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Let be a measurable set with infinite measure. Must contain the vertices of an isosceles trapezoid of area ? What about an isosceles triangle, or a right-angled triangle, or a cyclic quadrilateral, or a convex polygon with congruent sides?
Source: erdosproblems.com/353
An accepted solution exists. Settled in another form, for example when its parts resolve differently or the question is open-ended.
PROVED (LEAN): the site labels the problem proved with a Lean qualification, crediting Koizumi with the trapezoid question and the two triangle variants, recorded on the Koizumi claim page (2025); the cyclic quadrilateral (yes) and the polygon with congruent sides (no) are on the Kovač–Predojević claim page (2024). The statement asks five questions, listed as the problem's parts; four are answered yes and the convex polygon with congruent sides no. Because the parts differ in polarity, the standing derived from the two partial claims records an answer rather than the proof the label names. The Lean proof the label refers to is a third-party development, linked from both pages and under Formalization, which this corpus has not built.