Based on a historic approach taken by instructors at MIT, this text is geared toward junior and senior undergraduate courses in analytic and projective geometry. Starting with concepts concerning points on a line and lines through a point, it proceeds to the geometry of plane and space, leading up to conics and quadrics developed within the context of metrical, affine, and projective transformations. The algebraic treatment is occasionally exchanged for a synthetic approach, and the connection of the geometrical material with other fields is frequently noted. Prerequisites for this treatment include three semesters of calculus and analytic geometry. Special exercises at the end of the book introduce students to interesting peripheral problems, and solutions are provided.Prove that an algebraic curve in space intersected by a line in two (real, imaginary, coincident) points is a conic. 14. ... aIn a general positiona means that the nine equations for the ratio of the 111, , are independent. ... If P), = 0 is the polar plane of Aagt;, with respect to aagt;, , , xagt;.a:, , = 0, then the line connecting A1 (1:O: 0:O), with the pole B1 of face A2A3A4 is x=_Ar:x3:x.1 = a12:a1_~, :a14 (ax, cofactors). ... Take one of the parallel planes as a coordinate plane and project the sections on it. 6.
|Title||:||Lectures on Analytic and Projective Geometry|
|Author||:||Dirk J. Struik|
|Publisher||:||Courier Corporation - 2014-03-05|