- In my previous video,
I talked about the hidden science in Canadian bank notes,
and that seemed to be a popular video,
so here's another one where I look at a hidden feature
of Canadian money.
This time we're looking at the loonie, which is the $1 coin.
The $1 coin has 11 sides,
another way of looking at that is it has 11 bumps.
So, you know, one bump, two bump, three bumps, four bumps,
and there's 11 in there.
So you might think that if you were to use these coins
as a rudimentary wheel, you'd have a bad time,
because as you rolled around on them those 11 bumps
would cause you to have a bumpy ride.
And of course, wheels are circular, because circles,
as you rotate them, the width stays the same,
and so you have a smooth ride,
and surely that's the only shape that will work.
Wheels have to be circular, but it turns out
that this 11-sided shape works perfectly well as a wheel.
And to prove it, if you get two books and two loonies,
you can then roll the books side to side,
and you will feel no bumps.
The distance between those two books
will stay exactly the same.
And that's because even though these coins have 11 sides,
they are shapes of constant width.
And there are a whole family of shapes of constant width.
It's easier to see actually, with triangles and pentagons.
So here we go, we've got a triangular one and a pentagon,
you'll notice that the faces or the edges, I should say,
of these shapes have been rounded in a certain way,
and that causes them to be shapes of constant width.
As the books slide along and those shapes rotate,
they stay the same distance apart.
It's easy to make a shape of constant width.
You just take an odd-sided shape like a triangle,
and then with a compass, you put the point of the compass
at one of the vertices of the triangle,
and then you round off the opposite face like that.
And if you can't find your compass, that's fine.
You can just use a makeshift one like this.
And it's technically a pair of compasses, shut up!
And the shapes don't have to be based on regular polygons,
they can be based on irregular polygons,
so for example, here, this is a three, four, five triangle,
and you just have to extend some of the lengths,
and then round off and blah, blah blah.
Anyway, here's another one, this is a pentagon,
but the angles have been changed, and there you go,
as they rotate, the width stays the same.
Shapes of constant width.
And here we have a set of four shapes of constant width,
and these are available from mathsgear.co.uk,
which might be a website that I run.
So please do buy some.
My garage is full of these things
and I'd like the space back.
So please do go to mathsgear.co.uk and have a look.
Now you may have spotted
that the books I'm using are books about maths.
They're called "Things to Make and Do
in the Fourth Dimension" by Matt Parker.
And if you buy "Things to Make and Do
in the Fourth Dimension" by Matt Parker from mathsgear.co.uk
it will be a signed copy
of "Things to Make and Do in the Fourth Dimension"
by Matt Parker.
Not only are they signed by Matt Parker,
they're also signed by me.
Look, there's my name in the back.
So there we go, actually, Matt thanks me twice.
So might as well sign it twice.
So both of these books are signed by me,
and signed by Matt Parker, but amazingly,
these books also contain a confession by Matt Parker.
It says here in the front of the book,
"Tau is better than Pi".
And look, it's signed by the man himself,
so you know it's true.
And that is a total U-turn based on his previous position
about Tau and Pi, which you can check out
in this video here, link also in the description.
Canada isn't the only country that has these special coins.
In the UK, we have 50p and 20p coins.
They're seven-sided shapes, there you go.
So 20p coins, although they're seven-sided,
as you roll them between two books,
the books stay the same distance apart.
This is an important feature,
because when you pay for something at a vending machine,
the vending machine measures the width of the coin
as it rolls through.
So if that width were to change as it rolled through,
you wouldn't be able to get an accurate reading
of which coin it was.
So almost all coins are shapes of constant width,
even when they're not circular,
except for a few backward countries, for example, Australia.
And in fact, I have Matt Parker here with me.
So what are these coins?
- So I have 50 cent coins from Australia,
which, as you can see, have 12, an even number of sides,
and none of this rounded ridiculousness,
they're all perfectly flat sides.
So these are not shapes,
you can give them a go,
they are not shapes of constant width.
- [Steve] Why would you do that?
- [Matt] Why wouldn't you, look at it!
Okay. It's a bumpy road.
- [Steve] Oh yeah, that is, that is pretty horrible.
- So you can tell the difference, right?
So the other ones were constant width, these are not,
the advantage of these is they balance nicely.
In fact, you could even stack themm so five --
- Okay, that is nice. - Look at that.
- All right. - So now that's what
I look for in a good currency.
(laughter)
- Okay, so there you go, shapes of constant width,
oh, also there's a 3D equivalent of that.
Check out this video for details of the 3D version,
they're called solids of constant width.
And you can also get those from mathsgear.co.uk.
In my previous (laughs) --
- You get the book too, right?
So the first two people who buy the book from mathsgear,
if you're saving your checking out,
you want the one that Steve signed as well,
we'll give these to the first two people who do that.
- Yeah, 'cause I've signed these, as well.
Okay, so that's the other thing I wanna say, is,
in the previous video that I did about Canadian bank notes,
I got a lot of comments from people saying that
did you know that also the bank note smell like maple syrup?
And, you know, I smelled the bank note,
and it did seem to smell like maple syrup,
but there were a lot of people were commenting saying,
"Don't be stupid."
I mean, they used harsher words than that.
This is YouTube after all,
but there seems to be some disagreement.
Anyway, Canadian money is polymer money.
It's not the first country to make polymer money.
Australia was one of the first countries.
And in fact, most of the world's polymer money
is made in Australia, including Canadian money.
It's made in the same place.
So we're gonna do a smell test in the next video,
a blindfold smell test
between Australian money and Canadian money.
If they both smell like maple syrup,
then we know that it's just,
I guess, coincidence or something like that.
Anyway, that's in the next video.
So check that out. - What the F --