i'm not sure that we have an engineer that specializes in this type measurement on this forum. the sharpest apex can be measured; remember that we now have machines that can weigh a pencil mark.123456 i believe there is certainly an answer to your question but you will probably need to consult the editors of Scientific American or MIT university, another source is Cal Polytech. now my question is how this info can possibly aid your understanding of knife performance? if it's strictly academic get your self to the engineering xperts. i ca'nt possibly see how this will aid in making knives or even using them. did you count the angels yet?--cranky72