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
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Ok good and as always
Thanks for watching