**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.

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