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Questions on the calculus of variations, which deals with the optimization of functionals mostly defined on infinite dimensional spaces.

11 votes
0 answers
424 views

Maximizing the volume in a family of subsets of a cube

Starting from a question in probability, I arrived to the following optimization problem. Let $I:=[0, 1],$ and let $A$ be a Lebesgue measurable subset of the $n$-dimensional cube, $A\subset I^n.$ Co …
Pietro Majer's user avatar
  • 60.5k
10 votes
5 answers
1k views

Convex curves with many inscribed triangles maximizing perimeter

A classical nice result of Euclidean geometry states that the triangles maximizing the perimeter among all inscribed triangles of a given ellipse constitue a one-parameter family. Precisely, for each …
Pietro Majer's user avatar
  • 60.5k
8 votes
1 answer
726 views

Sticks and thread

In this recent question Math puzzles for dinner we had a nice time as we were asked to provide new maths puzzles for dinners. I suggested the following: Given three equal sticks, and some thread …
Pietro Majer's user avatar
  • 60.5k