This one might be a bit more difficult (or then again, maybe not ;-))
I was doing a bit of reading on some mathematics sites and ran into a reference to the attached picture. I looked it up and thought that it might be an interesting trivia question. There is some connection to woodworking as at least a form of it is used in the furniture industry. (probably not exactly as pictured)
It was patented in the early 1900's and there is still a company bearing the inventors name in existence today that makes them.
The questions are:
1) What is it called
2) What does it do?
Just as a reference, the shape in the lower part of the picture is the profile of the bottom part of the tool.
For extra credit, that profile is a modified version of the actual mathematical version. What is this version called and where else might you see it? (completely different application, although I am sure most have heard of it.)
There is a relationship to the rotor shape of the Wankel engine (but what is the shape called? ;-), but now, what does this particular tool do, and what is it called? Another hint: I found the reference to this tool while doing some reading about the math related to the shape of the rotor. There is also another hint in the above message. You only got one of them ;-)