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  "body": "\n## Summary\n\nLandau's constants are three numbers that measure how large a disc the image of a normalised holomorphic function on the unit disc must contain.\nThey are the Bloch constant $B$, the Landau constant $L$ and the univalent Landau constant $A$, and they satisfy $B \\le L \\le A$.\nThey are positive by [[Bloch's theorem|KW31KDX7TB]], but their exact values are open problems.\n\n## Explanations\n\n### L1 human\n\nTake a holomorphic function $f$ on the unit disc with $f(0) = 0$ and $f'(0) = 1$.\nNear $0$ it looks like the identity, so its image should contain some disc.\nLandau's constant $L$ is the largest radius that works for every such $f$, the disc being anywhere in the image.\nThe Bloch constant $B$ asks in addition that the disc be covered exactly once, and $A$ restricts to injective $f$.\nFor the identity $f(z) = z$, the image is the unit disc itself, which contains discs of every radius below $1$.\n",
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