## Continued Fractions

Arithmetic, algebra, number theory, sequence and series, analysis, ...
matq
Posts: 4
Joined: Sun Oct 27, 2013 1:18 pm

### Continued Fractions

What is the most motivating way to introduce continued fractions? Are there any real life applications of continued fractions?

nicolas.patrois
Posts: 118
Joined: Fri Jul 26, 2013 3:54 pm
Contact:

### Re: Continued Fractions

Do approximations of irrational numbers count as an application?

ggoyo
Posts: 25
Joined: Sun Jun 22, 2014 9:45 am
Location: Paris
Contact:

### Re: Continued Fractions

Note that you cannot express the square root of 2 other than saying that if you square it, it becomes 2 or using continued fraction.

hk
Posts: 10697
Joined: Sun Mar 26, 2006 9:34 am
Location: Haren, Netherlands

### Re: Continued Fractions

ggoyo wrote:Note that you cannot express the square root of 2 other than saying that if you square it, it becomes 2 or using continued fraction.
Oh yes, you can. Here it is: $\sqrt{2}$
Here's another one: the positive solution of the equation $x^2=2$.

ggoyo
Posts: 25
Joined: Sun Jun 22, 2014 9:45 am
Location: Paris
Contact:

### Re: Continued Fractions

Well, $\sqrt{2}$ is just a symbol, how do you want to define it ? If you define it to be the solution of the equation you gave it is basicaly saying that it is the number that becomes 2 when squared : nothing new. Other way that I forgot is with geometrical considerations

pj6444
Posts: 9
Joined: Fri Jan 02, 2015 2:30 am

### Re: Continued Fractions

There are RSA attack methods that use continued fractions. For example: https://en.wikipedia.org/wiki/Wiener%27s_attack

sinan
Posts: 15
Joined: Mon Sep 15, 2008 9:14 am

### Re: Continued Fractions

pj6444 wrote:There are RSA attack methods that use continued fractions. For example: https://en.wikipedia.org/wiki/Wiener%27s_attack
Here's a link to a challenge based on this method for those who might want to give it a try:
RSA Attack