Fields of Mathematics have often been inspired or popularized by someone 
posing a problem (or problems), and others trying to provide 
solutions.  The problems often identified for capturing the imagination of 
mathematicians and subsequently inspiring the creation of the Calculus of 
Variations are the Brachistochrone (shortest time) problem, the Soap Film 
Problem (minimum area of surface of revolution), Zermelo's problem 
(navigation problem), Dido's problem (isoperimetric problem) and the 
shortest distance problem.  The first three listed problems have been 
previously solved in this colloquium series.  The last two problems will be 
discussed in this talk, as well as the results of the other three (time 
permitting).  The talk will be designed to be accessible to students who 
have completed or are currently enrolled in Calculus III.