Moser's Worm Problem [Unsolved]

What's the smallest convex shape that can cover every unit-length curve?

A disk of diameter 1 covers every such curve but with area π/4≈0.7854 it's not the smallest shape

In fact we know that the minimal area is between 0.232239 and 0.270911861

— Tamás Görbe (@TamasGorbe) August 31, 2019

Panraksa and Wichiramala describe the problem in their introduction:https://t.co/t1MiFcBOvm

"L. Moser asked for the smallest set in the plane that is large enough to accommodate a congruent copy of each arc of unit length."

— La_Maudite 🐧 (@La_Maudite) August 31, 2019

One property of the lemniscate of Bernoulli is that a ball rolling down an arc of the lemniscate under the influence of gravity, will take the same time to traverse it as a ball rolling down a straight line segment connecting the endpoints of the arc https://t.co/hbcXKfC06Z pic.twitter.com/yyI1j3XGre

— Massimo (@Rainmaker1973) August 29, 2019

Nice puzzle ! Proof ? https://t.co/ZIAj6iXV0S

— Vincent Pantal🍩ni (@panlepan) August 24, 2019

Cubic Bézier Curve#mtbos #iteachmath #math #maths pic.twitter.com/oZ6FCxm2ZN

— Idan Tal (@MagicPi2) August 23, 2019