Post by Ross A. FinlaysonPost by Bret CahillOr at least Archimedes?
"To be the first and the greatest."
-- Nietzsche on the ancient Greeks
I didn't know until recently, that the form of
the Archimedean spiral, with distance between
rings of one, enables the trisection of angles,
the doubling the cube, and the squaring the circle.
There isn't any way to solve impossible problems nor would be for ever and FOR SURE
Post by Ross A. FinlaysonIt's not a classical construction though and the
Archimedean spiral isn't made in classical constructions
(which are finitely many, i.e., trisecting the angle
or squaring the circles takes "infinitely many"
classical constructions).
The tools and construction methods are so irrelevant to all those problems
Post by Ross A. FinlaysonIt might seems Democritus or atomism is closest to calculus
(as we know it today).
There is already exhaustion, though.
These days we have vector calculus.
And calculus is never any true discovery, it is simply and entirely a non-mathematical problem for estimating things not necessary exactly
Calculus is entirely an scientific and engineering problems that was invented solely by them and never by mathematicians, where they succeeded in their practical earthy purposes
And the impossibility of squaring the circle is absolutely because there is no circle to be squared, but regular existing polygons with many sides that seems like a circle for creatures like humans can be exactly squared
The impossibility of trisecting the arbitrary angle is because most of well-known angels in both old and modern mathematics don't strictly exist
And the impossibility of doubling the cube is because 2^{1/3} isn't any existing real number nor can be an exact existing distance relative to any arbitrary existing unity distance, (1^3 + 1^3 = (No number)^3)
Original References: only my public published posts
But everybody knows that people generally love to solve the problems by any means or for any need which is good enough and was made first by carpenter's skill approximations and since ages and before BC, where mathematicians are on the same line, FOR SURE
And as a sincere advice for people not to waste their lives on closed issues for ever, and to be so satisfied by the carpenter's skill for whatever reason you may have in mind
Or simply, go and trisect the trisectible angles by your Origami or paper folding or even by your own eyes, …, etc , or find a cube numbers that you feel are very close to two then claim it as your cube root 2, or find a regular existing polygon with many sides and claim that you got its square root, and the sheeple would be so empresses and very happy by all the magic you do practice on their minds, FOR SURE
Have fun with such problems since your masters were plying those silly games for thousands of years, and you may need some 100000 years to learn all about their tricks
BKK