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  "body": "\n## Summary\n\nLet $f$ be a continuous map between closed connected oriented manifolds of the same dimension.\nIts degree is an integer that counts, with signs, how many times the source wraps around the target.\nFor maps from the $n$-sphere to itself it is defined by the action on the top homology group $H_n(S^n; \\Z) \\cong \\Z$.\nThe degree is a homotopy invariant, and for maps to a sphere it is a complete invariant by the [[Hopf degree theorem|902X7EHFSC]].\nIt underlies the proofs of the Brouwer fixed point theorem, the hairy ball theorem and the fundamental theorem of algebra.\n\n## Explanations\n\n### L1 human\n\nThink of a rubber band wrapped around a circular post.\nThe degree counts how many times it goes around, counting clockwise turns as negative.\nThe map $z \\mapsto z^3$ on the unit circle in $\\C$ wraps the circle three times around itself, so it has degree $3$.\nSliding the band around without cutting it never changes this count.\n",
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