Traditionally, samurai used a variety of swords, but the most famous and widely recognized is the katana, which is characterized by its distinctive curved, slender, single-edged blade.

Before the katana, however, samurai used a sword called a "tachi," which was also curved but generally had a more pronounced curve and was typically longer. The tachi was worn hanging from the belt with the cutting edge facing down, contrasting with the katana which is worn with the cutting edge facing up.

Another type of Japanese sword is the "chokutō," which was one of the earliest swords used in Japan and has a straight, single-edged blade. This type of sword was used before the samurai class emerged and is not typically associated with the samurai.

So, while there have been straight swords in Japan's history, the curved katana is most strongly associated with the samurai class. The curvature of the katana was practical, serving both to facilitate the drawing of the sword and to improve its cutting ability.