Now what is it all used for? I use it all the time, constantly, almost minute by minute.

I'm a contractor carpenter and here are some examples:

I have to cut a 8' long 2 x 4 into thirds

I have to cut a 4 x 8 sheet of plywood into 8 pieces

I have to make a round table top, made up of pie shaped wedges

I have to find the exact centre of a circle in order to cut in a smaller circle

Here's a perfect example:

I have to build a cabinet exactly 23 7/8" wide to fit between two columns and 32" high

I have to make doors for that cabinet. The doors are made up of 2 rails (sideways pieces) and 2 stiles (vertical pieces). I have to make a filler panel to fit inside those rails and stiles. The rails and stiles are 1 3/4" wide each. I need a 1/8" gap around the cabinet where the doors overlap.

So, the formula is: 23 7/8" - 1/4" (gap 2 x 1/8") = X (aka door overall size)

Stile size b = 23 7/8" - 1/4" gap - (2 x 1 3/4")

Rail size c = 32" - 1/4" gap - (2 x 1 3/4")

Now I'm not even going to START with the size of the raw material that has to be machined down to 1 3/4". I did a kitchen for a customer who didn't like big gaps between the doors, drawers etc so I had to make the gap 3/16" wide, divided by 2 doors therefore each door had to be 3/32" narrower per side, except for the one on the end that didn't butt up against another cabinet....

Oh, almost forgot the filler panel:

Filler panel width d= 23 7/8" - 1/4" gap - (2 x 1 3/4") + (1/4" x 2) for the amount it sits inside the stiles

Filler panel height e = 32" - 1/4" gap - (2 x 1 3/4") + (1/4" x 2) for the amount it sits inside the rails