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erdős #216

← #215 · #217 → (packet.json; erdosproblems.com)

Let $g (k)$ be the smallest integer (if any such exists) such that any $g (k)$ points in $R^{2}$ contains an empty convex $k$ -gon (i.e. with no point in the interior). Does $g (k)$ exist? If so, estimate $g (k)$ .

Worked, still open.

geometry · solved · 0 attempts

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oeis

A381776 — Empty polygon numbers: a(n) is the smallest number of points in the plane (with no three of them collinear) such that an empty convex n-gon cannot be avoided.3,5,10,30

links

#2 in Ramsey Theory · link

Create a formalisation here · link

status

solved

finding.noted · reviewer:will-blair · 1 day

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