対称性<br>Symmetries (Springer Undergraduate Mathematics Series (SUMS)) （2001. XI, 198 p. w. 60 figs. 23,5 cm）

個数：

対称性
Symmetries (Springer Undergraduate Mathematics Series (SUMS)) （2001. XI, 198 p. w. 60 figs. 23,5 cm）

  • 提携先の海外書籍取次会社に在庫がございます。通常3週間で発送いたします。
    【重要ご説明事項】
    1. 納期遅延や、ご入手不能となる場合が若干ございます。
    2. 複数冊ご注文の場合、分割発送となる場合がございます。
    3. 美品のご指定は承りかねます。
  • 【入荷遅延について】
    世界情勢の影響により、海外からお取り寄せとなる洋書・洋古書の入荷が、表示している標準的な納期よりも遅延する場合がございます。
    おそれいりますが、あらかじめご了承くださいますようお願い申し上げます。
  • ◆画像の表紙や帯等は実物とは異なる場合があります。
  • ◆ウェブストアでの洋書販売価格は、弊社店舗等での販売価格とは異なります。
    また、洋書販売価格は、ご注文確定時点での日本円価格となります。
    ご注文確定後に、同じ洋書の販売価格が変動しても、それは反映されません。
  • 製本 Paperback:紙装版/ペーパーバック版／ページ数 210 p
  • 商品コード 9781852332709

基本説明

Written by a well-known author (the author of "Elements of Logic via Numbers and Sets"). Includes the derivation and classification of the 17 plane crystallographic groups.

Full Description

" ... many eminent scholars, endowed with great geometric talent, make a point of never disclosing the simple and direct ideas that guided them, subordinating their elegant results to abstract general theories which often have no application outside the particular case in question. Geometry was becoming a study of algebraic, differential or partial differential equations, thus losing all the charm that comes from its being an art." H. Lebesgue, Ler;ons sur les Constructions Geometriques, Gauthier­ Villars, Paris, 1949. This book is based on lecture courses given to final-year students at the Uni­ versity of Nottingham and to M.Sc. students at the University of the West Indies in an attempt to reverse the process of expurgation of the geometry component from the mathematics curricula of universities. This erosion is in sharp contrast to the situation in research mathematics, where the ideas and methods of geometry enjoy ever-increasing influence and importance. In the other direction, more modern ideas have made a forceful and beneficial impact on the geometry of the ancients in many areas. Thus trigonometry has vastly clarified our concept of angle, calculus has revolutionised the study of plane curves, and group theory has become the language of symmetry.

Contents

1 Metric Spaces and their Groups.- 1.1 Metric Spaces.- 1.2 Isometries.- 1.3 Isometries of the Real Line.- 1.4 Matters Arising.- 1.5 Symmetry Groups.- 2 Isometries of the Plane.- 2.1 Congruent Triangles.- 2.2 Isometries of Different Types.- 2.3 The Normal Form Theorem.- 2.4 Conjugation of Isometries.- 3 Some Basic Group Theory.- 3.1 Groups.- 3.2 Subgroups.- 3.3 Factor Groups.- 3.4 Semidirect Products.- 4 Products of Reflections.- 4.1 The Product of Two Reflections.- 4.2 Three Reflections.- 4.3 Four or More.- 5 Generators and Relations.- 5.1 Examples.- 5.2 Semidirect Products Again.- 5.3 Change of Presentation.- 5.4 Triangle Groups.- 5.5 Abelian Groups.- 6 Discrete Subgroups of the Euclidean Group.- 6.1 Leonardo's Theorem.- 6.2 A Trichotomy.- 6.3 Friezes and Their Groups.- 6.4 The Classification.- 7 Plane Crystallographic Groups: OP Case.- 7.1 The Crystallographic Restriction.- 7.2 The Parameter n.- 7.3 The Choice of b.- 7.4 Conclusion.- 8 Plane Crystallographic Groups: OR Case.- 8.1 A Useful Dichotomy.- 8.2 The Case n = 1.- 8.3 The Case n = 2.- 8.4 The Case n = 4.- 8.5 The Case n = 3.- 8.6 The Case n = 6.- 9 Tessellations of the Plane.- 9.1 Regular Tessellations.- 9.2 Descendants of (4, 4).- 9.3 Bricks.- 9.4 Split Bricks.- 9.5 Descendants of (3, 6).- 10 Tessellations of the Sphere.- 10.1 Spherical Geometry.- 10.2 The Spherical Excess.- 10.3 Tessellations of the Sphere.- 10.4 The Platonic Solids.- 10.5 Symmetry Groups.- 11 Triangle Groups.- 11.1 The Euclidean Case.- 11.2 The Elliptic Case.- 11.3 The Hyperbolic Case.- 11.4 Coxeter Groups.- 12 Regular Polytopes.- 12.1 The Standard Examples.- 12.2 The Exceptional Types in Dimension Four.- 12.3 Three Concepts and a Theorem.- 12.4 Schläfli's Theorem.- Solutions.- Guide to the Literature.- Index of Notation.