The Final Eucleidian Solution for the Trisection of Random Acute Angle First Ever Presentation in the History of Geometry

Authors : Giorgios (Gio) Vassiliou

Volume/Issue : Volume 6 - 2021, Issue 5 - May

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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 Eucleidian Geometry. 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 ruler. 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.


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