geometry-topology / Convex geometry
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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Append-only history
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.
Research memory
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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