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My professor began discussing branch cuts in class today and mentioned that he did not know the origin of the term. Does anyone know the origin of the term and perhaps a source that talks about it?

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The use of "branch" in branch cut is the same as the use of the word "branch" in the sense of different branches of a function. A branch cut is a cut in the plane made to ensure that you can choose a single valued branch of the function at hand. So I would guess that the expression "branch of a function" came first, and that the expression "branch cut" was derived from it. –  Matt E Jun 9 '11 at 2:07
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