Famous Problems Of Elementary Geometry: The Duplication Of The Cube, The Trisection Of An Angle, The Quadrature Of The Circle

Famous Problems of Elementary Geometry is a book written by Felix Klein that explores three classical problems in geometry: the duplication of the cube, the trisection of an angle, and the quadrature of the circle. These problems have been studied for centuries and have captured the imagination of mathematicians and non-mathematicians alike. The first problem, the duplication of the cube, involves constructing a cube with twice the volume of a given cube using only a compass and a straightedge. The second problem, the trisection of an angle, involves dividing an angle into three equal parts using only a compass and a straightedge. The third problem, the quadrature of the circle, involves constructing a square with the same area as a given circle using only a compass and a straightedge. Klein provides a historical overview of each problem, discussing the attempts of ancient Greek mathematicians to solve them and the contributions of later mathematicians such as Archimedes, Euclid, and Gauss. He then presents his own solutions to each problem, using modern mathematical techniques such as algebraic geometry and group theory. The book is written in a clear and accessible style, making it suitable for both students and professionals in the field of mathematics. It is a valuable resource for anyone interested in the history of mathematics and the development of geometric concepts.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.