The moving sofa problem: What rigid two-dimensional shape has the largest area $A$ that can be maneuvered through an L-shaped planar region with legs of unit width?

So far the best results are $2.219531669\lt A\lt 2.37$.

The moving sofa problem: What rigid two-dimensional shape has the largest area $A$ that can be maneuvered through an L-shaped planar region with legs of unit width?

So far the best results are $2.219531669\lt A\lt 2.37$.

The moving sofa problem: What rigid two-dimensional shape has the largest area $A$ that can be maneuvered through an L-shaped planar region with legs of unit width?

So far the best results are $2.219531669\lt A\lt 2.8284$ (approximately).

The moving sofa problem: What rigid two-dimensional shape has the largest area $A$ that can be maneuvered through an L-shaped planar region with legs of unit width?

So far the best results are $2.219531669\lt A\lt 2.37$.