Battles were usually in cavalry form. Nihonto were made to level enemies to the ground from the back of the horses. Nihonto were long and greatly curved at "Koshizori", the very bottom of the cutting part.
[What's going on outside Japan] It's around the time Charlemagne was crowned Emperor for Holy Roman Empire. Then European feudalism started evolving.
Towards the middle of Kamakura era, Nihonto was needed to be strong enough to cut through "Yoroi", the sturdy armors. The level of curve and the difference of width of body and the tip increased. The focal point of curve moved to the middle of Nihonto for better stability.
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The form of Nihonto kept evolving accordingly to the change in battle form: Nihonto became wider and longer, and the focal point of curve was set in the middle of Nihonto.
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In this chaotic era, the battle form changed from cavalry to foot soldiers. A big, long Nihonto were not suitable for the purpose, and the "Uchigatana", the secondary Nihonto instead of "Tachi" became the main arms for foot soldiers. "Uchigatana" is a little less than a yard long with a curve at the tip, which was effective for close battle. "Nihonto" were held with one hand (right hand) at the beginning of this era, but later holding them with both hands came into the battle scene and "Nihonto" changed its form again to wider ones, especially at the tip of them.
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This era was relatively stable one with fewer battles. Samurais learn "Kenjutsu (way of samurai)" as an intellectual and cultural necessity rather than preparation for the battle. "Nihonto" requires less practicality and became either simpler (just as a practice wooden Nihonto) or beautifully accessorized ones.
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