Genaille-Lucas Rulers

Last week, Michael Stevens posted a fascinating video about Genaille-Lucas Rulers, a 19th-century tool to simplify multiplication and division.

It’s the kind of thing that’s just begging to be made on a Glowforge (the set in the video was laser-cut by Creative Crafthouse), so I thought I’d give it a whirl.

I started out with the SVGs on the Wikipedia page linked above, but they’re designed to the printed on paper and cut out, not laser-cut. So I re-drew my own versions from scratch.

(Note: SVGs re-uploaded Jan 17, 2018 at 2:33:02 PM PST to fix a minor error)

Genaille-Lucas multiplication

Genaille-Lucas division

I decided to make mine with the multiplication version on one side and the division on the back. To keep everything aligned, I used a combined SVG with everything in separate colors:

Genaille-Lucas both

Engrave/score/cut the multiplication side (while ignoring the division stuff), then flip the rulers and engrave & score the division side (ignoring the multiplication stuff).

I used :proofgrade: Thick Cherry Plywood. The numbers and text are all engraved with the “HD Graphic” setting. The triangles on the multiplication side are SD engraved and all of the lines are HQ scored. Before cutting the whole project, I created a single test ruler with a variety of settings for the engrave:

Genaille-Lucas test

I preferred one of my manual engrave settings, but the rest of my family was unanimous in their preference for SD Engrave.


Oh, wow.


Almost makes math look like fun. :smile:
(Great job!)


I never heard of such a thing; but you’re right, it’s perfect for the Glowforge!


These are awesome! I think I’ll have to give it a try now. They would make an awesome display in my tutoring center.

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I’ve just re-uploaded the multiplication and “both” SVGs on the original post to fix a minor error. If you downloaded the originals, don’t worry. They’ll cut just fine. I’m just being a little pedantic about how the layers and groups are named.


Thanks! Great Find.

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Okay, so that is a wicked cool thing (like my slide rule) :slight_smile:

I have absolutely no use for one but I want to make one now myself. Maybe I can have my wife bring it to school and the math teachers can play with it.


I love it when you see something you have never seen before.
Thank you for the great post and information


Yeah, had to go down the rabbit-hole. I’m trying to figure out if you could change the engraved < sections so that it would read left to right rather than right to left to get the correct left to right sequence.

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Very nice!

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Thanks for sharing. I want to make a set and just trying to clarify which layers i need to use to create the multiplication vs the division side. When i upload the svg to the GFui it shows 6 layers the top three are engraving by default and the bottom three are cut. So i think i need to first do:

Then flip and

is that correct?

Close. You need to ignore 1 on the second side. I ordered the layers so that all the engraves are first, then the scores, then the cut. I probably should have ordered multiplication first, then division. Ah, well.

Here’s the rundown:

Layer Color Description Action
1 #000000 (black) multiplication text engrave side 1
2 #0072b2 (blue) multiplication triangles engrave side 1
3 #cc79a7 (reddish purple) division text engrave side 2
4 #009e73 (sky blue) multiplication lines score side 1
5 #d55e00 (vermillion) division lines score side 2
6 #e69f00 (orange) cuts cut side 1

I think that would be tough to do. The right to left flow comes from the nature of place value. The triangles are essentially a graphical representation of “carries” you’d do in longhand multiplication (which also flow right-to-left).

So cool! Awesome combination function and presentation. Love it!

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These are so beautiful and your file is perfect. Thank you for sharing!

I used Medium Walnut Ply since that’s what I had on hand, but I am going to redo them in Thick Cherry for better legibility (glamour shot is higher contrast than real life) and heft. Good thing there’s time to place a PG order before Valentine’s Day.


These were just too cool looking not to make set. I think I’ll gift it to my math professor buddy.
Proofgrade Thick Maple Ply, BB box.


Thanks for outlining your process. This is such an awesome project!

Cool box too. I like the QR code to the wikipedia article (yes it can be read from the PC screen :slight_smile: )

I was thinking of making sets for my kids. Nerdy geek chic :smile:


I was about to reply to @reliablepants that I thought the contrast would look really nice in maple and you’ve gone and done it. Beautiful.

Right about now is when someone will discover a mistake I made in creating the SVGs. :wink: (I don’t know of any, mind you, it would just figure…)