Geometry is an important part of a lot of woodworking. Most of the time, the work is based on straight lines and a fixed set of angles (90, 45, 22.5 ...) but still a compass can be useful to lay things out. And even more useful is a set of dividers as shown here. Dividers differ from compasses in that they don't "draw" anything. There is no pencil or pen on the end of them, just two sharp points. When people used to draw things by hand dividers were used to transfer measurements and they take their name from dividing a line into parts. One sets the width of the divider to an approximate size and then "walks" the divider down the line. A little fine adjustment is then done to make sure that the last step ends up at the end of the line and then you can use the points to mark the divisions.
In wood working such a tool is also handy to transfer measurements with much higher accuracy than reading a tape measure. Because of the sharp points you can measure and mark at the same time.
I use a set of dividers from a drafting set because in my experience these are of much higher quality and precision than those commonly sold for carpenters and the like. And, fortunately thanks to the rise of CAD and the death of manual drafting there are tons of old drafting sets out there on ebay for very resonable prices. If you are only after the divider a set with missing pieces is probably the best buy. Just look carefully at the pictures to see if it has a set of dividers (typically there are a pair or a small and large one).
Given better quality, higher precision and cheap price, cannablizing an old drafting set is a good way to improve your toolbox.
