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In the June 2011 issue we have Jim Tolpin building the “Ultimate Router Table.”

He’s actually building a wombat house.

Ha. Got you.

In truth, Tolpin wrote a great article about how to build and use a “sector.” What’s a sector? It is like magic wands that have been hinged together. With just two sticks and a little hinge, you can use a sector to solve many workshop math problems that would involve nutty fractions, a calculator, or…. horrors…. the metric system.

I prepared a short video about the simple sector I built for our shop. This little video shows only two of the many tricks a sector can do. Look for the complete article in the June 2011 issue of Popular Woodworking Magazine.

— Christopher Schwarz

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• edf

I was trained in advanced math. One of the mathematicians that taught us (Walter Noll) said over and over again, “Mathematics is the art of avoiding unnecessary calculation.” Seems, that’s what this tool does. And, it replaces measuring with transferring, which is more accurate, no?

• Steve Branam

Cool! As others have pointed out, this is math, just not arithmetic. It’s applying the law of similar triangles from geometry. It’s like the method of angling a ruler between two parallel lines to locate evenly spaced divisions. And the nice thing is, it reduces the human error in transferring numerical values.

Although you did need some arithmetic to divide 12 into 6 even sections…

The 13 divisions simply appear to be some convenient short length stepped off repeatedly down the length of the sector. It could have been 10 and worked just as well, though the more divisions the more known points where you can take off the width.

• lawrence

Great video–

EXCELLENT article (I’ve read it twice now and am sure to read it a third time tomorrow) I’ll be making some of these soon or buying the new “rockler sector sticks” as soon as they become available (sure to be in the next couple of months)

Seriously though,
The quality of material/writing in PopWW’ing is so very good (these last couple of issues especially) and I just wanted to throw out a thanks to those of you out there that are working so hard to keep your customers pleased. You’ve certainly earned your paychecks once again.
Lawrence

• Mitch Wilson

Sorry, people. Your terminology is all wrong. You are not eliminating “Math” (like calculus, differential equations or string theory). You’re avoiding simple, basic, second or third grade arithmetic. That’s pretty sad. This is just another form of illiteracy that permeates our society. You cannot play banjo (nor dobro or mandolin) without arithmetic. (Bach, Beethoven, Mozart and Me-P. Ochs)

• JWatriss

This reminds me of a book on technical drafting that I was reading the other day, circa late 1800s, before photo-stat blueprints. They had a lot of interesting mechanical methods for dividing spaces, laying things out, or laying out a scale to set dividers to measurements that were accurate to hundredths of an inch.

So much to rediscover. Very exciting.

• Steve_OH

I don’t know–I’ve never been able to understand why there is so much aversion to math. Watching the video, I couldn’t help thinking that a pencil and a piece of scratch paper are just so much quicker and easier to use than yard-long nunchaku.

-Steve

• John J

Such simple elegance.
So if I understand what’s going on here, you might want to somehow highlight #1, #2, #3, #5, #8 and #13. This way you could effortlessly use the sector to develop proportions based on a Fibonacci series. The 8 to 13 ratio (1.625) is very close to Phi the golden section proportion of 1.618.
This device has some promising possibilities worth exploring.

• Fred West

I really like this as well but have a question. You wrote that you divided the two sticks into 13 equal portions. How do you determine the length of each equal portion? Another thumbs up for the banjo music. 😮 If my Dad was not playing his guitar he was playing his banjo so I grew up loving it. Fred

• Dean

Looks like an analog computer.

• Graham Hughes

I’ve been meaning to make one of these for years, although I had in mind one more the size and form factor of a four-fold rule. Does anybody sell the hinges for those things?

• rmcnabb

I’m slightly speechless. Apparently, if I were better educated I wouldn’t be as impressed as I am. But this is a tremendous device. Sheesh – I can’t get any work done for building all the great tools you write about, Chris!

• B Jackson

It is math, but of a different and more direct kind, like geometry. I like it. It saves my punching numbers into a calculator and using algebraic maneuvers to determine where I need to set the center line, as an example. I wished I learned that way back in high school, but you know how it is, if you’re “college prep”, you’re expected to solve things by coming in sideways through the back door.

• cgooding

Where’s the banjo music??? Did you guys finally run out??

• thompmj

I have to agree with Ryan on this one…I don’t think that the math is eliminated at all. In fact, it would seem to me that this is actually a non-electronic fractional calculator, which prevents the user from having to do the math.

Which, of course, means I LOVE it. Thanks for the tip!

PS – I miss the banjo for this one…would have seemed more apropos.