What ∮ means
It means integrate along a closed path.
That path is the contour: a line integral that comes back to its start, even if it has corners. A subscript such as C names the route. In complex analysis, contour integrals appear in Cauchy's theorem and residue calculations.
Who invented the contour integral symbol?
The mark emerged through several conventions.
The history of closed contour integral notation starts with the method, not this mark. Cauchy's 1846 work used the ordinary integral sign for integration over a closed curve. E. B. Wilson placed a small circle below the integral in works from 1901, 1909, 1911, and 1912. Arnold Sommerfeld used the familiar circle-through-integral form in 1917. These examples show gradual adoption rather than one uncontested invention.
How do I type ∮ in LaTeX?
Use \oint in LaTeX math mode.
This typesetting command produces the operator in a mathematical expression; it is not a keyboard shortcut for entering the Unicode character in ordinary text.
Formal mathematical notation; it signals a closed-path integral, often in calculus or complex analysis.
The contour closes; it does not have to be circular.
Don't confuse it with
3Combination ideas
3Questions people ask
1Does reversing a contour change the integral?
Yes. Reversing the direction changes the sign of the integral, even though the closed route is the same.
How to type ∮
∮\222ECodes and encoding1 code points
A visible symbol can contain several code points. JS .length counts UTF-16 units; UTF-8 counts bytes.