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. |
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Elementary Mathematics From an Advanced Standpoint: Geometry; 2 Felix 1849-1925 Klein No preview available - 2021 |
Common terms and phrases
a₁ affine geometry affine transformation analytic geometry angle arbitrary axes axioms axis b₁y b₂y called coefficients complete components configurations conic consider coordinate system corresponding course cross ratio curve defined definite determinant directed line-segment discussion elementary equation Euclid Euclid's Elements euclidean geometry example expression fact finite follows formulas free plane-magnitude free vector functions fundamental given Grassmann Hence homogeneous coordinates imaginary spherical circle infinitely distant infinity intersection invariant theory Leipzig linear substitution magnitudes manifolds mathematics means metric geometry Möbius motion non-euclidean geometry obtain origin P₁ parallel parallel axiom parameters plane at infinity point coordinates polar polygon position postulates projective geometry projective transformations quadratic rays real points rectangular coordinate relation represent rotation scalar segment sense space sphere straight line surface syzygies tangent tensor tetrahedron theorem theory of invariants tion translation triangle unchanged values variables дх