TeXipedia

eqcirc

Denotes a circle relation symbol indicating equality by definition or geometric congruence between mathematical expressions.

Overview

Primarily used in mathematical notation where a specific type of equivalence or geometric relationship needs to be shown using circular symbolism. Common applications include:

  • Geometric proofs and constructions to show congruent circles
  • Set theory when defining circle-based relations
  • Mathematical logic where standard equality symbols need variation
  • Topology and abstract algebra for specific circular equivalence relations

Examples

Showing that two angles are equal in circle geometry.

∠ABC≖∠DEF\angle ABC \eqcirc \angle DEF 
\angle ABC \eqcirc \angle DEF

Indicating equal arcs in a circle.

AB^≖CD^\widehat{AB} \eqcirc \widehat{CD} 
\widehat{AB} \eqcirc \widehat{CD}

Denoting congruent circles in geometric proofs.

◯P≖◯Q\bigcirc P \eqcirc \bigcirc Q 
\bigcirc P \eqcirc \bigcirc Q