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The sector was invented or at least first deployed by Thomas Hood or Galileo Galilei at the turn of the 17th century. Although capable of many functions, you can use the sector to find proportions -- thus its other name, the proportional compass.

The phenomenon of the sector is a dramatic paradox. The sector was created to eliminate the need for tedious arithmetic, but its use accelerated the mathematics of natural science. According to Wikipedia, the sector advanced science itself.

The sector was a very useful instrument at a time when artisans and military men were poorly educated in mathematics and, often, were unable to perform even elementary arithmetical operations. The inaccuracy induced by the analog scales of the sector were usually of no concern to those attempting to find a rapid solution to an approximate problem. It is striking, however, that the disciplines to which these instruments were applied, particularly perspective, music, architecture and fortification, traditionally classed as mechanical sciences, soon emerged as mathematical sciences in the seventeenth century. Indeed there is evidence that the universality of these practical applications helped to make possible the universality of science at a theoretical level. Hence this technology was not simply a consequence of advances in science. Rather, the technology helped make possible the mathematical sciences that led to modern science.

As you can see from the fancy version, the sector serves many functions. You might find yours useful if not for fortification and gunnery practice, but as a good way to explore proportional equations. If you make a sector with 13 sections, you'll be able to approximate the golden ratio (1.618:1). Or in my case, as an American in London, I can use it as a quick currency or temperature conversion tool.

http://cogtoys.wordpress.com/2014/08/12/sectors/

Step 1: Tools and Materials

I've made these with index cards and standard fasteners, but this version is made with coffee stirrers and 1/8 inch brads. Both aren't so common, but they are available and cheap.

One of the tools I am using is non-standard; it is the twist gimlet. I almost bought the twist gimlet for the name alone. I wonder if the gimlet drink was named for its potent and stabbing effect. They are very good -- the tool, that is -- for working with soft wood. You can probably find a twist gimlet in your local hardware store for less than five dollars. I bought this one at the local iron mongers for less than three pounds.
wow this is really interesting and useful! I never ear about it, they should show it in school. I'm going to make one. <br>
This is cool! I'd never heard of these before!<br> <br> Unfortunately the &quot;how to use&quot; picture was a little hard to read, but after a little googling about I found this great instructional video:<br> <a href="http://www.popularwoodworking.com/article/jim-tolpin%E2%80%99s-%E2%80%98secret-of-the-sector%E2%80%99" rel="nofollow">http://www.popularwoodworking.com/article/jim-tolpin%E2%80%99s-%E2%80%98secret-of-the-sector%E2%80%99</a><br>
PS118, thanks for the heads up about the &quot;how to use&quot; picture. I'l be working on that. Also, I loved the &quot;Popular Woodworking&quot; video. I tried, but failed, to find an on-line link to the accompanying article, &quot;The Science of the Sector.&quot; I will look further, though. <br> <br>I should give proper credit to the video, which recommends using thirteen sections.
This is interesting. I've learned about two new tools. I have never heard of the twist gimlet before. But I still don't quite understand how the sector is used. You lost me there at step 3.
I'm looking forward to seeing it. Small applications if trigonometry can move mountains.
This is very interesting, thanks for sharing. <br> <br>I discovered this week that to measure little angles is far better measure the distance between two ends of a drafting compass and apply a little trigonometry. I will post an instructable about that and a contraption I did in order to use that method.

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