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