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How did Hannibal use a double envelopment at the Battle of Cannae?

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Illustration of Hannibal the Carthaginian general wearing a metal helmet and armor, holding a shield decorated with a horse. — Hannibal Hannibal, engraving by John Chapman, 1800.

At the Battle of Cannae, Hannibal executed a double envelopment by utilizing the elasticity of his formation to trap the numerically superior Roman army.

Hannibal initially arranged his infantry in a crescent shape, with his Gallic and Spanish troops in the center and his elite African infantry on the flanks. As the Romans massed their infantry in a deep, narrow formation to push through the center, Hannibal’s center gradually retreated without breaking, drawing the Roman forces into a trap.

As the Roman center advanced, the crescent shape inverted, allowing the African troops on the flanks to press inward. Simultaneously, the Carthaginian cavalry, having defeated the Roman wings, swept around to attack the Roman rear. This maneuver completely surrounded the Roman legions, rendering them unable to maneuver or effectively use their weapons, leading to their near-total destruction.1