We will use the picture above to prove that .

First, we note that
 
 

Since the area of a triangle is given by the formula and the area of a circular sector is given , the above inequality becomes
 
 

as the base of both triangles, as well as the radius of the circle are "1", and the height of the triangles are, respectively,
and .

Now, we multiply the inequality above by
 
 

to obtain the new inequality
 
 
 

which simplifies to
 
 

Now, we take the reciprocal of each term in the inequality (which reverses the direction of the inequality) and rearrange the terms in increasing order, to obtain
 
 

We obtain the desired result upon noting that the first and last term
 
 
 

and so the term
 
 

also has, by applying the Squeeze Theorem, a limit of 1.