Oh
Hi, I didn't see you come in
Do you feel this... connection that we have?
I've been feeling it all day
I know
Are you thinking what I'm thinking?
No no, you say it first
You... okay, I'll say it
Six thousand six hundred and six point forty-eight
divided by two
Oh
There are a lot of people watching this right now?
I guess we should explain what we just did
six thousand six hundred and six point four eight
is the approximate value of this mathematical expression
A hundred and twenty eight
times the square root of the base of the natural logarithm
times nine hundred and eighty
Divided by two is important
because if you take this expression and divide it in half
you get "I love you"
But love isn't always easy
sometimes there will be arguments, differences
but love can endure any...
inequality?
Specifically this inequality
discovered by Albert Einstein
but not really I'm just making all of this up
Anyway, this inequality tells us that
9x plus 7i
You have to use some imagination with love
is less than three times (3x plus 7u)
Now, let's simplify this inequality and see what we get
Well let's distribute the three
and so we'll wind up with
9x plus 21u
and that is less than
9x plus 7i
Now what we can do is
subtract 9x from both sides
and that will give us
7i is less than 21u
We can divide both sides by 7
to find the true meaning of my entire life
Divided by 7 we get
I
I heart
I heart you
But why "say" how you feel when you can
show..."how" you feel?
What I mean by that is
Neurotransmitters
Serotonin and dopamine necklaces
are a great way of showing what's happening in your brain
when you see that special someone
My favorite romantic gift comes from MathsGear.co.uk
I actually got a pair of these for me and my wife
I think she's lost her half
But it doesn't matter because it's the thought that counts
These are amicable numbers
What are amicable numbers?
Well there are two numbers that share a special bond
Take the number 220
What positive numbers evenly divide into it?
Well... 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and a 110
If you sum all of those up, you get 284
But what positive numbers divide evenly into 284?
Well in that case we've got 1, 2, 4, 71 and 142
...whose total sum is 220
Beautiful right?
That relationship touches my heart in all kinds of special ways
But let's talk about heart shapes
because heart shapes can be mathematically generated
my favorite way of course is the Cardioid
The path traced by a point on the circumference
of a circle rolling around the outside of a circle
whose diameter is equal
But...
But(t)... is what it looks like
a butt
But also Cardioids don't have points
If you want a point, there are equations for those kinds of hearts
There's even an equation for a great heart surface
but I know what you're thinking
Michael...
I watch Rick and Morty, okay
I don't want a symbol for a heart
I know that anatomically hearts look different
Well, you're in luck
Because anatomically correct diagrams of hearts
can be found on cards, on posters, on mugs...
this pendant is just wonderful
But look at this vase
ah it's just so heart-like
it's kind of macabre
but hold on a second
If you really really want a romantic gift
that is extremely pedantic
why get an anatomically correct diagram of a heart
when you could get a literal heart
PrestonsMasterButchers.co.nz
will sell you literal animal hearts
And if that doesn't say "I love you"
then you've got a lot of other better options
at the end of the day, the most romantic gift
is the gift you made yourself
Let's make some mathematical romance
we're gonna begin with a strip
a strip of paper
I can take a strip of paper and turn it into a hoop shape
a cylinder with no top or bottom
when I have some tape
now if I tape this hoop together
and cut it in half
what will I get?
Well I will get two halves
I can prove it to you in case you don't believe me
I'll make a snip right there
and I'm gonna start cutting around the middle of the strip
all the way around
and when I meet back up
lo and behold I've got two hoops
Nothing too surprising here
You could turn this into some kind of mathematical
you know, love bracelet
or maybe it's like a ring
if your partner has extremely fat fingers
But we're not here to talk about simple hoops
We're here to talk about the Mobius strip
A Mobius strip is made just like a hoop
except before you connect both of the ends of the strip
you give one end a 180 degree turn
we'll call that a flip
so watch what I do as I turn this 180 degrees
Now I will tape these two sides together
make sure I get plenty of tape
so that nothing comes loose
and now I have myself a mobius strip
I'm sure many of you have played with these before
have you ever cut one in half?
the way we cut the hoop in half
Let's see what happens when I try
if I cut it right there so that there's a little hole to pull my scissors through
and I start cutting right down the middle
I should of course wind up with two thinner Mobius strips
It's not cut in half
I've just made a thinner wider loop
that actually has more twists
There are four twists in this now
Numberphile has a fantastic series of videos
about why this happens
You might be wondering where's the romance
well here's what we're gonna do
We're going to take two strips of paper
and we're gonna make two mobius strips of opposite chirality
Chirality has to do with
which direction we turn the strip in
before we tape it
so for this first one I'm going to turn it what is clockwise to me
Perfect and I will tape this
Always be sure to use lots of tape
because if it comes loose while you're cutting
Well, you're gonna be single for the rest of your life
now with my other strip, I'm going to turn counterclockwise
from my perspective and tape it
what I'm gonna be left with is two mobius strips
that have opposite handedness, or chirality
They will be mirror reflections of each other
See that? Mirror reflections
And now I'm going to tape them together
You can tape them however you want
But again, the rule always stands to use plenty of tape
so that after the cutting the pieces stay together
all right, so there's..
I'm gonna put more tape on
I'm just really nervous about this falling apart
I'll put a piece in here
and now I've got something that just looks like
a big old pile of puke, maybe like a hairball
But the romance will come soon
Now that I've got
these two opposite chirality Mobius strips taped together
it's time to start cutting them both
right down the middle the way we did earlier
so I'll cut this pink one first
Right down this way
I'm gonna cut right through the part where they join
And continue going around
until I've completed my loop
Good, now the pink one's been cut
now it's time to cut the red one
all the way around through the middle
just like this
Great
And I will continue cutting it on this side
right through the middle
and what you'll find is
that the whole thing doesn't come apart
Instead what I now have is
two
two interlocked
two interlocked hearts
Now if that's not love then I don't know what love is
So go out there
spread some love
I know that Valentine's Day has passed
But
But that doesn't mean
that love has ceased to exist
all it really means is that we were too late in making this video and
And as always
Thanks for watching
I learned about the beautiful interlocked hearts trick
from Matt Parker
if you're not subscribed to his channel
then you're missing out on some fantastic math
AND comedy, I know
He makes them come together like
Um, well like true lovers
Now if you want to learn more about Mobius strips
I hope to do many more videos on them
but Numberphile, as I said before
has some fantastic videos on them
I'll leave you with this
Why does a Mobius strip
when cut down the middle
not fall into two parts?
One way to think about it
and I'll let you experiment with this at home
cause it's super fun, is to look at a strip of paper
This one I've built so that
each half is extremely clear one's green and ones black
If you just make a simple hoop, a cylinder
You can see that a cut right around the center line
all the way around will definitely separate the black and the green parts
but if you make a mobius strip
Giving the strip a 180 degree twist
now the black and green halves aren't just connected lengthwise
They're also connected here horizontally
Creating a loop that is twice as long
That's all I have to say about it for now
but please check out Numberphile and Matt Parker
I've got those videos linked down below
and again as always
Thanks for watching