Greek Why does the sword have a leaf-shaped blade?

Answer 1

This is pure speculation but here goes:

A curved edge has superior cutting power over a straight edge when slashing. That's why the samurai sword cuts so well. However the samurai sword sacrifices a whole edge, some handling (due to it being asymmetrical) and some stabbing ability to achieve this. Leaf shaped blades offer a curved edge on both sides, while still offering symmetry along the long axis, which should improve handling and speed, and a good stabbing tip, aligned with the handle and the long axis.

Also, Greek Metallurgy was not as advanced as in the Medieval period. It's possible the broader blade shape was less prone to breaking in the field.