Extra Example 5.  Use the Schwarz Christoffel formula to show that    will map the upper-half-plane onto an equilateral triangle.
Hint: For convenience we have chosen  .

Explore Extra Solution 5.

We shall investigate three cases of this formula.

(i)    

(ii)    

(iii)    

For our next construction we will start with the unit disk and map it onto the upper half plane, then onto the triangle.

(c) 2006 John H. Mathews, Russell W. Howell