The moving sofa constant is conjectured to be 2.2195..., which is computable as the implicit solution of a set of equations (see Eqs. 1-4 in Romik 2018). On the other hand, while not immediately obvious, the fact that the moving sofa constant is computable is reasonably intuitive, and in fact, Dan Romik and I proved that it is.
Yoav Kallus
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