This One Goes to 13
Jim Tolpin’s article “Secrets of the Sector” in the June 2011 issue has stirred up a lot of interest and discussion among our readers. A sector is a way to eliminate arithmetic, especially division (multiplication’s tricky friend).
To help readers understand the sector, I made a couple short videos:
One of the questions readers are asking is: Why did Jim make his sector’s divisions go to 13? One reader offered this suggestion:
Dear Jim Tolpin,
I got my copy of the June 2011 issue in Tuesday’s mail. I read the article “Secrets of the Sector” with joy. It twigged a memory of long ago when I studied with an old carpintero near Santa Fe. He had something similar hanging on his tool rack, but didn’t show me what it was. Wednesday morning, I explored the Popular Woodworking web page and found the video on “Make a Sector From a Crappy Folding Rule.” I had one of those “crappy” modern rules sitting in the toolbox, and went into the shop and made my sector.
In the article, Jim states that it should have 13 divisions, but doesn’t indicate why. I almost ignored that directive and used 12, but made mine with 13. It intrigued me as to why. To my surprise, I wasn’t able to research much info off the web. Then it hit me!
I’ve been doing a lot of experimenting with using phi, or the Golden Section, in my turning; using it to refine relationships. I’ve no idea if this is Jim’s reason for using 13 divisions, but the ration of 13 to 8 is insanely close to phi; 1.625 ~ 1.618…! Certainly for most woodwork, it would be accurate enough.
I REALLY like the sector; it simplifies so much shop math and layout. Thank you for publishing the article!
The reason I went to 13 divisions is close to what Bear discovered: you can proportion to 8 to 13 which creates the most pleasing (according to actual research!) rectangle. (Regardless of whether that’s a “golden” rectangle or not – turns out that whole Golden Ratio thing is largely a Victorian-era fabrication!)
Also, you want to go to at least 12 so you can easily scale in thirds, fourths, sixths. There is rarely any need to go beyond 13 as all the proportioning you might want happens below 13!
— Jim Tolpin
Port Townsend School of Woodworking