I heard that if you flank them, they can’t turn, and then they all die.
Yep! Even a small force getting around to the flanks can completely ruin a much larger group of men in a phalanx. ~2500 men in the Battle of Cynoscphelae routed a distracted Macedonian phalanx of 16,000.
Later Medieval pike formations would mix in men with halberds and swords to prevent that very scenario.
I do late 16th century reenactment, including pike drill and demonstrations. We all have swords, but the only way to use them is for everyone to drop the 5 meter long pole and draw swords. And you really really don’t want to be armed with only a sword on a battlefield.
The alternative is either wheeling around (the turning circle of a unit of pikemen is horrendous), or raising the pike straight up and reforming into a square, and those aren’t exactly snap maneuvers.
And the guys pictured here have at least an extra meter of pike to deal with, and a shield too.
I’ll pass!
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