A generalized Gerver sofa for angled corridors
The moving sofa problem asks for the maximal area of a two-dimensional object capable of being moved through a right-angled corridor of unit width. J. L. Gerver constructed a sofa of area $2.2195\dots$, which was only recently proven to be optimal by J. Baek. Here, I consider the moving sofa problem in an angled corridor, $C_{\varphi}$, of unit width for turn angles $0 < \varphi \le \frac{\pi}{2}$. I first generalize Hammersley's arguments to devise simple analytical lower and upper area bounds for all $0 < \varphi \le \frac{\pi}{2}$. ChatGPT-6 Astra (Codex) is prompted to derive a…
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