Elementary Mathmatics from an Advan

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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.