Interesting questions. Japanese sword steel (which may have incorporated technology from the Middle East and/or India) is basically a composite material which is layered from hard iron & soft steel. The hardness comes from the hard iron, while the soft steel supports the hard iron to keep it from breaking. Think of plywood, except with alternate layers of hard iron & soft steel. I don't know the ideal shape for a cutting implement, and this ideal shape may vary depending upon what material it has to cut through, but I would imagine that Japanese swords are probably pretty close to the ideal shape for their intended purpose, since non-ideal sword owners tended not to live very long! In order to cut a tomato, which has a relatively tough skin covering a very delicate almost-liquid inner portion, the blade has to quickly pierce the skin without bruising the tomato. After the blade pierces the skin, the sides of the blade can't adhere to the skin, which may require some sort of wax or teflon on the side of the blade. At 08:13 AM 2/3/2013, Simon Plouffe wrote:
We know that there are those japanese sabre that are very good but they are made of many 'plys' of steel like 32768 since they fold the blade 15 times to produce a particular shape which is optimal in this case. Is there a definite geometric argument for this ?