TL;DR
This paper solves the moving sofa problem by proving Gerver's construction with 18 curves achieves the maximum possible sofa area of approximately 2.2195.
Contribution
It provides a rigorous proof that Gerver's sofa construction is optimal, settling a long-standing geometric optimization problem.
Findings
Gerver's sofa construction is proven to be optimal.
Maximum sofa area is approximately 2.2195.
The proof confirms the conjectured optimal shape.
Abstract
We resolve the moving sofa problem by showing that Gerver's construction with 18 curve sections attains the maximum area .
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Taxonomy
TopicsMathematics and Applications · Point processes and geometric inequalities · Geometric and Algebraic Topology