Lassak’s area bound for reduced planar convex bodies
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Lassak’s proposed bound is area(R)≤(π/4)Δ(R)² for every reduced planar convex body R of thickness Δ(R). A focused counterexample target has thickness one and area 0.7862156027…>π/4.
Why it matters and what counts as progress
Why it matters: It tests a sharp geometric bound relating area to minimum width within the reduced-body class.
What counts as progress: A reduced convex body exceeding the proposed thickness-normalized area bound, or a corrected sharp upper bound.
How the problem developed
AI contribution
A reduced planar body with area greater than πΔ²/4
An explicit reduced planar convex body of thickness 1, with support-function parameters m=15/16 and ε=13/20, has area 0.7862156027…>π/4. It refutes Lassak’s proposed bound area(R)≤(π/4)Δ(R)² for all reduced planar bodies.
Sources
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Publication dates and editorial changes.