Euler formula poem

     Sometimes I try to write a poem that explains a mathematical concept -- it's a difficult task  My effort usually results in something that sounds more like a textbook paragraph than a poem.  And I was thereby hugely delighted (following a lead from Colm Mulcahy) to discover this poem by Grant Sanderson that has fun with a famous mathematical formula due to Euler:

e^iπ + 1 = 0     or, stated differently      e^iπ = -1

Euler Formula    by Grant Sanderson 

Famously
start with e,
raise to π
with an i,
we've been taught
by a lot
that you've got
minus one.

Can we glean
what it means?
For such words
are absurd.
How to treat
the repeat
of a feat
πi times?

This is bound
to confound
'til your mind
redefines
these amounts
one can't count
which surmount
our friend e.

Numbers act
as abstract
functions which
slide the rich
2d space
in its place
with a grace
when they sum.

Multiplied,
they don’t slide,
acting a
second way.
They rotate,
and dilate,
but keep straight
that same plane.

Now what we
write as e
to the x
won’t perplex
when you know
it’s for show
that “x” goes
up and right.

It does not,
as you thought,
repeat e
product e.
It functions
with gumption
on functions
of the plane.

It turns slides
side to side
into growths
and shrinks both.
Up and downs
come around
as turns round,
which is key!

This is why
π times i,
which slides north
is brought forth
and returned,
we have learned,
as a turn
halfway round.

Minus one,
matched by none,
turns this way,
hence we’re done.

The text of Sanderson's poem is online here.  -- and even more fun is found by following this link to an animated video version.