Saint-Venant's conjecture for pentagons

About 5 years old · traced to

Let Ω\Omega range over planar pentagons with a fixed area, and let T(Ω)T(\Omega) denote their Torsional rigidity. Saint-Venant's conjecture. Among all pentagons of given area, the regular pentagon achieves the maximal Torsional rigidity. This is presented as a famous conjecture about the shape optimizing torsional rigidity; the supplied text does not state whether it has been resolved.

References

Primary source

F. Calabrò, S. Cuomo, F. Giampaolo, S. Izzo, C. Nitsch, F. Piccialli and C. Trombetti, “Deep Learning for the Approximation of a Shape Functional”, arXiv:2110.02112 (2021).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.