Clockwise Contour Integral Symbol
∲ is the clockwise contour integral symbol, used in complex analysis to indicate a positively oriented loop.
U+2232
The symbol ∲ (U+2232) is known as the clockwice contour integral. It’s used in mathematical writing to specify the orientation of a contour. Use it when you want notation that emphasizes clockwise traversal.
Clockwise Contour Integral Symbol Meaning
∲, Unicode U+2232 (HTML entity ∲), is the “clockwise contour integral” symbol. In complex analysis, contour integrals are often written with an orientation (direction) to indicate how a closed curve is traversed. The clockwise direction is the focus of this symbol, distinguishing it from the common counterclockwise convention. When you see ∲ in equations, it typically signals that the integral is taken along a contour with clockwise orientation, affecting the sign and the interpretation of residue-related results. It is primarily a mathematical notation symbol used in textbooks, papers, and technical documents.
Common uses
- •Writing complex analysis notes where contour orientation matters
- •Labeling integrals in solutions that specify clockwise traversal
- •Typesetting equations in LaTeX/MathML or plain Unicode for academic work
- •Creating diagrams or captions for oriented contour integration steps
- •Improving clarity in technical blogs, tutorials, and documentation
Examples
∲ Clockwise Contour Integral Symbol
- ∲∲ f(z) dz around C
- ∲Compute ∲_C \\frac{f(z)}{z-z0} dz
- ∲Let I = ∲ g(z) dz for the clockwise path
- ∲Evaluate ∲_C h(z) dz using the residue theorem
- ∲The clockwise contour integral ∲ equals the oriented line integral
Variations
Ready to copy
Technical codes
| Unicode | U+2232 | |
| HTML Entity | ∲ | |
| HTML Code | ∲ | |
| CSS | \2232 | |
| Alt Code | Alt + 8754 | |
| Decimal | 8754 |
How to type Clockwise Contour Integral Symbol (∲)
On Windows
Hold Alt and type 8754 on the numeric keypad. In Word, type 2232 then press Alt + X.
On Mac
Switch to the Unicode Hex Input keyboard, then hold Option and type 2232. Or press Control + Command + Space and search.
On Linux
Press Control + Shift + U, type 2232, 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 the Clockwise Contour Integral symbol mean?
∲, Unicode U+2232 (HTML entity ∲), is the “clockwise contour integral” symbol. In complex analysis, contour integrals are often written with an orientation (direction) to indicate how a closed curve is traversed. The clockwise direction is the focus of this symbol, distinguishing it from the common counterclockwise convention. When you see ∲ in equations, it typically signals that the integral is taken along a contour with clockwise orientation, affecting the sign and the interpretation of residue-related results. It is primarily a mathematical notation symbol used in textbooks, papers, and technical documents.
What is the Unicode name of ∲?
The Unicode name is “CLOCKWISE CONTOUR INTEGRAL.”
What is the codepoint for the symbol ∲?
The Unicode codepoint is U+2232.
How can I copy ∲ for use in HTML?
You can use the HTML entity: ∲ or paste the character directly.
When should I use a clockwise contour integral symbol?
Use it when your notation specifically requires clockwise orientation of a contour in complex analysis, since orientation affects the integral’s interpretation.