- 几何导论(第2版)(英文版)
- - 作者：(加)H.S.M.考克斯特|责编:陈亮
  - 出版社：世图出版公司
  - ISBN：9787519285906
  - 出版日期：2022/06/01
  - 页数：469
- 售价：47.6

内容大纲
第一部分三角形：欧几里得几何学；基本概念和公理；驴桥定理；中线和重心；内切圆和外接圆；欧拉线和垂心；九点圆；两个极值问题；Morley定理；正多边形；分圆法；三等分角；等距变换；对称；群；两镜面反射的乘积；万花筒；星形多边型。欧几里得平面几何学：正反等距变换；平移；滑移反射；反射和180度旋转；等距变换结论总结；定律；长条形上的图案模式。二维空间晶体结构：格及Dirichlet区域；一般格上的对称群；埃舍尔的艺术；积木的六种模式；晶体结构约束；正则镶嵌；多点共线问题。欧几里得平面的相似性：伸缩。
作者介绍
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 kaleidoscope
    15.8  Discrete groups generated by inversions
  16  HYPERBOLIC GEOMETRY
    16.1  The Euclidean and hyperbolic axioms of parallelism
    16.2  The question of consistency
    16.3  The angle of parallelism
    16.4  The finiteness of triangles
    16.5  Area and angular defect
    16.6  Circles, horocycles, and equidistant curves
    16.7  Poincaré's "half-plane" model
    16.8  The horosphere and the Euclidean plane
Part Ⅳ
  17  DIFFERENTIAL GEOMETRY OF CURVES
    17.1  Vectors in Euclidean space
    17.2  Vector functions and their derivatives
    17.3  Curvature, evolutes, and involutes
    17.4  The catenary
    17.5  The tractrix
    17.6  Twisted curves
    17.7  The circular helix
    17.8  The general helix
    17.9  The concho-spiral
  18  THE TENSOR NOTATION
    18.1  Dual bases

    18.2  The fundamental tensor
    18.3  Reciprocal lattices
    18.4  The critical lattice of a sphere
    18.5  General coordinates
    18.6  The alternating symbol
  19  DIFFERENTIAL GEOMETRY OF SURFACES
    19.1  The use of two parameters on a surface
    19.2  Directions on a surface
    19.3  Normal curvature
    19.4  Principal curvatures
    19.5  Principal directions and lines of curvature
    19.6  Umbilics
    19.7  Dupin's theorem and Liouville's theorem
    19.8  Dupin's indicatrix
  20  GEODESICS
    20.1  Theorema egregium
    20.2  The differential equations for geodesics
    20.3  The integral curvature of a geodesic triangle
    20.4  The Euler-Poincaré characteristic
    20.5  Surfaces of constant curvature
    20.6  The angle of parallelism
    20.7  The pseudosphere
  21  TOPOLOGY OF SURFACES
    21.1  Orientable surfaces
    21.2  Nonorientable surfaces
    21.3  Regular maps
    21.4  The four-color problem
    21.5  The six-color theorem
    21.6  A sufficient number of colors for any surface
    21.7  Surfaces that need the full number of colors
  22  FOUR-DIMENSIONAL GEOMETRY
    22.1  The simplest four-dimensional figures
    22.2  A necessary condition for the existence of(p, q, r)
    22.3  Constructions for regular polytopes
    22.4  Close packing of equal spheres
    22.5  A statistical honeycomb
TABLES
REFERENCES
ANSWERS To EXERCISES
INDEX

内容大纲

作者介绍

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