/sci/ - Science & Math

>>11510004
>>11510048
I've figured out a way to rephrase the problem that might or might not be convenient.
Assume anon's conjecture is true for [math]n=3[/math] (specifically, that there is at least one way of arranging [math]A, B, C[/math] such that the triple intersection maximizes area and any of the individual intersections also maximizes area).
Assume that we've placed [math]A[/math] and [math]B[/math] somewhere on the plane, and call [math]A \cap B = C[/math]. Then, the area of the triple intersection (under motions and rotations) is at least [math]C[/math], which implies that [math]C [/math] admits some embedding in [math]D[/math], where [math]D[/math] is some solution of the problem of maximizing the area of [math]A \cap B[/math], by anon's conjecture.
Conversely, if any intersection of [math]A[/math] and [math]B[/math] arranged somewhere in the plane can be contained in some intersection which maximizes area, we obtain anon's conjecture back.

I might have made some mistake somewhere, tho.