Love on the spectrum. How much do I love thee?
Three π on two

Exactly how much do I love thee?
Without your love, my heart is empty.
Love for you fills up my core.
—lub dup lub dup lub dup—
Every beat cries out for more.

… So, how much do I love thee? …

Love must attempt the mensuration;
A cardioid invites summation.
Rectilinear forms won't play
—Abandon orthonormal axes—
Polar systems, show the way.

Let's model with the function:

Radius, r, equals one minus sine of the
Angle of θ with range
(Closed interval):
Nought below
Up to
2π.

… Drum roll …

A double integral is taken,
With element of this summation:
r dθ times dr
—We must respect the proper order—
θ shall be summed before.

… Evaluating limits …

Integrand after the first integration
Is 2πr minus nought r;
Limits about
Half⋅r squared⋅2⋅π:
Three π
On two.

?Ahhh?

Q-E-diddly-D

~~~~~~~~
It's all about the timing …