Thursday, November 21, 2019
Impacts of Johann Carl Friedrich Gauss as a Mathematician Term Paper
Impacts of Johann Carl Friedrich Gauss as a Mathematician - Term Paper Example In his lifetime, Gauss had hardly made a contribution to the field of mathematics. It is said that the German mathematician was aloof to the pubic world of the mathematicians notable in his days. Gauss only communicated to a few of his trusted friends who were also strongly inclined to mathematics. Besides Bolyai, Schumacher was one of Gaussââ¬â¢s trusted correspondence in which the latter confided to the former about his spending a ââ¬Å"considerable time on geometryâ⬠(Tent, 2006, p. 214). On the other hand, upon the death of the gifted mathematician -- and the subsequent discovery of his mathematical notes and ideas -- the world of mathematics had never been the same. Particularly his contribution to the shaping of the so-called non-Euclidean geometry, Gauss had made an impact to the sphere of geometry. His schoolmate Bolyai had asked him, for several times, pertaining to his view to Euclidââ¬â¢s fifth postulate -- also known as the parallel postulate. But Gauss did no t disclose his discovery concerning the existence of the non-Euclidean geometry for the reason that he did not want to ââ¬Å"rock the boatâ⬠(Tent, 2006, p. 215). True, Gaussââ¬â¢s non-Euclidean geometry -- first he called it as anti-Euclidean -- had caused a stir in the area of mathematics marked in the late 18th century. Non-Euclidean geometry is basically defined as an area in geometry in which Euclidââ¬â¢s first four postulates are held but the fifth postulate has a quite different and distinct version in contrast to what is stated in the Elements (Weisstein, 2011). Among various versions of non-Euclidean geometry, the so-called hyperbolic geometry is where Gauss belongs to. In one of their conversations, Gauss revealed to Schumacher about his anti-Euclidean geometry: ââ¬Å"I realized that there also had to be triangles whose three angles add up to more or less than 1800 in the non-Euclidean world. I had it all mapped outâ⬠(Tent, 2006, 214, my italics). Here, Gauss categorized the fundamental elements of his newly found mathematics. That is to say, Gaussââ¬â¢s non-Euclidean geometry is a departure from two-dimensional geometry characterized in Euclidean mathematics. Gaussââ¬â¢s hyperbolic geometry, in fact, works greatly in three-dimensional geometry or space. Thence, the impact of Gaussââ¬â¢s mathematical discovery, if not innovation, was quite evident especially within the field of mathematics. For one, Gauss had opened up a new world or knowledge about the wider space or scope of mathematics, particularly geometry. That is, man does not live in a narrow two-dimensional space. Based from this paradigm (i.e., hyperbolic geometry), one can explore the multifarious possibilities laid open by non-Euclidean geometry. Perhaps the greatest impact of Gaussââ¬â¢s hyperbolic mathematics is found in the sphere of astronomy. In 1801, for instance, Gaussââ¬â¢s mathematics had greatly facilitated the discovery of a dwarf planet named Ceres (Tyson, 2004). Evidently, this is the triumph of mathematics. Utilizing the non-Euclidean geometry, it became possible for man to calculate the universe even without the use of advanced technology such as the telescope. Using Gaussââ¬â¢s hyperbolic geometry, man is able to see the cosmos beyond the Euclidean geometry can offer. Space, after all, is three-dimensional -- be it space in/on earth or in the universe. Generally, non-Euclidean geo
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