encircling

Encircling is the act of surrounding something by forming a circle around it or moving around it in a circular path. The term applies to literal actions, as well as metaphorical or symbolic uses, and can describe both the motion of objects and the arrangement of people or objects around a center.

In military and strategic contexts, encirclement or encircling refers to surrounding an opponent to cut off access to reinforcements, supplies, and escape routes. The surrounding force aims to force surrender or destruction by denying any viable exit. Notable historical examples include the double envelopment at the Battle of Cannae in 216 BCE and the Soviet Operation Uranus in 1942, which encircled German forces at Stalingrad.

In geometry and computing, encircling denotes enclosing a set of points or a polygon with a circle or circular region. A common computational problem is finding the smallest circle that encloses a given set of points, known as the smallest enclosing circle or minimum enclosing circle problem. Encircling also describes constructing a circumscribed circle around a polygon, called the circumcircle.

Beyond physical and mathematical uses, encircling can function as a broader descriptive concept: surrounding or enclosing something through processes, strategies, or motifs that create a circular boundary. In diplomacy or geopolitics, encirclement can describe efforts to surround a nation with allies or allied forces to constrain its actions.

Overall, encircling encompasses both tangible ring-like surroundment and the transfer of the idea into strategic, geometric, or symbolic contexts.