Elementary Mathematics from an Advanced Standpoint: Geometry"Nothing comparable to it." — Mathematics Teacher. This comprehensive 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. 1939 edition. 141 figures. |
Other editions - View all
Elementary Mathematics From an Advanced Standpoint: Geometry; 2 Felix 1849-1925 Klein No preview available - 2021 |
Common terms and phrases
affine afline transformation analytic curve analytic geometry angle arbitrary axes axioms axis called coefficients coeflicients complete components configurations conic consider coordinate system corresponding course cross ratio defined definite determinant directed line-segment discussion distance elementary elements equation Euclid euclidean geometry example expression fact field figure finally find first fixed follows formulas four points free vector functions fundamental given Grassmann Hence homogeneous coordinates imaginary spherical circle infinitely distant intersection invariant theory lectures Leipzig linear substitution manifolds mathematics means metric geometry motion multiplication non-euclidean geometry obtain origin parallel parallel axiom parameters pencil plane at infinity point coordinates polar polygon position postulate principle projective geometry projective transformations quadratic form rays real points rectangular coordinate reflection relation represent rotation satisfied scalar field segment sense significance space sphere straight line surface syzygies tangent tensor tetrahedron theorem theory of invariants tion trans translation triangle unchanged values variables