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Lectures on Analytic and Projective Geometry [Pehme köide]

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  • Formaat: Paperback / softback, 304 pages, kõrgus x laius x paksus: 203x136x14 mm, kaal: 280 g
  • Sari: Dover Books on Mathema 1.4tics
  • Ilmumisaeg: 24-Oct-2011
  • Kirjastus: Dover Publications Inc.
  • ISBN-10: 0486485951
  • ISBN-13: 9780486485959
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Lectures on Analytic and Projective GeometrySuurem pilt
  • Formaat: Paperback / softback, 304 pages, kõrgus x laius x paksus: 203x136x14 mm, kaal: 280 g
  • Sari: Dover Books on Mathema 1.4tics
  • Ilmumisaeg: 24-Oct-2011
  • Kirjastus: Dover Publications Inc.
  • ISBN-10: 0486485951
  • ISBN-13: 9780486485959
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780486485959.html
Märksõnad:
This text is based on a historic approach used at MIT to teach projective geometry to junior and senior undergraduates. The author develops the geometry of plane and space, leading up to conics and quadrics, within the context of metrical, affine, and projective transformations. Prerequisites include three semesters of calculus and analytic geometry. 1953 edition.


This undergraduate text develops the geometry of plane and space, leading up to conics and quadrics, within the context of metrical, affine, and projective transformations. 1953 edition.
Chapter 1 Point Sets on a Line
1(24)
1-1 The oriented line
1(1)
1-2 Division ratio
2(2)
1-3 Harmonic sets
4(3)
1-4 Cross ratio
7(3)
1-5 Projectivity
10(2)
1-6 Projectivities on the same line
12(3)
1-7 Involutions
15(5)
1-8 Introduction of imaginary elements
20(5)
Chapter 2 Line Pencils
25(27)
2-1 The Cartesian equation of a line
25(4)
2-2 Invariance of the orientation
29(2)
2-3 Pencils of lines
31(1)
2-4 Three and four lines
32(3)
2-5 Theorem of Desargues
35(3)
2-6 Division ratio
38(3)
2-7 Cross ratio
41(2)
2-8 Duality
43(2)
2-9 Complete quadrilateral and quadrangle
45(4)
2-10 Projectivity in a pencil
49(3)
Chapter 3 Line Coordinates. Homogeneous Coordinates
52(32)
3-1 The "new" geometry
52(2)
3-2 Line coordinates
54(2)
3-3 Duality in point and line coordinates
56(2)
3-4 Homogeneous Cartesian coordinates
58(2)
3-5 Other homogeneous coordinates
60(2)
3-6 Projective coordinates
62(2)
3-7 Properties of projective coordinates
64(4)
3-8 Transformation of projective coordinates
68(4)
3-9 The projective plane
72(3)
3-10 Orientable and nonorientable surfaces
75(5)
3-11 Affine geometry
80(4)
Chapter 4 Transformations of the Plane
84(26)
4-1 Active and passive transformations
84(1)
4-2 Collineations
85(1)
4-3 Classification of collineations
86(3)
4-4 Correlations
89(2)
4-5 Affine transformations
91(1)
4-6 Vectors in affine geometry
92(4)
4-7 Affine transformations as deformations
96(2)
4-8 Orthogonal transformations
98(3)
4-9 Vectors in Euclidean geometry
101(3)
4-10 Groups
104(2)
4-11 The Erlangen program
106(4)
Chapter 5 Projective Theory of Conics
110(24)
5-1 Curves of the second order
110(2)
5-2 Singular curves of the second order
112(1)
5-3 Curves of the second class
112(2)
5-4 The nonsingular conic
114(3)
5-5 Poles and polars
117(3)
5-6 Self-polar triangles
120(1)
5-7 Polarity
121(1)
5-8 Projective classification of conics
122(4)
5-9 Pencils of conics
126(2)
5-10 Theorems of Pascal and Brianchon
128(6)
Chapter 6 Affine and Euclidean Theory of Conics
134(29)
6-1 Conjugate diameters
134(2)
6-2 Affine classification of conics
136(3)
6-3 Some affine constructions
139(1)
6-4 Euclidean classification of conics
140(3)
6-5 Reduction to the normal form
143(6)
6-6 The circle
149(8)
6-7 Foci
157(6)
Chapter 7 Projective Metric
163(11)
7-1 Metric with respect to a singular conic
163(1)
7-2 Angle with respect to a nonsingular conic
164(2)
7-3 Distance with respect to a nonsingular conic
166(1)
7-4 Non-Euclidean geometry
167(2)
7-5 Klein's interpretation of hyperbolic geometry
169(2)
7-6 Elliptic geometry
171(3)
Chapter 8 Points, Lines, and Planes
174(20)
8-1 Projective coordinates
174(2)
8-2 Projective transformations
176(1)
8-3 Line coordinates
177(3)
8-4 Affine space
180(1)
8-5 Vectors and bivectors
181(3)
8-6 Euclidean geometry
184(3)
8-7 Oriented Euclidean space
187(3)
8-8 Points, lines, planes in Euclidean geometry
190(4)
Chapter 9 Projective Theory of Quadrics
194(12)
9-1 Intersections and tangents
194(2)
9-2 Class quadric
196(1)
9-3 Polar relationship
197(2)
9-4 Projective classification of quadrics
199(2)
9-5 The regulus
201(5)
Chapter 10 Affine and Euclidean Theory of Quadrics
206(24)
10-1 Center and conjugate directions
206(2)
10-2 The affine normal forms
208(2)
10-3 Paraboloid and cylinder
210(3)
10-4 The S-equation
213(5)
10-5 Double roots of the S-equation
218(2)
10-6 Paraboloids
220(3)
10-7 Pencils of quadrics
223(4)
10-8 Confocal quadrics
227(3)
Chapter 11 Transformations of Space
230(31)
11-1 Collineations
230(2)
11-2 Central projection
232(1)
11-3 Perspective
233(4)
11-4 Parallel projection
237(3)
11-5 Orthogonal axonometry
240(3)
11-6 Orthographic projection
243(3)
11-7 Drawing in solid geometry
246(2)
11-8 Correlations
248(2)
11-9 Null system, projective theory
250(2)
11-10 Null system, affine and Euclidean theory
252(4)
11-11 Forces
256(2)
11-12 Force systems
258(3)
Special Exercises 261(5)
Collateral Reading 266(2)
Answers to Exercises 268(14)
Index 282