From the Cartesian plane, adviceto keep challenging "Impossible!".
Favard’s New Echo
In circles squared and well-aligned,
Search for quadrature stay'd confined.
"Impossible!" mathematics oft said,
Yet patterns winced "Awake instead!"
A constant first, then two appeared,
From Fourier, as if they’d neared.
And circle echoed back the sound:
"Favard’s numbers still be found!"
Despite old lectures on sacred Pi,
In powers still climbing to the sky,
More constants sing, oft soft y'know -
Favard’s New Echo begins to grow.
"Infinitesimal points!" they shout
upon circumference round about.
Yet eight of these secure the lock
where circle's, square's area dock!
So, ask again with mind thus flared
"How can circle not be squared?!"
For quadrature hides in concord sweet,
Pythagorean guidance so complete!
Pi^2/8 and constants mate,
in Pi corral o'er Cartesian plate.
Derisive "Cyclometricus!"
energizes these Morbus.
"Impossible!" task all agree,
but fewer doubt, incredibly,
that areas, mathematically,
exist in squares - not reverie.
Upon such square a circle's eight
connecting points, concentric fate.
In g'ometry with math perspective,
new ratios rise, Favard reflective.
Very long story short ...diameter/(perimeter/4) = perimeter/circumference
proves a circle and its square have the same area,
but cannot prove the "circle is squared".
Rod
