encirclements

Encirclement is a military tactic in which a force attempts to surround an opponent, with the aim of denying retreat and cutting off access to supplies, reinforcements, and communications. The encircling force may employ a complete ring around the enemy position or execute a pincer movement that closes from multiple directions. Successful encirclements often force surrender or destruction of the enemy's core combat power; poorly coordinated attempts risk becoming exposed to flanking action or a breakout by the forces inside the ring.

Historically notable examples include the double envelopment at the Battle of Cannae (216 BCE) by Hannibal, which enveloped a larger Roman army; and the 1942–43 Soviet encirclement of Axis forces at Stalingrad, where the 6th Army was trapped and forced to surrender after Operation Uranus. Such operations demonstrate both the potential to destroy or collapse an opponent’s cohesion and the risks of overextension, supply problems, or relief efforts breaking the ring.

In modern warfare, encirclement remains possible but is hindered by mobility, air power, and long-range artillery, as well as the logistics challenges of maintaining a secure ring. It is more likely to appear in operational planning for irregular warfare or urban combat, where surrounding a defended position may be achieved incrementally. Legal and humanitarian considerations also figure into encirclement scenarios, including protections for civilians under international law.

Outside military contexts, encirclement can appear in mathematics and related fields. In complex analysis, a curve that winds around a point describes the encirclement or winding around that point, a concept central to contour integration and the winding number. The term is also used metaphorically in business or sports to describe an enclosing strategy, though it remains most common in military usage.