it not rational, it is transcendental!

A transcendental number is a number that is not the root of any whole number. What does that mean? It means that transcendental number is not algebraic number of any degree (you can't express it as a degree of any other number). This also means that every transcendental number is irrational number since a rational number is, by definition, an algebraic number of degree one.

Rational numbers are also defined as fractions of integers and irrational as not being able to be expressed as fractions of two integers.

Pi has baffled people through the ages. It is because you cannot measure Pi to total accuracy. Pi is, very simply, ratio between circumference and radius (or diameter) of a circle - it is the same for each and every circle.

Because Pi cannot be expressed as a fraction of two integers, you can either have a very accurate measurement of your radius (or diameter), in which case you get approximate measurement of the circumference, or otherwise you can start by having exact measurement of the circumference and end up with an approximation of the radius.

Or

Various people have tried to get the closest and most accurate approximation of Pi. Some of their efforts include the examples below.

See how Archimedes calculated an approximation to Pi.

Ptolemy (c. 150 AD) thought Pi is 3.1416

Chinese mathematician Zu Chongzhi (430-501 AD) thought Pi should be   355 / 113

al-Khwarizmi (c. 800 ) calculated Pi to be 3.1416.

We usually take Pi to be 3.14, although you can see the first 10 000 decimal places of Pi by clicking here.

 

   

 

hmmm... what a tasty pi!

Learn more about the properties of circle by clicking on the picture above or just plain here.

Click here to see the interractive applet describing Archimedes' way of approximating Pi.

 

artefacts | numerals | concepts | people | places | pythagoreans | egyptians | babylonians

 

Google
Search WWW Search www.mathsisgoodforyou.com

_____________________________________________________________________________________________________________________

Acknowledgements | Copyright | Contact | Mission Statement | Tell a friend about this site