One Straight Line Between Two Points example essay topic

Euclid Of Alexandria may be the best-known mathematician of the world, he is best known for his work on mathematics The Elements. The fact that his work has survived so long, 2000 years in fact, is a tribute to his mathematical genius, however very little of him is known. Three theories abound as to the true nature of this historical figure. Not all historians agree that Euclid was in fact a historical figure, some argue that the school in Alexandria took up the name Euclid to publish their works. But the more accepted theories are that Euclid was in fact a real historical figure who may have been the leader of a team of mathematicians. In Euclid's first postulate he states that it is possible to draw a straight line from any point to any point.

The first postulate gives meaning to the term "point". For example, any two points such as A and B, there is a line AB that has them as endpoints. In Euclid's second postulate, it is assumed that it is possible to produce a finite straight line continuously in a straight line. In the third postulate, Euclid states that a circle may be drawn with any center and distant (that is radius.) A compass, for example, demonstrates this postulate. When one draws a circle using a compass, one is plotting all the points a certain distance 'r' from the center point. In the next postulate, all right angles are equal to one another.

In the last postulate, it states that through a given point not on a given line exactly one line can be drawn parallel to a given line. Euclid's best-known work, The Elements has survived for over 2000 years and the compilation became the focus of mathematical teaching. Although Euclid (or the school) may have not been first proved by him, (in fact much of his work may have been based upon earlier writings, ) he did manage to insert assumptions and definitions of his own to strengthen the various postulates into the form we know today. The Elements begins with the five postulates and their definitions, these postulates prove or define the existence of points, lines and circles and from there on go to define other aspects of geometry based upon the simpler concepts. The Elements consists of thirteen books. Some assumptions are not totally provable, such that there is only one straight line between two points.

Euclid makes some assumptions that make his form of mathematics, Euclidean Geometry, sometimes at odds with other forms. His fifth postulate, states that only one line can be made through a point parallel to a given line, eventually, sometime during the 19th century this postulate was dropped in an attempt to study non-Euclidean geometries. Euclid's assumptions about his postulates have set the groundwork for geometry today. He provided society with definitions of a circle, a point, and line, etc and for 2000 was considered "the father of geometry". His postulates proved to be a framework from which mathematics was able to grow and evolve, from two thousand years ago, till Newton and even to all our classrooms today.

Bibliography

1. Heath, Sir Thomas. The Thirteen Books of The Elements. New York: Dover Publications, Inc., 1956.
2. "Euclid". Encyclopedia Of World Biography; Volume 5. Encyclopedia Of World Biography, Inc., 1985.