Anticlockwise Contour Integral Symbol
∳ denotes an anticlockwise contour integral in mathematical notation.
U+2233
The symbol ∳ represents an anticlockwise contour integral. It’s commonly used alongside the clockwise contour integral to specify the integration direction around a curve. Use the provided codes to copy it into documents, LaTeX-like workflows, or code editors.
Anticlockwise Contour Integral Symbol Meaning
∳ (U+2233) is the “ANTICLOCKWISE CONTOUR INTEGRAL” symbol. In complex analysis and related mathematical writing, contour integrals describe integration of a function along a curve in the complex plane. The “anticlockwise” direction indicates the orientation of the path, which affects the sign of the integral. When comparing with the clockwise contour integral, many texts use one symbol for the standard (anticlockwise) positive orientation and the other for the reverse. You’ll often see it in contexts such as evaluating integrals using residues, applying the Cauchy integral theorem, or specifying path orientation in explanations and worked solutions.
Common uses
- •Writing contour integrals in complex analysis with an explicitly anticlockwise orientation
- •Labeling equations in notes or textbooks where path direction matters for the sign
- •Formatting solutions in homework, worksheets, or online math comments
- •Specifying orientation in technical documentation for complex-variable calculations
- •Including consistent notation in academic slides and diagram callouts
Examples
∳ Anticlockwise Contour Integral (U+2233)
- ∳∳_C f(z) dz
- ∳Let I = ∳_\\Gamma \\frac{f(z)}{z-a} dz.
- ∳Evaluate ∳_C g(z) dz using residues.
- ∳For the anticlockwise path, compute ∳_{\\gamma} h(z) dz.
- ∳We take the contour as ∳_\\Gamma to match the orientation.
Variations
Ready to copy
Technical codes
| Unicode | U+2233 | |
| HTML Entity | ∳ | |
| HTML Code | ∳ | |
| CSS | \2233 | |
| Alt Code | Alt + 8755 | |
| Decimal | 8755 |
How to type Anticlockwise Contour Integral Symbol (∳)
On Windows
Hold Alt and type 8755 on the numeric keypad. In Word, type 2233 then press Alt + X.
On Mac
Switch to the Unicode Hex Input keyboard, then hold Option and type 2233. Or press Control + Command + Space and search.
On Linux
Press Control + Shift + U, type 2233, then press Enter or Space.
Anywhere
Copy ∳ with the button above and paste it wherever you need it — this works on every device and in every app, with no keyboard shortcut to remember.
FAQ
What does ∳ mean?
∳ is the “Anticlockwise Contour Integral” symbol, used to denote an integral over a contour with anticlockwise orientation.
What is the Unicode and HTML for ∳?
Unicode code point is U+2233. HTML entity is ∳.
How do I type or paste ∳ in different contexts?
You can paste the character directly. For code or text rendering, use the provided escapes: CSS \\2233 or JavaScript \\u{2233}.
Is the direction important for contour integrals?
Yes. Changing the contour orientation can change the sign of the integral, which is why anticlockwise vs clockwise symbols are used.