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  "body": "\n## Summary\n\nThe Chebyshev constant of a compact set $K$ in the plane measures how small a monic polynomial can be on $K$.\nFor each degree $n$ one takes the least maximum of $\\abs{p}$ on $K$ over [[monic polynomials|0C3QBCR46M]] $p$ of degree $n$.\nThen one takes its $n$-th root and lets $n$ tend to infinity.\nThe extremal polynomials generalize the classical [[Chebyshev polynomials|M6EAR1JHPP]] of an interval.\nA theorem of Fekete and Szegő says that the Chebyshev constant equals the [[logarithmic capacity|DBQXRTC0VN]] of $K$.\n\n## Explanations\n\n### L1 human\n\nA monic polynomial of degree $n$ has leading coefficient $1$, so it cannot be small everywhere: far from the origin it is about $\\abs{z}^n$.\nThe question is how small it can stay on a given set $K$.\nOn the unit circle the best choice is $z^n$, with maximum $1$, so the Chebyshev constant is $1$.\nOn the interval $[-1, 1]$ the best choice is the Chebyshev polynomial divided by $2^{n-1}$, with maximum $2^{1-n}$, so the Chebyshev constant is $1/2$.\nA small set lets monic polynomials stay small, and so has a small Chebyshev constant.\n",
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