# Minimum fencing when dividing triangle into 4 parts

1. Sep 29, 2007

### jonas.hall

So I have an equilateral triangle an I want to divide it in 4 parts, all having the same area. This can be done in a multitude of ways of course. But assuming it's a garden and the division is about putting up a fence, which division uses the least fencing?

Now I have two alternatives so far.

The first is to create a cirle in the middle and add three short segments from the circle to the midpoints of the sides. There should be a uniqe such solution and I just haven't bothered calculating it yet.

The second is, in my opinion more interesting. Cut of the corners with a curve symmetrical around the bisectors. Now if this curve was a straight line at right angles to the bisector it would be uniquely determined. Also if it was a circle centered in the vertex. After calculating some special cases one might be satisfied and pick the best but I was thinking one might set up a differential equation to find the best possible curve. But how would I set this up?