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  "body": "\n## Summary\n\nThe regulator of an [[algebraic number field|MWBDFS2KJ5]] $K$ is a positive real number $R_K$ that measures the size of the unit group.\nBy [[Dirichlet's unit theorem|1D99CSKX6N]], the logarithms of the units form a lattice.\nUp to normalisation, $R_K$ is the volume of a fundamental domain of that lattice.\nIt appears with the [[class number|KTKK9B1X41]] in the [[class number formula|55XX5A7XZV]] for the residue of the [[Dedekind zeta function|KXS5DQDFYD]].\n\n## Explanations\n\n### L1 human\n\nThe units of a number field are generated by a few fundamental units, up to roots of unity.\nIf the fundamental units are large numbers, the regulator is large.\nFor a real quadratic field with fundamental unit $\\varepsilon \u003e 1$, the regulator is $\\log \\varepsilon$.\nFor $\\Q(\\sqrt{2})$ the fundamental unit is $1 + \\sqrt{2}$, so the regulator is $\\log(1 + \\sqrt{2}) \\approx 0.881$.\n",
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