Euclid and His Contributions to Mathematics
Euclid and His Contributions to Mathematics
Euclid was an ancient Greek mathematician from Alexandria who is best known for his major work,
Elements.
Although little is known about Euclid the man, he taught in a school that he founded in Alexandria, Egypt, around 300 b.c.e. For his major study,
Elements,
Euclid collected the work of many mathematicians who preceded him. Among these were Hippocrates of Chios, Theudius, Theaetetus, and Eudoxus. Euclid 's vital contribution was to gather, compile, organize, and rework the mathematical concepts of his predecessors into a consistent whole, later to become known as Euclidean geometry. Euclidean constructions are the shapes and figures that can be produced solely by a compass and an unmarked straightedge. Although these tools were indeed simple, their range of abilities seemed unlimited. Not only could they produce a multitude of angles and lengths, but also elegantlooking regular polygons and a wide variety of 2D shapes with desired area. These basic tools seemed to be able to do or produce anything. When, after countless attempts, they were unable to solve the three classical problems of trisecting an angle, doubling the cube, and squaring the circle, the Greeks were forced to reach out to new and more complicated instruments. It was the inadequacy in these three problems that helped make mathematicians realize that some aspects of mathematics could not be done with real world instruments and that sometimes it must rely on purely symbolic methods. Yet, some still held on to the belief that the traditional compass and straightedge could answer all their questions and were persistent in their efforts to find the means. However, after almost 2000 years of use, the limitations of the compass and unmarked straightedge were discovered by one of the most abstract and symbolic areas of mathematics: field theory and abstract algebra. These subjects showed, once and for all, exactly what the
Euclid was an ancient Greek mathematician from Alexandria who is best known for his major work,
Elements.
Although little is known about Euclid the man, he taught in a school that he founded in Alexandria, Egypt, around 300 b.c.e. For his major study,
Elements,
Euclid collected the work of many mathematicians who preceded him. Among these were Hippocrates of Chios, Theudius, Theaetetus, and Eudoxus. Euclid 's vital contribution was to gather, compile, organize, and rework the mathematical concepts of his predecessors into a consistent whole, later to become known as Euclidean geometry. Euclidean constructions are the shapes and figures that can be produced solely by a compass and an unmarked straightedge. Although these tools were indeed simple, their range of abilities seemed unlimited. Not only could they produce a multitude of angles and lengths, but also elegantlooking regular polygons and a wide variety of 2D shapes with desired area. These basic tools seemed to be able to do or produce anything. When, after countless attempts, they were unable to solve the three classical problems of trisecting an angle, doubling the cube, and squaring the circle, the Greeks were forced to reach out to new and more complicated instruments. It was the inadequacy in these three problems that helped make mathematicians realize that some aspects of mathematics could not be done with real world instruments and that sometimes it must rely on purely symbolic methods. Yet, some still held on to the belief that the traditional compass and straightedge could answer all their questions and were persistent in their efforts to find the means. However, after almost 2000 years of use, the limitations of the compass and unmarked straightedge were discovered by one of the most abstract and symbolic areas of mathematics: field theory and abstract algebra. These subjects showed, once and for all, exactly what the
Cited: 1 Aug. 2015< http://www.encyclopedia.com . Web. 1 Aug. 2015.