An Overview of the Different Types of Geometry and Their Purposes

An Overview of the Different Types of Geometry and Their Purposes

Document details
Category: Mathematics Essay
Subcategory: Statistics and Probability
Words: 628
Pages: 3

Euclidean Geometry EssayThere are many different types of geometry. Some examples include, Euclidean, elliptic, and hyperbolic. But what do they do? And how do you use them? Euclidean geometry is a system consisting of that assuming a small set of intuitively appealing axioms, and deducing many other propositions. Elliptic geometry is as in which, given a line L and a point p outside L, there exists no line parallel to L passing through p, as all lines in elliptic geometry intersect. Finally, hyperbolic geometry is, in two-dimensional space, for any given line R and point P not on R, there is exactly one line through P that does not intersect R that is parallel to R.Euclidean geometry was founded by none other than Euclid himself. For more than two-thousand years, the word Euclidean was not included in the title, because there were no other types of geometry before Euclidean. Euclidian geometry is an example of synthetic geometry. That means it logically uses axioms and propositions without coordinates. Euclidean geometry has two fundamental types of measurements angle and distance. The right angle is the basic unit in this geometry, and all the other measurements are based off of 90 degrees. Measurements of area and volume are derived from distances. For example, a rectangle with a width of 3 and a length of 4 has an area that represents the product, 12. Elliptic geometry was founded by Bernhard Riemann. The name "elliptic" is possibly misleading. It does not imply any direct connection with the curve called an ellipse, but only a rather far-fetched analogy. A simple way to picture elliptic geometry is to look at a globe. There are two different types of line around a sphere, latitude and longitude. In Euclidean geometry, a figure can be scaled up or scaled down indefinitely, and the resulting figures are congruent. This is not the case in elliptic geometry. For example, in the spherical model we can see...

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