ARTICLES MATHEMATICS
Why is Euclid’s fifth postulate unproven and invalid? Chloe ditches the fifth postulate as she turns this fundamental mathematical rule we're all used to on its head. Ching, UC4 Maths has always been a part of our society. From Euclid to Pythagoras to Archimedes to Gauss, all these people have made significant discoveries in the field of mathematics to become the famous mathematicians we know today. One person that stands out to me is Euclid.
prepared to interpret them as we learn, in order to search for absolute perfection. One controversial topic discussed largely amongst mathematicians would be Euclid’s fifth postulate seen in Euclid’s Elements, book 1.
The fifth postulate
Who was Euclid?
The fifth postulate, also known as the parallel postulate, states that
“If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which the angles are less than the two right angles.” In easier words, this postulate says that if angle alpha and angle beta shown in the figure below do not sum to 180 degrees, then there will be a point were line 1 and 2 will eventually intersect.
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Euclid was most famous for his works in geometry, inventing many of the ways we conceive space, time, and shapes. He wrote one of the most famous books that is still used today to teach mathematics: "Elements", which was well received at the time and is praised today for its thought and understanding. In school, we often memorise theorems and proofs given to us by our maths teachers, but how many of us truly understand why the theorem exists, and how the proof came about, be it the area of shapes, circle theorems or The Poincare Conjecture? I’ve certainly never paid much attention to it. But more importantly than simply understanding it, we must keep an open mind to these mathematical formulas and be
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The reason why some people think that the parallel postulate is wrong and thus invalid is because it cannot be drawn if you could draw and satisfy the first four postulates. However, the question is, even if it cannot be drawn, does that mean the geometry is wrong? Furthermore, if we hardly know anything about the universe, can we really understand if the parallel postulate is valid or not?
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