Circles and angles, part 1

I had a couple thoughts about circles and using circles to approximate angles and using circles to reduce angles.
The first (covered here) is that when you are using a bench grinder to rough grind a tool to a particular angle, the larger the wheel, the closer you will get to the actual angle - with a 12 inch wheel the difference is quite small. My illustration exaggerates the differences by showing 3" thick tools. Even a Hock iron for a Stanley handplane is only 3/32 inch thick. There are two schools of thought. First, if you like the look of a true angle, the larger 12" wheel size (which is nearly synonymous with the Tormek system) is better. Second, if you are re-honing the tool fairly frequently to keep a sharp edge, you will have to do less work if you started with a smaller diameter wheel & will only have to regrind when you finally bottom out / completely flatten the concavity created by a 6 inch or 8 inch wheel. At least that is what we folk without a Tormek grinder keep telling ourselves! Hehehe.
If you are grinding to shape the edge and then using oil or water stones or "scary sharp" sandpaper sharpening or any other flat sharpening system out there, simply sharpening the tool edge and the heel really does make a lot more sense. It is nice to have a hollow in the middle. The hollow keeps the tool from rocking (which can cause rounding) and causes you to hone less surface area. It does look weird to some people, however.