<    1    >

---

Continued fraction for pi

A continued fraction for the number π = 3,1415… is

 

---

Explanation

We will start with the development of

By substituting  in Euler's formula you get

Therefore

Substitution of z = i in the continued fraction for the logarithm then gives

and because i ² = – 1 you get

 

---

History In his book Aritmetica infinitorum the English mathematician John Wallis described in 1665 this formula.

---

Deutsch   Español   Français   Nederlands   中文