May I note that SOME swords WERE actually used AGAINST heavier armors.. The claymore for instance was developed just for that purpose, as was the 'German Longsword' or sword-and-a-half (bastard sword). These weapons were used up into the Rennaissance Period, when Heavy Armor reached it's (Gothic) highest point. The introduction of crossbows and firearms slightly diminished the need for these weapons, but they were still quite popular even in late medieval times.
The plate armor (especially breastplates and full Gothic plate) were worn well into the 17th century and became 'ceremonial wear' in certain countries like Germany and Britain, where certain special guard units (lancers on horseback mostly) still wear them today.
Even Napoleon's armies still had active lancers in them with breastplates: the Cuirrassiers a cheval.
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