TeXipedia

circlearrowright

Represents a clockwise circular arrow, commonly used to denote cyclic processes, rotations, or circular operations in mathematics and physics.

Overview

Essential in various mathematical and scientific contexts where circular or cyclic motion needs to be depicted.

  • Frequently used in group theory to represent cyclic groups or permutations
  • Common in thermodynamics for depicting cyclic processes or cycles
  • Appears in differential geometry when describing rotations or orientation
  • Used in diagram theory to show circular compositions or loops
  • Valuable in physics for illustrating angular momentum or circular motion concepts

Examples

Representing a cyclic group operation in abstract algebra.

G={g∈Z∣g↻n}G = \{g \in \mathbb{Z} \mid g \circlearrowright n\} 
G = \{g \in \mathbb{Z} \mid g \circlearrowright n\}

Indicating clockwise rotation in a physical system.

ω↻=2πf\omega \circlearrowright = 2\pi f 
\omega \circlearrowright = 2\pi f

Denoting a closed path integral in complex analysis.

∮Cf(z) dz=2πi↻\oint_{C} f(z)\,dz = 2\pi i \circlearrowright 
\oint_{C} f(z)\,dz = 2\pi i \circlearrowright