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Janos Bolyai was born in December 1802 in Kolozsvar, Hungary. Janos’ father, Farkas Bolyai, was also a mathematician. This most likely where Janos attained his touch in mathematics. He taught Janos much about mathematics and other skills. Janos proved to be a sponge soaking up every bit of knowledge given to him. Farkas Bolyai was a student of mathematical genius Carl Friedrich Gauss, a German mathematician who had made many mathematical discoveries. He tried to persuade Gauss to take Janos and give him the education that Farkas himself had gotten, but Gauss turned him down. This didn’t slow down Janos in his education. He had an amazing learning ability and was able to comprehend complex mathematics at a young age as well as quickly learning new languages. Farkas claimed that Janos had learned everything that Farkas could teach him by the time he was fifteen. Janos could speak many languages, and was very knowledgeable in calculus, trigonometry, algebra, and geometry. He was also a student at the Academy of Military Engineering in Vienna at the young age of 16. He studied for 4 years completing his degree in a little over half the time it took most students. Janos became interested in the problem of the axiom of parallelism or Euclid’s 5th postulate which states, “if a straight line falling on two straight lines make 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 are the angles less than the two right angles.” This was a theory that many mathematicians had tried to prove or disprove using the other postulates since it was created. He was determined to solve the problem despite the attempted dissuasion of his father as his father had also studied the subject extensively with little result. Janos continued to study this subject for sometime even though the college he attended did not have much to teach him in the mathematics field as he already knew most all of it. There is evidence that while still in college, Janos had created a new concept of the axiom of parallelism and a new system of non-Euclidian Geometry. Janos found that it was possible to have consistent geometries that did not fall under the rule of the parallel postulate. Janos’ conclusion was this “The geometry of curved spaces on a saddle-shaped plane, where the angles of a triangle did not add up to 180° and apparently parallel lines were NOT actually parallel.

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## Odysseus: A True Hero

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## odysseus: an epic hero

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## Odysseus, A Hero

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## Greek Influences on Western Civilization

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## Euclid and Mathematics

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