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  "body": "\n## Summary\n\nThe circle average of a function is its mean value over a circle, taken with respect to normalized arc length.\nIt is the basic quantity in the mean value property of harmonic functions and in the sub-mean value property of subharmonic functions.\nMany results of planar potential theory, such as Jensen's formula, are identities between circle averages.\n\n## Explanations\n\n### L1 human\n\nWalk once around a circle at constant speed and record the value of a function along the way.\nThe circle average is the average of all the recorded values.\nFor $f(z) = \\abs{z}^2$ and the circle of radius $r$ around $0$, every recorded value is $r^2$, so the average is $r^2$.\nFor $f(z) = z$ and the same circle, the values point in all directions equally and cancel, so the average is $0$, the value at the centre.\n",
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