0
$\begingroup$

Consider a boundary given by vertices (0,a), (0,0) and (1,0) (an 'L' shaped boundary).

The problem is to find the equation that passes between the endpoints (0,a) (1,0) of minimum length that encloses a specified area A.

A trivial case would be A=a/2 in which case the solution would be a line.

This is one dimensional Laplace problem with two boundaries (area and verticies) but how do I try to get a series solution for A

Improve this question
$\endgroup$
3
  • 1
    $\begingroup$ What's your motivation for this problem, if you don't mind me asking? $\endgroup$
    – David Roberts ♦
    Commented Jan 5, 2013 at 0:37
  • $\begingroup$ Homework, voting to close. $\endgroup$
    – Igor Rivin
    Commented Jan 5, 2013 at 1:06
  • $\begingroup$ In addition to voting to close, I removed the tag "Laplace transforms." $\endgroup$
    – Michael Renardy
    Commented Jan 5, 2013 at 2:06

1 Answer 1

Reset to default
1
$\begingroup$

The solution should be an arc of circle enclosing appropriate area.

Improve this answer
$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .