Appendix Six

 

The continued fraction is a strange type of fraction constructed by an infinite process of additions and divisions.

When phi is expressed as a continued fraction it looks like this:

 

 

image

 

 

To understand how this works, let’s take the fraction line by line and see that it closes in on phi:

 

 

image

 

 

And so on.

 

 

Continued fractions provide mathematicians with a way of rating how irrational a number might be. Since the expression for phi contains only 1s, it is the ‘purest’ continued fraction that there is, and hence is considered the ‘most irrational’ number.

Alex's Adventures in Numberland
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