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∳

anticlockwise contour integral

Anticlockwise Contour Integral

∳ marks an integral taken around a closed contour, directed anticlockwise. In complex analysis, reversing the same path changes the integral’s sign. The mathematical operation predates this specialized mark.

Text symbol
Search it as
aoint · contour integral · closed contour integral · anticlockwise integral · counterclockwise integral
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Anything that takes text · its shape is whatever your font draws

What ∳ means

The circle closes the contour; the arrow points anticlockwise. A contour is the integration path; a closed one returns to its start.

Cauchy’s contour-integral work developed in the 19th century. Wilson used circle-marked closed-path notation in 1901; an early circle-in-integral example by Sommerfeld followed in 1917.

Don't confuse it with

1

Questions people ask

1

Can right-to-left text flip the arrow?

No. Unicode’s bidirectional layout rules keep the clockwise and anticlockwise marks pointing as encoded.

How to type ∳

Windows (Word)
Alt+XType 2233, then Alt+X to get ∳.
Windows
Win+Rrun charmap for the full table, or use the emoji picker's Ω symbols tab (Win + .).
macOS
Control+Command+SpaceOpen the character viewer and search “anticlockwise contour integral”.
Linux
Ctrl+Shift+UType 2233, then Enter or Space.
HTML
∳
CSS
\2233
Word
In Word’s linear UnicodeMath equation input, type `\aoint`.
LaTeX
Use `\ointctrclockwise` with a package that defines directional contour integrals.
Codes and encoding1 code points
HTML decimal
∳
HTML hex
∳
CSS content
content: "\2233";
Each escape is closed by the next backslash; a trailing space is needed before a literal hex digit.
URL encoded
%E2%88%B3
1
On screen
1
Code points
1
JS .length
3
UTF-8 bytes

A visible symbol can contain several code points. JS .length counts UTF-16 units; UTF-8 counts bytes.

Families this belongs to

1

Maths & numbers1,835 symbols