Genaille-Lucas Rulers

Genaille-Lucas Rulers


Hey, would you like to play with my toys well you’re in luck because this show is called Michael’s toys But you may be wondering, how are Michael’s toys a DONG Well let’s see you can watch me play with my toys online for free, which means they are by definition a DONG That’s something you can do online now guys Plus I know the password to this channel and can upload whatever I want and I really want you to see this toy It’s called a Genaille-Lucas Ruler set they are beautiful They were invented in 1891 as a way of multiplying numbers without having to do a lot of mental calculation Look at how beautiful. They are oh, yes these wooden rulers were created By a company called creative craft house. I just got them right on Amazon, but you can make these at home yourself Just look up a guide online Wikipedia has a great one look at these beauties. Let’s take these out of the case and see how they look Wonderful, now each of these rulers has a number at the top a digit 0 through 9 and These can be used to multiply numbers together. I’ll show you how this works let’s start out really really simple with just the two ruler as you can see 2 times 1 is 2 2 times 2 is 4, 2 times 3 is 6, 2 times 4 is 8 we always look at the Rightmost top number in each row for the answer now. Let’s make this a little bit more complicated and try another number Hanna, what month were you born in, April, that’s the fourth month, right? Here’s a 4 Eric how old is Barry five, five years old Barry is a dog okay now. I have 45. Let’s multiply 45 by a number Eric what month were you born in? January, okay. Multiplying 45 by one is kind of simple, so I was born in January as well shoot, ooh Here’s what we can do Let’s use a 10 sided die and it’s got a 5 digits on both sides of its little Pentagon pyramids This will be completely random now you know that it really works, and I’m not just fishing for numbers that these rulers work with And I rolled a zero, 45 times zero is zero. We don’t need rulers for that so I’m gonna roll again 3, 45 times 3 now 45 isn’t a really hard number to do mental math with but just for the sake of learning how these rulers Work we will take 45 which I have up here and multiply it by 3 So we look at this 3 row and we see 5 in the upper right part of this row but we then follow the 5 down the funnel to the next number which is a 3 we followed the next funnel to a 1 Which tells us that 45 times 3 is 135 so notice that we’re reading these rulers from right to left which is the opposite of how we read books But when you do multiplication? Longhand out on a sheet of paper you’re often moving from the right to the left because you work with the ones column then the tens column in the hundreds column and so on So let’s make this a little more interesting and pick a bigger number than 45 what number should we pick well? That’s what this die is for we’re gonna do 900 let’s make this a 5 digit number, okay, so 90,000 I just rolled a 0 there’s 90 and the next three digits are 90,230 – all right, I only have one ‘two’ ruler, so we’re gonna roll again, one, perfect 90 thousand 231 and we’re going to be multiplying that five digit number by Zero, no we won’t use zero it’s too easy. We’re we’re gonna multiply it by four now You could do this longhand on a sheet of paper But it would take you a bit longer than just looking at these rulers so the answer to ninety thousand two hundred and thirty-one times four is reading from right to left four, two, nine, zero, six, three Perfect, beautiful, simple and so well-crafted So how did this work? Well a clue to how they work is in the fact that we have to read the answer from right to left What’s going on is that when we multiply two numbers together for instance Let’s go back to the two because it’s a very easy way to see how these work We’ll notice that two times one gives us two, two times two gives us four, two times three gives us six 8, uh oh, two times five is ten But there’s just a zero in this upper right part of the row The reason for that is that zero is in the ones digit of ten, so where does the one go Well, the one is carried over to the next ruler That’s why the funnel coming off of this zero takes us not to the top number in the next ruler but down One that is where we add the one that we’re carrying over from the ten If we use a larger number like nine now We’ve got many different numbers that we’re going to be carrying over because 9 times 1 is 9 but 9 times 2 is 18 There’s the 8 which is in the ones digit place, the 1 is carried over by the fact that this funnel brings us down One on the next ruler in this case is just the index because I’m only multiplying 9 as a digit, but 9 times 3 is 27 There’s the 7 in the ones place of 27 And then the funnel takes us down not one, but two places so we’re adding 2 to the next number for instance if I take 29 and multiply it by 3, I take 3 times 9, which the ruler gives us as 27, there’s the 7 in the ones place the funnel takes us down two places so we add 2 To what 2 times 3 is Which is 6, we add the two from here because the funnel takes us down to more places so that becomes an 8 now We get carried straight up to the 0 because nothing winds up in the hundreds place nothing carries over further This funnel just takes us up to the top so the number is 0, 8, 7, aka 87, 29 times 3 is 87 thank you Genaille-Lucas Rulers you might notice that some of these rulers have more than one triangle in some of their cells That is caused by the fact that sometimes you carry over so much you wind up actually changing Not just the first number that you’re adding it to but even the next number over so for instance with 29 times 7 We’re told that the answer is 3 because 7 times 9 is 63 so we have to add 6 more oh no! But 2 times 7 is 14 You add 6 more to that and you get 20 you’ve actually changed two of the digits You need to carry over not just a 1 to your next figurine you have to carry over a 2 So at that point where we’re carrying over 2 we get a new triangle that takes us not one down but 2 down We’re adding 2 to our next figure So there you have it Genaille-Lucas Rulers that are beautiful They of course have obsolesced in the last 100 years or so we now have calculators and computers to do figuring like this But they’re still useful as a way to Investigate, play around with and visually appreciate how our number system works, so thank you mr.. Genaille and mr. Lucas as well for posing the problem that led Genaille to invent these in the first place As you can probably tell I like learning new things I’m always hunting out new challenges new things I can study to make myself a better person If you’d like to do that you might want to check out this episode sponsor Skillshare Skillshare has more than 17 thousand courses online where you can learn new skills from experts, skills ranging from business to graphic design I gotta tell you one of the best things I ever did in my life is learn how to edit By learning how to edit video in Adobe Premiere, which is what I use I was able to take control of my career I don’t just have to write scripts, and then hand the job off to other people to help me I’m able to make the video the way I want to and I had to learn from other people Which is what skill share allows you to do now many things I talk about in my episodes require visuals that aren’t just flat and 2d which I can do in Photoshop pretty easily But things that are 3d they have a course on cinema 4d which I’m going to be diving into so look forward to how Amazing my videos will become when you sign up for Skillshare be sure to use this Link because we are giving you your first 3 months for only 99 cents you can’t afford to miss out on this Ok good and as always Thanks for watching

100 thoughts on “Genaille-Lucas Rulers

  1. 1:46 genuinely scared me because he said my name and looked right at "me" and I was kinda freaking out like "what do I say"

  2. but how do you double digit multiplied by double digits, and why is there only one of each number when that is so limiting?

  3. They atrike me as being as useful as Common Core. Perhaps they are Common Core slide rules? They don't slide, so that checks out. They are idiotic… check. Makse simple tasks complex – check.

    Yeah, these things are not terribly interesting for anything practical.

  4. In high school math class I had my slide rule out on my desk. The girl next to me asked if she could borrow my rule. I handed it to her and went back to my work. There was a little scream and she said "The numbers are not even!" She was trying to use it as a ruler.

  5. Wouldn’t mind learning from you if you could pull down the pedophilic banter to like maybe zero out of 10 right at the beginning. Thanks

  6. So you can't multiply by numbers that have the same digit twice or more and it has to be by a single digit number.
    I'll stick to a calculator.

  7. 2:28 you threw the dice over and over until you get 3 and then you only showed us that, prove me wrong, you can't, i just ruined your whole career

  8. This guy looks like mike from vsauce just kind of chubier, hence less hyperactive.. … oh this is mike ? Gush he aged in funny way.

  9. As cool and as useful as these could be, it's just a lot easier and way more practical to pull the iPhone out of my pocket and use that handy dandy little Calculator App, and I don't have to worry about not having deep enough pockets or a briefcase to lug all of those sticks around.

  10. agreed, this is a new way to take a new interest in numbers and stop watching so much tv. I sent links to this vid to my two engineer bros in laws.
    That being said, you need a whole backpack full of these sticks just to do your taxes let alone put a man on the moon. I think I'll just stick to my CommonCore math which only requires a few reams of paper…

  11. Ok I see that's what is now its like ten pumpkins ! Congratulations on your foot plan renegade foil artist and great job to be hamburger meat . Grey clowns brought in the ham sandwich and it's ok.

  12. Now imagine if you had a time machine and made this ruller back in like…1800 sell it, making your own product, mathematician would buy it like crazyXD

  13. Quite interesting and if we want to multiply by numbers larger than 9 we can simply do this several times and add the results (while making sure we shift the place and add a zero).

  14. Fascinating! It works and gives the right answers but doesn’t teach math, in my opinion, as well as the Stretchy Calculator which uses a rubber band and reference ruler: https://www.hineslab.com/stretchy-calculator.

  15. Can the rulers solve double-digits/triple-digits multiplied by double-digits/triple digits, or just single-digit with multiple-digits?

  16. No not Ruler Set! It is a RULE SET.  Only the Monarch, Emperor or Government are called the Ruler because they MAKE the RULES.  Yes it sounds petty but what's next calling a hammer a "bodger"

  17. Why didn't you discuss what to do when you have a digit that appears twice in the multiplicand? I can see how one could get round it, but still… I was expecting you to cover it.

  18. The problem with our public school system is that they stopped teaching basic math (addition, subtraction, multiplication, division) with pencil and paper and also having children learn multiplication tables. So, waitresses can no longer figure out your check or make a correction without a calculator and engineering students get answers wrong by orders of magnitude and don't realize it. They did this over 20 years ago, so a whole generation has lost those skills.

  19. Cool post , Thanks !   I've always get a kick out of graphic calculating  devices  https://www.youtube.com/watch?v=2EYPW3Rmbms  .

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