A brief introduction about the Eucleidian
solution’s “impossibility” of the trisection problem…
The historic problem of Eucleidian trisection for a
random acute angle, was involved humanity, from 6th
century BC without any interruption untill the late 19th
century, by not finding a satisfied solution according to
The trisection is an equal achievement of making
the "impossible" into possible, because there is a huge list
of names, that includes the greatest genius
mathematicians of all times, such as: Hippocrates of
Chios, Archimedes, Nicomedes, Descartes, Pascal and
Lagrance that all failed to give a satisfied solution
according to Eucleidian Geometry!
Never the less non-Eucleidian solutions have been
presented in the past, such as the Archimedes's Neusis
method, that requires a measured straight edge with
The ancient Greeks found that certain angles could
be trisected rather easily. The problem of trisecting a
right angle is a relatively simple process.But the real
trisection problem emerges, when we have to deal with an
unknown acute angle.
Furthermore Pierre Wantzel's theorem of trisection
impossibility, presented in the mid 19th century (1837),
gave birth to more speculations about the already existing
myth of the problem.
Since then almost two centuries have passed, and
now in 21st century, things have changed dramatically.
We all realise that future overcomes the limitations of the
past and what remained "impossible" , now becomes
possible. The most difficult achievement for human
intellectuality, always remains this: to make something
that is simple to become simplier!And whenever this is
happened as a fact, is regarded by all historians as a
milestone. This very moto is the basis (or the inspiration if
you ou want) of the newly arrived final solution of
random acute angle's trisection, presented in this paper.!
As we have already mentioned, the limitations of the
past becomes the offspring for the future!
This future has just arrived as present time and
after so many centuries since antiquity, the Eucleidian
solution for angle's trisection is a fact.
2500 years of "impossibity" have just ended and by
doing so, this fact arrises new hopes to scientific
researcher, amateurs or professionals, for even greater
accomplishment in the future of humanity.