A cardioid (from the Greek καρδία "heart") is a plane curve traced by a point on the perimeter of a circle that is rolling around a fixed circle of the same radius. It is therefore a type of limaçon and can also be defined as an epicycloid having a single cusp. It is also a type of sinusoidal spiral, and an inverse curve of the parabola with the focus as the center of inversion.
The name was coined by de Castillon in 1741 but had been the subject of study decades beforehand. Named for its heart-like form, it is shaped more like the outline of the cross section of a round apple without the stalk.
A cardioid microphone exhibits an acoustic pickup pattern that, when graphed in two dimensions, resembles a cardioid, (any 2d plane containing the 3d straight line of the microphone body.) In three dimensions, the cardioid is shaped like an apple centred on the microphone which is the "stalk" of the apple.
Based on the rolling circle description, with the fixed circle having the origin as its center, and both circles having radius a, the cardioid is given by the following parametric equations:
They don’t know,
They won’t see,
They won’t change,
They won’t be,
They won’t love,
They won’t go,
They won’t touch,
So they don’t know,
How much it takes for me to stay awake,
Dodging the poisonous darts you throw with your face,
I try to avoid the dark but it’s hard,
When you let go of me like rose pedals in the front yard,
One card, we play till we pass out,
Used to be my ace, now I’m feeling assed out,
So I back out the front porch,
While you reconsider what you really want more,
Me? Nah, I got a knack at leaving you breathless,
Bringing out the smiles that the angels eat for breakfast,
You deadest on watching me step,
Across a bed of coals just to see which arguments next,
Stress don’t leave when you’re next to me,
I’m my kinder side, you’ve got the best of me,
So let’s act like we don’t care,
There’s a moonlit path outside,
We should go there,
And make the clouds part,
I’ll grab you by the wings and you can guide me through the wild part,
Then that smile starts to speak,
Telling me why it’s been gone for weeks,
If it was all on me,
We’d get together right now,
Debate our different lifestyles,
And this is how it might sound,
They don’t know,
They won’t see,
They won’t change,
They won’t be,
They won’t love,
They won’t go,
They won’t touch,
So they don’t know,
What it’s like to wake up to a princess,
Eyes like a lighter, you spark my interest,
We invest too much to be selective,
Ingest solitude then redefine my objective,
Cause that necklace really makes me want to choke you,
Kill all the demons that grab your soul and hold you,
If I could mold you to just my shape,
I’d change absolutely nothing,
Mm that’s great,
Now that we got it all out on the table,
Come here baby girl I want to fuck with your halo,
Grab you by the hips and settle the score,