The Real Projective Plane (Hardcover)

Product Description
This introduction to projective geometry can be understood by anyone familiar with high-school geometry and algebra. The restriction to real geometry of two dimensions allows every theorem to be illustrated by a diagram. The subject is, in a sense, even simpler than Euclid, whose constructions involved a ruler and compass: here we have constructions using rulers alone. A strict axiomatic treatment is followed only to the point of letting the student see how it is done, but then relaxed to avoid becoming tedious. After two introductory chapters, the concept of continuity is introduced by means of an unusual but intuitively acceptable axiom. Subsequent chapters then treat one- and two-dimensional projectivities, conics, affine geometry, and Euclidean geometry. Chapter 10 continues the discussion of continuity at a more sophisticated level, and the remaining chapters introduce coordinates and their uses. An appendix by George Beck describes Mathematica scripts that can generate illustrations for several chapters; they are provided on a diskette included with the book. (Both PC and Macintosh versions are available) Mathematica is a registered trademark.

First Sentence:
1.1 Introduction. The ordinary geometry taught in school, dealing with circles, angles, parallel lines, similar triangles and so on, is called Euclidean geometry because it was first collected into a systematic account by the Greek geometer Euclid, who lived about 300 B.C. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
quadrangular involution, degenerate polarity, harmonic net, hyperbolic projectivity, absolute involution, quadrangular set, trilinear pole, elliptic projectivity, given projectivity, hyperbolic involution, one invariant point, trilinear polar, hyperbolic polarity, two invariant points, harmonic homology, real projective geometry, three distinct collinear points, harmonic conjugates with respect, harmonic homologies, elliptic involution, opposite correspondence, right bisector, conjugate lines, elementary correspondences, ordered correspondence Key Phrases - Capitalized Phrases (CAPs): (learn more)
Alex Rosenberg, Blaise Pascal New!
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