While I mostly use the sector for doing design and layout work in my shop, I realized recently that it’s also a great tool for showing someone (especially your kids) an intuitive approach to understanding fractions. Here’s how I’d describe what’s going on in the drawing above:
Because I want to find out where a point four-sevenths of the width of a board would come to, I set the legs of the sector to touch each edge of the board to denominate (i.e. to name) the kind of divisions I’m looking for. Here, that would be seven – the denominator. Now I want to enumerate (i.e. give a number) to how many of those sevens I’m looking for – in this case the numerator is four. The job of the dividers is to grab this numerator above the denominator value on the legs of the sector in order to transfer the setting to the face of the board. For me (and my kid), this drawing offers a decent visualization of why the numerator goes over the denominator. You can learn more about the sector in excruciating detail in “By Hand and Eye;” and in a somewhat less excruciating matter in “By Hound and Eye.”
— Jim Tolpin, by handandeye.com