Genaille—Lucas rulers also known as Genaille's rods are an arithmetic tool invented by Henri Genaille , a French railway engineer, in The device is a variant of Napier's bones. By representing the carry graphically, the user can read off the results of simple multiplication problems directly, with no intermediate mental calculations. Genaille, already known for having invented a number of arithmetic tools, created his rulers in the course of solving the problem. The popularity of Genaille's rods was widespread but short-lived, as mechanical calculators soon began to displace manual arithmetic methods. A full set of Genaille—Lucas rulers consists of eleven strips of wood or metal.
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Last week, Michael Stevens posted a fascinating video about Genaille-Lucas Rulers , a 19th-century tool to simplify multiplication and division. So I re-drew my own versions from scratch. 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:. I used Thick Cherry Plywood. 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:.
I preferred one of my manual engrave settings, but the rest of my family was unanimous in their preference for SD Engrave. Almost makes math look like fun. Great job! These are awesome! They would make an awesome display in my tutoring center. Okay, so that is a wicked cool thing like my slide rule. 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. 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: 1-engrave 2-engrave 3-skip 4-score 5-ignore 6-cut. 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. I think that would be tough to do.
The right to left flow comes from the nature of place value. These were just too cool looking not to make set. Cool box too. I like the QR code to the wikipedia article yes it can be read from the PC screen. I was thinking of making sets for my kids. Nerdy geek chic. Right about now is when someone will discover a mistake I made in creating the SVGs.
Genaille-Lucas Rulers Made on a Glowforge. You Rule, Valentine Rulers. Proofgrade Frustration: Thick Walnut Plywood. Okay, so that is a wicked cool thing like my slide rule I have absolutely no use for one but I want to make one now myself. So i think i need to first do: 1-engrave 2-engrave 3-skip 4-score 5-ignore 6-cut Then flip and 1-engrave 2-skip 3-engrave 4-ignore 5-score 6-ignore is that correct? So cool! Awesome combination function and presentation.
Love it! These are so beautiful and your file is perfect. Thank you for sharing! Thanks for outlining your process. This is such an awesome project! I like the QR code to the wikipedia article yes it can be read from the PC screen I was thinking of making sets for my kids.
Multiplying large numbers before calculators led to a number of ingenious inventions to make things easier, like these Genaille-Lucas rulers demonstrated by the fine folks at DONG. In the days before calculators, methods of simplifying calculations were of much interest. In Napier also published a book describing a method to multiply, divide and extract square roots using a set of bars or rods. These became known as Napier's Bones. In the late s, Henri Genaille, a French civil engineer, invented an improvement to Napier's Bones that eliminates the need to handle carries from one digit position to the next. There are also sets for division. You can get your own set online or print your own from these free files.
Napier's Bones and the Genaille-Lucas Rulers
Watch how 19th-century Genaille-Lucas calculating rulers work