It’s Valentine’s Day, girl.
The day of love.
And I’m gonna speak love to you.
I’m gonna speak love to you
In the universal language
Of . . . mathematics.
(It’s Valentine’s Day...)
Yeah, girl.
Talkin’ love.
“r” equals one minus the sine of theta, baby.
Oh, yeah.

Am I goin’ too fast?
That’s alright, baby . . .
We can take it slow . . .
I’ll show you what to do . . .
Here we go . . .

Watch me trace around this unit circle.
At every point, we’re lookin’ for a sine.
We’ll put each y-value on the Cartesian plane
And then watch as theta continues to grow.
(It’s Valentine’s Day...)
Oh yeah, baby -- that’s right.
You’re gettin’ it now.
Trace your pencil along those
Sinusoidal curves . . .

And now baby,
Let’s move to the table
And see what happens
When you start with one,
And then take away all those “y”s . . .
That’s it.
Yeah -- just like that.
There’re no negatives any more,
Are there, baby?
Mmmmm . . .

Now let’s take it to the next level;
Switch to polar coordinates
And start graphing “r” against theta . . .
Yeah.
That’s nice.
See how things start to
Move in a new direction
When theta gets to ninety degrees?

(It’s Valentine’s Day...)
Yeah, you see what’s happening.
You like it, don’t you?
This cardioid graph?
Well, that’s just the first half,
‘Cause baby?
We’re just gettin’ started . . .

Let’s get . . . topological.

Alright, baby.
Just lean over
And grab a construction paper
Strip.
Make a loop.
Give one end a half-twist,
And tape those ends together.

That’s right.
Now grab another
Strip.
And do it again,
But this time,
Twist it in the opposite direction.

Yeah -- you’re doin’ it.
That’s fine, girl.
You just made a couple of
Enantiomorphic Möbius strips.

Now baby,
Choose a spot on each strip
And put a big piece of tape
Orthogonally across each band.
Then use that tape to join
Those two Möbius strips together
So their . . . intersection
Is . . . perpendicular.

Now cut each strip
Lengthwise in half.
Yeah, baby.
Keep goin’.
Don’t stop.
Cut the second strip, too.
See what you get?
Two interlocked hearts?
That’s me and you, baby.
Our love is true, baby.
(It’s Valentine’s Day...)
It’s Valentine’s Day . . .

Lesson’s over, baby.
Whad’dya wanna do now?