The book explores the relationship between the geometric properties of the icosahedron and the solution of quintic equations. In the first part, it delves into the theory behind the icosahedron's rotations, while the second part focuses on applying these concepts to understand and solve equations of the fifth degree. Through a blend of geometry and algebra, Felix Klein presents a groundbreaking approach that intertwines mathematical theory with visual representation, making complex concepts more accessible.
German mathematician FELIX KLEIN (1849-1925), a great teacher and scientific thinker, significantly advanced the field of mathematical physics and made a number of profound discoveries in the field of geometry. In his scholarly supplement to Riemann's complex mathematical theory, rather than offer proofs in support of the theorem, Klein chose to offer this exposition and annotation, first published in 1893, in an effort to broaden and deepen understanding. This approach makes Klein's commentary an essential element of any mathematics scholar's library.
The German mathematician Felix Klein (1849-1925), though best known for his systematizing of non-Euclidean geometry, was also an inspiring teacher. This volume -- taken, like its companion volume (Elementary Mathematics from an Advanced Standpoint: Arithmetic, Algebra, Analysis), directly from Professor Klein's exciting lectures to mathematics teachers -- is particularly valuable in the way it uses other fields of mathematics to interpret, adjust, and illuminate geometry.The three-part treatment begins with a consideration of the simplest geometric manifolds: line-segment, area, and volume as relative magnitudes; the Grassmann determinant principle for the plane and the Grassmann principle for space; classification of the elementary configurations of space according to their behavior under transformation of rectangular coordinates; and derivative manifolds. The second section, on geometric transformations, examines affine and projective transformations; higher point transformations; transformations with change of space element; and the theory of the imaginary. The text concludes with a systematic discussion of geometry and its foundations.
Widely regarded as a classic of modern mathematics, this expanded version of Felix Klein's celebrated 1894 lectures uses contemporary techniques to examine three famous problems of antiquity: doubling the volume of a cube, trisecting an angle, and squaring a circle. Today's students will find this volume of particular interest in its answers to such questions as: Under what circumstances is a geometric construction possible? By what means can a geometric construction be effected? What are transcendental numbers, and how can you prove that e and pi are transcendental? The straightforward treatment requires no higher knowledge of mathematics. Unabridged reprint of the classic 1930 second edition.
Originating from Felix Klein's 1895 lectures, this work delves into the mathematical study of the theory of the top. It offers a rich exploration of concepts that remain relevant and enlightening for both students and mathematicians today, making it a valuable resource for understanding the complexities of this field.
Founder of the National Society for Graphology, Felix Klein began his study of graphology in his birthplace, Vienna, Austria, at the age of thirteen. He was a practicing graphologist all of his life and lectured and gave seminars throughout the United States and in Canada, England, Germany, Israel and Mexico. Mr. Klein came to the United States in 1940 after spending six months each in the concentration camps at Dachau and Buchenwald. While in those camps he formulated his theory of directional pressure as a result of studying changes in the handwriting of his fellow inmates. Mr. Klein did extensive work in personnel selection for major companies and banks, vocational guidance, and individual analyses, as well as forensic document examination for such entities as the U.N., AT&T, and a major political figure in Ghana, Africa. It was probably as a teacher that Felix was most known and loved. He held classes and offered correspondence courses in all levels of elementary, intermediate, advanced, Master Research, and Psychology for Graphologists. Wherever Felix spoke, his warm, caring personality and his naturalness and keen sense of humor generated enthusiastic responses from young and old alike.
This work examines the 1st part of Riemann's Theory of Abelian Functions and is extremely useful in its formulations of the topological equivalents of Riemann's surfaces. 1893 edition. Includes 43 figures.
