Thursday, April 23, 2009
Does the circle minimise every measure?
Does the circle minimise every measure?
What shape minimises the perimeter for a given area. The Circle.
I was trying to work out what shape a birds territory should be given various
conditions for defending it against its neighbours. Average distance from a random point
inside to a random point on the perimeter. The maximum distance from a random point
to a random point of attack. etc etc.
I reckon all the answers are a circle. And probably the same is true for higher dimensional
objects as well.
what would the theorem look like, and what is its proof?
I leave as a short exercise for the student
cheers
martinw
