几何导论(第2版)(英文版)
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作者(加)H.S.M.考克斯特
出版社世界图书出版有限公司北京分公司
ISBN9787519285906
出版时间2022-06
装帧平装
开本16开
定价119元
货号31465650
上书时间2024-11-11
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作者简介
H.S.M.考克斯特（Harold Scott MacDonald Coxeter），英国出生的加拿大数学家，他被认为是20世纪伟大的几何学家之一。考克斯特于1931年在英国剑桥大学圣三一学院取得数学博士学位，1936年加入多伦多大学数学系，1980年退休，并一直保留着荣休教授直至1997年过世。考克斯特教授是加拿大皇家学会、英国皇家学会和美国人文与科学院院士，并获得过英国皇家学会的西尔维斯特奖章（Sylvester Medal）和加拿大优选荣誉勋章（Companion of Order of Canada）。他还曾担任加拿大数学会的主席和国际数学家大会的主席。考克斯特教授的研究成果为美国有名建筑师、设计师、发明家、思想家巴克敏斯特•富勒（Buckminster Fuller）的测地线穹顶概念提供了灵感。荷兰有名版画艺术家莫里茨•科内利斯•埃舍尔（M. C. Escher）的经典作品也是深受其影响。考克斯特教授一生著作很多，《几何导论》为其经典代表作品之一。
目录
Part Ⅰ
1 TRIANGLES
1.1 Euclid
1.2 Primitive concepts and axioms
1.3 Pons asinorum
1.4 The medians and the centroid
1.5 The incircle and the circumcircle
1.6 The Euler line and the orthocenter
1.7 The nine-point circle
1.8 Two extremum problems
1.9 Morley's theorem
2 REGULAR POLYGONS
2.1 Cyclotomy
2.2 Angle trisection
2.3 Isometry
2.4 Symmetry
2.5 Groups
2.6 The product of two reflections
2.7 The kaleidoscope
2.8 Star polygons
3 ISOMETRY IN THE EUCLIDEAN PLANE
3.1 Direct and opposite isometries
3.2 Translation
3.3 Glide reflection
3.4 Reflections and half-turns
3.5 Summary of results on isometries
3.6 Hjelmslev's theorem
3.7 Patterns on a strip
4 TWO-DIMENSIONAL CRYSTALLOGRAPHY
4.1 Lattices and their Dirichlet regions
4.2 The symmetry group of the general lattice
4.3 The art of M. C. Escher
4.4 Six patterns of bricks
4.5 The crystallographic restriction
4.6 Regular tessellations
4.7 Sylvester's problem of collinear points
5 SIMILARITY IN THE EUCLIDEAN PLANE
5.1 Dilatation
5.2 Centers of similitude
5.3 The nine-point center
5.4 The invariant point of a similarity
5.5 Direct similarity
5.6 Opposite similarity
6 CIRCLES AND SPHERES
6.1 Inversion in a circle
6.2 Orthogonal circles
6.3 Inversion of lines and circles
6.4 The inversive plane
6.5 Coaxal circles
6.6 The circle of Apollonius
6.7 Circle-preserving transformations
6.8 Inversion in a sphere
6.9 The elliptic plane
7 ISOMETRY AND SIMILARITY IN EUCLIDEAN SPACE
7.1 Direct and opposite isometries
7.2 The central inversion
7.3 Rotation and translation
7.4 The product of three reflections
7.5 Twist
7.6 Dilative rotation
7.7 Sphere-preserving transformations
Part Ⅱ
8 COORDINATES
8.1 Cartesian coordinates
8.2 Polar coordinates
8.3 The circle
8.4 Conics
8.5 Tangent, arc length, and area
8.6 Hyperbolic functions
8.7 The equiangular spiral
8.8 Three dimensions
9 COMPLEX NUMBERS
9.1 Rational numbers
9.2 Real numbers
9.3 The Argand diagram
9.4 Modulus and amplitude
9.5 The formula eπi + 1 = 0
9.6 Roots of equations
9.7 Conformal transformations
10 THE FIVE PLATONIC SOLIDS
10.1 Pyramids, prisms, and antiprisms
10.2 Drawings and models
10.3 Euler's formula
10.4 Radii and angles
10.5 Reciprocal polyhedra
11 THE GOLDEN SECTION AND PHYLLOTAXIS
11.1 Extreme and mean ratio
11.2 De divina proportione
11.3 The golden spiral
11.4 The Fibonacci numbers
11.5 Phyllotaxis
Part Ⅲ
12 ORDERED GEOMETRY
12.1 The extraction of two distinct geometries from Euclid
12.2 Intermediacy
12.3 Sylvester's problem of collinear points
12.4 Planes and hyperplanes
12.5 Continuity
12.6 Parallelism
13 AFFINE GEOMETRY
13.1 The axiom of parallelism and the \"Desargues\" axiom
13.2 Dilatations
13.3 Affinities
13.4 Equiaffinities
13.5 Two-dimensional lattices
13.6 Vectors and centroids
13.7 Barycentric coordinates
13.8 Affine space
13.9 Three-dimensional lattices
14 PROJECTIVE GEOMETRY
14.1 Axioms for the general projective plane
14.2 Projective coordinates
14.3 Desargues's theorem
14.4 Quadrangular and harmonic sets
14.5 Projectivities
14.6 Collineations and correlations
14.7 The conic
14.8 Projective space
14.9 Euclidean space
15 ABSOLUTE GEOMETRY
15.1 Congruence
15.2 Parallelism
15.3 Isometry
15.4 Finite groups of rotations
15.5 Finite groups of isometries
15.6 Geometrical crystallography
15.7 The polyhedral kaleidosc
内容摘要
本书是英国皇家学会院士H.S.M.考克斯特所著的几何学名著。考克斯特用现代的观点阐释了从欧几里得平面几何到仿射几何、射影几何、微分几何和拓扑等经典几何的内容。书中汇集了基础几何的各种定理、变换、几种几何的公理化发展、曲线和曲面的微分几何以及曲面的拓扑等主题。正如考克斯特在序言中所说，“贯穿整部作品的统一主线是变换，或者说是对称性的思想”。变换提供了动态的，而非静态的几何观点。本书被认为是最重要的几何学书籍之一，任何对几何感兴趣的读者都应该阅读。
主编推荐
•英国皇家学会院士H.S.M.考克斯特所著的经典名著
•经典几何的现代观点阐释
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