{"schema":"vela.problem-packet.v0.1","problem":353,"statement":"Let $A\\subseteq \\mathbb{R}^2$ be a measurable set with infinite measure. Must $A$ contain the vertices of an isosceles trapezoid of area $1$? What about an isosceles triangle, or a right-angled triangle, or a cyclic quadrilateral, or a polygon with congruent sides?","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}