free-symbols

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

UnicodeU+2232
HTML Entity∲
HTML Code∲
CSS\2232

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.

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