Continued fractions and golden mean

In Uncategorized on settembre 10, 2009 at 9:37 am

The golden mean is one of the most popular number in mathematics:

Let us study the representation of this number in continued fraction. In a previous post we have seen that any quadratic irrationality has a periodic expansion in continued fraction. So the golden mean has a periodic expansion in continued fraction too. We remember that the golden mean is the root of the equation


So it satisfies the relation x^2-x-1=0:


So we can write the golden mean as:


i.e. the golden mean is represented by a sequence of 1.

  1. spettacolo… sei uno zarro ippaso! un tamarro della matematica!

  2. Today, I went to the beach front with my children. I found a sea shell and
    gave it to my 4 year old daughter and said “You can hear the ocean if you put this to your ear.” She put the shell to her ear and screamed.

    There was a hermit crab inside and it pinched her ear.
    She never wants to go back! LoL I know this is
    entirely off topic but I had to tell someone!

  3. I know this site presents quality based posts and additional
    data, is there any other web page which gives these stuff in quality?


Inserisci i tuoi dati qui sotto o clicca su un'icona per effettuare l'accesso:

Logo WordPress.com

Stai commentando usando il tuo account WordPress.com. Chiudi sessione / Modifica )

Foto Twitter

Stai commentando usando il tuo account Twitter. Chiudi sessione / Modifica )

Foto di Facebook

Stai commentando usando il tuo account Facebook. Chiudi sessione / Modifica )

Google+ photo

Stai commentando usando il tuo account Google+. Chiudi sessione / Modifica )

Connessione a %s...

%d blogger hanno fatto clic su Mi Piace per questo: