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Results tagged with calculus-of-variations
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user 6101
Questions on the calculus of variations, which deals with the optimization of functionals mostly defined on infinite dimensional spaces.
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 …
- 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 …
- 60.5k
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 …
- 60.5k