## Continued Fractions

### 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-
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### Re: Continued Fractions

Do approximations of irrational numbers count as an application?

### 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.

### Re: Continued Fractions

Oh yes, you can. Here it is: $\sqrt{2}$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.

Here's another one: the positive solution of the equation $x^2=2$.

### 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

### Re: Continued Fractions

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

### Re: Continued Fractions

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

RSA Attack