The Sector: the calculator of the 1500s

An antique ivory sector, from the late 1800s. Also called the proportional compass, or the military compass. Invented very slowly over about 2000 years, ending up in 1500s Europe.
This is episode 83 of my video series about old calculating methods.
Printable sector: www.thingivers...
Printable dividers: www.thingivers...
Iranian Astrolabe photo by Wikimedia user Masoud Safarniya CC-BY-SA-3.0
en.wikipedia.o...
Galileo sector photo by Wikimedia user Ragesoss CC-BY-SA-3.0
en.wikipedia.o...
End song inspired by "Hotter than a Molotov" by The Coup. • The Coup: Hotter Than ...
Chris Staecker webarea: faculty.fairfi...
#clampin

[@AngrocSound]

"Before he was buildin' scopes n vexin' popes, he was clampin'!" What a line! Great episode as always!!

[@tomnewsom9124]

"Buildin' scopes and vexin' popes" As the kids say, MC Staecker your bars are fire.

[@jogloran]

I love that the design by “Mordente” indeed has more teeth.

[@lafcursiax]

And of course, Mordente itself means "biting." (And ivory is made of teeth!) CHOMP CHOMP

[@michaelmuffin]

The standard carpenter's trick for dividing a line into seven equal segments is to strike a perpendicular line at the end of the original line, then form a hypotenuse with your ruler such that the 7" mark intersects the perpendicular line and the 0" mark meets the end of the line being divided, then use a square to project whatever measurements you want from the ruler onto the original line. Compared to using a sector and dividers, this method has the advantage of being both fast and not accumulating errors, but has the disadvantage of sometimes requiring three hands.

[@someonespadre]

Drafting is the same, easy to divide by equal parts on paper with a ruler or scale.

[@brodiepellerin4806]

I can't believe I am only coming across this channel now! Gonna be binging

[@JustSomePasserby]

I had heard that Galilean Sectors often had a mark showing the height of a person at a fixed distance and were used on the battlefield as rangefinders. I never really understood how that worked. But seeing you use the compass to do proportions made it click for me. Thanks.

[@biquinary]

I'm really happy you've started making more videos again!!!

[@andrewkrahn2629]

@ChrisStaecker The hinged ruler was pretty common in woodworking. If you want their origin, I'd look into "story sticks" and "pinch rods". A story stick was a physical representation of the measurements needed to make a project. The whole length would be the length of the back post of a chair, for example, and there would be cutouts the correct length for the front legs and different rungs. Pinch rods of different sizes were used similarly. They were a pair of sticks designed to slide parallel to eachother and lock in place, sometimes with little tabs on the ends. They were useful for making a semi-permanent record of a specific distance. If, for example, you're making a cabinet to fit in a cutout in a client's wall but need to with in your shop, you just put the sticks in the cutout and expand them as far as they'll go. Physical records you can touch are generally more accurate than written numbers, at least when you need to use them over and over.

[@ChrisStaecker]

Yes I've heard of story sticks, but not pinch rods- sounds interesting. Both sound similar to ticking sticks. Thanks-

[@andrewkrahn2629]

​@@ChrisStaecker Of course! I know you usually do math objects and they're less relevant, but I thought they might be interesting! I'm fascinated by the older ways of "doing geometry without doing math" that let illiterate people build buildings that are still square and true 500 years later. The book "Euclid's Door" by Lost Art Press covers how to bootstrap yourself into having an accurate straightedge, square, and winding sticks (for judging parallel by eye). Also, it looks like some people are still using Sectors kzbin.info/www/bejne/eqG1oHSnrLyobaM

[@johnnzboy]

"you're clampin'!"/using sector like a chomping crocodile/Fabreze for Fabrizio/"buildin' scopes and vexin' popes" - is it any wonder that I get inordinately excited when this channel releases a new video?

[@NigiriCat]

The history of the tools used for calculation is always fascinating.

[@BrianTRice77]

I’d like to see how one would use one of these with navigation charts. Before the 1800s, when angles were more critical for navigation from known coastal points, like a portolan chart! Anyway I can see how the angular measurement plus the basic trigonometric functions and scale divider, in combination with a compass, would be more practical onboard a ship.

[@outofsyncrock7788]

Hey, I'm pretty sure the one you have predates your estimate. I have a very similar example (from the pins to style of markings) from a drafting set dated to around the very turn of the 18th century. Not to say yours is from the same era, but I doubt its a newer item, as late 19th century have much clearer and mechanized style of divisions due to the newer marking engines and such.

[@ChrisStaecker]

Very interesting- really my estimate was just a guess. I wish it had some marks on it to help identify it better. Thanks for the tip!

[@leiladekwatro3147]

71 views in 15 minutes? You're blowing up!

[@ChrisStaecker]

Welcome to the z-list !

[@creamwobbly]

So that's why they're called dividers… not whatever line my technical drawing teacher fed me.

[@pyglik2296]

I can't believe it! Recently, I saw some sectors at a museum witha note that those are calculating devices. I was curious how were they used, but couldn't find a nice explanation anywhere, and now you post a video about them! I love simple devices like this; you could easily make one on your own, but it can still be very useful. That's the same reason I love slide rules and keep one in my desk drawer, because sometimes it is faster to pull it out and slide the scale, than to open the calculator app and type the numbers.

[@alexstone691]

Honestly quite a genius tool even for today

[@Salsmachev]

Oh my god! I've been looking for a video on this! Finally! edit: chomp chomp chomp

[@jaapsch2]

Fascinating video! I'd not seen one of these before. Thanks!

[@ChrisStaecker]

The highest praise!

[@peterjaimez1619]

Thank you. I of course know about the slide-rule, first time i hear about this. Cheers.

[@LeoStaley]

I would pay money for a video of you collaborating with Cliff Stoll, nerding out about old calculation devices. Like, I'd join your channel for 5$ a month for at least a year for that sort of thing.

[@michaelbauers8800]

Great video, of a device I knew nothing about. I know a bit about slide rules, and own a few fancy ones like a log decitrig. But didn't know the sector. You said clamp so many times, I started thinking about this Furturama episode with a robot "gangster"

[@maxinehardy9411]

im very much looking forward to a video on adjustable proportional dividers!!

[@txikitofandango]

forty-a-little times twenty-a-lot is eleven hundred something. amazing. EDIT: I don't mean to be snarky, but I'm curious why instruments like this and the slide rule were so commonly used for multiplying, when an abacus could give you the exact answer in seconds

[@ltva8781]

they are simpler and easier to learn how to use, I guess

[@ChrisStaecker]

I would say a slide rule is easier to use than an abacus, and also the slide rule & sector can be easily tricked out with trigonometric and other scales, giving more functionality using more or less the same form factor. The abacus isn't extensible at all.

[@BillRicker]

The abacus and other adding machines are good for accountancy, mostly adding, where balancing to the cent is desirable. In engineering one is only interested in the significant digits, so 42*27=eleventy-hundred and change is fine. And having once been proficient at each, i can say that, yes, the sliderule is faster for proportions, multiplication, roots, and even pythagorean-formula than abacus or even scientific calculator, but abacus was faster for addition, which is why early digital calculators in Japan were built into the end of a Soroban (1 over 4 bead Japanese abacus), where it would be used for percentages to feed into a sum on the beads.

[@michaelbauers8800]

I am willing to race most people with a slide rule vs an abacus for multiplication and roots. I know people can be really good at the abacus, and I have seen videos of abacus competitions. But not sure they can calculate the cube root of 11 before me, given a slide rule and some practice time to become comfortable doing it again.

[@BigJohn4516]

To divide a line in 7th with a compass: create a rectangle with 1 side as the line to be divided. Draw the diagonals. Draw a perpendicular line from the point of intersection to the line. Now, draw a diagonal across the new rectangle. That line intersects the original diagonal. Draw a perpendicular line there. That’s a third. Continue drawing diagonals and marking where they cross the original diagonal. You can even skip ahead by dividing the third in half and repeating the intersection of a new diagonal crossing the original diagonal. If you don’t believe me, do the algebra. It’s pretty simple to prove using algebra, but I would love to see a proof using geometry.

[@_D_P_]

5:50 That could be really useful for carpentry, if I'm doing something that needs roughly even divisions as opposed to specific values. Don't have to calculate a number that comes out to something like 23.641143 mm. A device like a pantograph can be used to mark even divisions, but they become cumbersome and impractical the larger the number of divisions and scale of measurement. You could measure out divisions for landscaping with basically a few sticks. I know a lot of these are non-issues for modern devices. Just do the calculation and round to however many decimal points the project requires. But for pre-industrial societies, this sort of thing must have been so convenient.

[@davidegaruti2582]

I like these ! They are from a time when math was done via geometrical drawings

[@j.aaronkambeitz9848]

"and that's not all. This sector came with the ~~original~~ elephant"

[@najroe]

I have a good pair in bronze as well as several other instruments (astrolabe, sextant...). interesting parts of our history.

[@fr4n_c13]

Awesome video as always! Keep it up :D

[@petejandrell4512]

Came for the clamp, stayed for the 'Chomp'!

[@joecassidy2887]

can't believe I've never heard of these before. kinda want to figure out how to do a production run with modern plastics instead of ivory

[@glarynth]

The pope vexer missed a trick not branding his version as "Galileo's Bones"

[@tiredtait9660]

That conpass collection looks like they could double as interrogation tools

[@davidegaruti2582]

I have a question : could you geometrically make a slide rule with one of these ? I am not sure if one could make logaritms with this one

[@ChrisStaecker]

No you can't- this is a great question though. IF you could make a logarithmic scale with this, then in particular it would be possible to construct a scale with the number e on it. But this is not possible using only a sector because the number e is irrational and transcendental. By doing simple ratios using the linear scale, the sector is only capable of constructing rational numbers. If you additionally used the sector to measure the hypotenuse of triangles, you can also get some irrational numbers like √2. But you can't get e, since e is transcendental (ie it can't ever be constructed even using radicals).

[@ptonpc]

That is ingenious.

[@TomCarlson]

Oh crap, now I need to save another eBay search.

[@reversev9778]

Were the trig lines notched through trial and error or was there someway to know where to put the notches?

[@BillRicker]

laborious hand calculation (which is why Babbage thought the Navy or Army would be willing to pay to build his Analytical Engine, as it could compute tables mechanically)

[@okancanarslan3730]

amazing device

[@2bfrank657]

I've not seen a sector in real life, but know that chords rules have been manufactured in modern times and probably still are. The tool set I started my apprenticeship with had one in it.

[@Salsmachev]

Do you know what companies manufacture them?

[@Pedritox0953]

Great video!

[@jimscheltens2647]

Kinda wish someone would make these again.

[@ChrisStaecker]

There is one person making them at redrosereproductions.com/sector/. I’ve never seen one in person, but it looks pretty nice…

[@cion191]

Nice vid!

[@hopscotchoblivion7564]

You can't fool me mason

[@zaquery8]

We’re back baybeeeee

[@VitorGuerreiroVideos]

Golden! .. yea that's it, that's all I wanted to say here. k tks for the vid! :D

[@richardl6751]

At 5:45 Try the angled ruler method.

[@ryanprasad2090]

Awesome vid

[@jimiwills]

Nice!

[@mikemcguire1160]

Might have been pretty hard to use with Roman numerals....

[@markgreco1962]

Cool

[@jurjenbos228]

Do that why the foldable carpenter's rules have this hinge