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?(adsbygoogle = window.adsbygoogle || []).push({});

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?

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Minimum fencing when dividing triangle into 4 parts

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

Loading...

Similar Threads - Minimum fencing dividing | Date |
---|---|

I What happens if you divide by a differential? | May 23, 2016 |

Dividing differential equations | Nov 4, 2013 |

Dividing differentials | Nov 4, 2013 |

Finding the maximum and minimum values | Feb 21, 2012 |

Am looking for minimum | Jul 12, 2004 |

**Physics Forums - The Fusion of Science and Community**