KnifeMasters The Convex Edge
Proverbs 27:17   "As iron sharpens iron, so one man sharpens another."
The Convex Edge

The Convex edge on a knife is an edge that is curved or sharpened with an arc.  Instead of a fixed, flat bevel throughout, the convex edge angle gradually changes across the entire bevel.  For years, experienced knifemen have known that a "smaller bevel angle" would cut better, but is more fragile; while a "larger bevel angle" will last longer, but won't slice as finely. The convex edge does away with this problem and creates the best of both worlds.  The convex edge will hold the longest edge and produce the finest cutting.
Knife makers have been putting convex edges on knives for hundreds, even thousands of years. Only since the invention of machine-made knives, has the convex edge dropped in popularity.  In recent years this art of knife sharpening has quickly risen to the top as the technique of choice.

Some people like a highly polished convex edge while others prefer an edge that is a little toothy.  Any convex edge can be made to have either of these characteristics. The more polished the edge, the better it push-cuts. A push cut is where you push the knife through the material without a "back-or-forth" action, like you would chop celery. The more toothy the edge, the better it draw cuts. A draw cut is a slicing or back and forth action, like how you would slice bread or a tomato.
The convex edge can be kept razor sharp just by stropping it on a leather strop after any serious use.  The beauty of the convex edge is in the ease of achieving and maintaining a durable, and razor sharp edge.  

There are many different types of convex edges.  If it has a curved bevel, it is considered convex. However, that is where the similarities end. It is up to the knife maker to make a knife that is designed for the intended use.  In today’s age, we encounter many uses and specialized tasks for our knives.  In light of that, most individuals will have many different knives. Would just one knife do everything demanded in the kitchen? Work as a slicer, cleaver, dicer and a parer? Likely not. "Use the tool most appropriate to the task." That alone accounts for the many different designs, shapes, sizes and grinds you can find in knives today. 
"World's Best Sharpening System"