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  "body": "\n## Summary\n\nA branch point of a [[multivalued function|03CPD1HGF3]] is a point with this property: going once around it along a small loop changes the value.\nSee the [[definition|XDNRXKH3KT]].\nThe square root has branch points at $0$ and $\\infty$, and so does the [[complex logarithm|02QGGD5G87]].\nBranch points are the reason for [[branch cuts|0W8QHVSN95]].\nWhen the function is made single-valued on a [[Riemann surface|5K0N8QMV6Q]], they become the ramification points of a [[branched covering|YARENZRXTD]].\n\n## Explanations\n\n### L1 human\n\nFollow $\\sqrt{z}$ continuously while $z$ walks once around the circle $\\abs{z} = 1$, starting at $z = 1$ with $\\sqrt{1} = 1$.\nWhen $z = e^{it}$ goes from $t = 0$ to $t = 2\\pi$, the chosen root $e^{it/2}$ goes from $1$ to $-1$.\nSo you come back to the same $z$ with a different value of the root.\nThe point $0$ that you walked around is a branch point.\nFor $1/z$ nothing like this happens, because $1/z$ has only one value at each point.\n",
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