On the Measurement of a Circle, in verse

any form inside the circle's round
has area pi's smaller bound

and has area pi's larger bound
any form which girths the circle round

a square of width the circle's same,
can cover all the circle's frame





a square two by two has area more
so we do know pi is less than four

and where the circle and square do touch
these four points they are enough





to draw a square inside its mentor
also formed by folding corners to center





so area half of the square outside
and sitting so behind the circle hide,

completely covered from our view
it must be pi is more than two.

simple forms such as squares are clear
numerous sides make the bounds cleave near

as the number of sides forever increases
man's uncertainty of pi gently ceases

as the ever tightening of a sailboat's tack
can be none other than the ship's true track 


following the line of the sailboat's wake,
archimedes increases from four to eight





the inside square he expanded, each side nearer
adding four triangles to the form's included area

the square's side length as pythagorous knew
is an irrational quantity called radical two

so each triangle will be radical two wide,
its height will be one minus half the side

to these four triangle's area add the square's two
this is the calculation are to do,

ponder this formula, let the soul wait,
until clear be two radical two the area of the
    inscribed eight.





by four triangles we cut the outside square down
thus more tightly beholding the circle's round

the height of each triangle thus dismissed
is half the square's diagonal minus the radius

and these triangles, they are so tame,
that twice their height and the base are same,

so from four remove four times these triangle's height squared
and to pi's true value we've slowly neared

now again the soul must quietly wait
while the mind calculates radical two minus one, all times eight.

from eight to sixteen to thirty-two to sixty-four
to refine, to calculate, on and on, forevermore

though Zeno claims all motion is futile
by argument both clever and brutal

to arrive at the value which pi must be
i dream this process completed at infinity

and if denied the target for material stuff
in weightless dreams my thought is fleet enough