Elementary Mathematics from an Advanced Standpoint
Geometry| By: | Felix Klein |
| Publisher: | Dover Publications |
| Print ISBN: | 9780486434810 |
| eText ISBN: | 9780486167411 |
| Edition: | 0 |
| Format: | Reflowable |
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"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.