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Is it possible to cut the quadrilateral (0,0), (1,0), (0,1), (2,2) into an odd number of triangles of the same area?

Mikhail Borovoi
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Paulo Caetano
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    This question would be more suitable for Mathematics StackExchange – Mikhail Borovoi Aug 14 '23 at 14:38
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    Seems fine for MathOverflow, since the only answer we have so far quotes a recent research paper (and implies that one cannot give an elementary answer by exhibiting such a dissection, because such a dissection is impossible). – Noam D. Elkies Aug 14 '23 at 18:39

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According to a result by Kasimatis and Stein quoted in the paper Equidissections of kite-shaped quadrilaterals, the answer should be no. The convex hull of $((0,0),(0,1),(1,0),(a,a))$, $Q(a)$ in their notation, here with $a=2$, has $2$-adic valuation $\nu_2(a)=\nu_2(2)=1>-1$, which implies that only even equidissections are possible (see Theorem (i) in Section 2).

Pietro Majer
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