Problem detail · source-aware
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Lassak conjectured that a reduced planar convex body of thickness $\Delta$ has area at most $(\pi/4)\Delta^2$, the value for the disc. False: an explicit reduced body of thickness $1$ has area $0.786215\ldots > \pi/4 = 0.785398\ldots$, given by a closed-form support function.
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Provider: OpenAI / Anthropic · Prompt public: unknown · Independence: unknown
The counterexample is given by an explicit support function with the area stated to six decimal places, so the refutation reduces to evaluating a closed-form integral. Single-author arXiv preprint, not peer-reviewed.
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