- #1
Esran
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Homework Statement
Show that the shortest distance between two points in three dimensional space is a straight line.
Homework Equations
Principally, the Euler Lagrange equation.
The Attempt at a Solution
I understand how to do this for a plane, but when we move into three dimensions, our distance element is then ds=(dx2+dy2+dz2)(1/2), which throws me off with the added variable. How do I handle calculus of variation problems like this in more than two variables? What will be my functional?