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    • 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

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