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Euclidean Vs Non Euclidean Geometry Essay

806 words - 4 pages

Euclidean Geometry is a type of geometry created about 2400 years ago by the Greek mathematician, Euclid. Euclid studied points, lines and planes. The discoveries he made were organized into different theorems, postulates, definitions, and axioms. The ideas came up with were all written down in a set of books called Elements. Not only did Euclid state his ideas in Elements, but he proved them as well. Once he had one idea proven, Euclid would prove another idea that would have to be true based on what he had just discovered. Euclid was the first person to create this type of mathematical deduction. Out of all the mathematical discoveries Euclid made, one of the most famous would have ...view middle of the document...

For example, look at Riemannian Geometry and how it studies curved surfaces. It is based off of a negation of the fifth postulate that was put forward by Euclid. The negation that Riemann uses is expressed saying that there are no lines that are parallel from an exterior point to another line. Moreover, Lobachevskian Geometry, or otherwise known as Hyperbolic Geometry, works off yet another negation of the fifth postulate. Lobachevsky’s basis consists of having two parallel lines coming from one exterior point to another line. So, from what we have deducted, it seems that any one person can create a geometry just as Lobachevsky and Riemann did. If I were to create my own geometry it would be formed off of the statement of three or more lines being parallel to a line from an exterior point. It would consist of 3-Dimensional concave objects that have been indented inward. This geometry would reveal startling new discoveries in the field of mathematics. To find it, type Tartaglian Geometry in your local database.
In essence, there is a vast variety of geometry types, which each serve to have their own purpose and significance in the mathematical world. Euclidean geometry expressed in Elements has laid the foundation for math involving shapes, planes, points, lines, and astoundingly more. It is because of this geometrical branch of math that students and adults are able to comprehend the basics and specifics of the subject, using easily understood...

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