Transformation geometry : an introduction to symmetry

George E. Martin

This is a modern approach to Euclidean geometry. This study of the automorphism groups of the plane and space gives the classical concrete examples that serve as a meaningful preparation for the standard undergraduate course in abstract algebra. The detailed development of the isometries of the plane is based on only the most elementary geometry and is appropriate for graduate courses for secondary teachers. A separate instruction manual is available.

「Nielsen BookData」より

Transformation Geometry: An Introduction to Symmetry offers a modern approach to Euclidean Geometry. This study of the automorphism groups of the plane and space gives the classical concrete examples that serve as a meaningful preparation for the standard undergraduate course in abstract algebra. The detailed development of the isometries of the plane is based on only the most elementary geometry and is appropriate for graduate courses for secondary teachers.

「Nielsen BookData」より

[目次]

  • Properties of transformations
  • translations and halfturns
  • reflections
  • congruence
  • the product of two reflections
  • even isometries
  • classification of plane isometries
  • equations for isometries
  • the seven frieze groups
  • the seventeen wallpaper groups
  • tessellations
  • similarities on the plane
  • classical theorems
  • affine transformations
  • transformations on three-space
  • space and symmetry
  • hints and answers.

「Nielsen BookData」より

[目次]

  • 1 Introduction.- 1.1 Transformations and Collineations.- 1.2 Geometric Notation.- 1.3 Exercises.- 2 Properties of Transformations.- 2.1 Groups of Transformations.- 2.2 Involutions.- 2.3 Exercises.- 3 Translations and Halfturns.- 3.1 Translations.- 3.2 Halfturns.- 3.3 Exercises.- 4 Reflections.- 4.1 Equations for a Reflection.- 4.2 Properties of a Reflection.- 4.3 Exercises.- 5 Congruence.- 5.1 Isometries as Products of Reflections.- 5.2 Paper Folding Experiments and Rotations.- 5.3 Exercises.- 6 The Product of Two Reflections.- 6.1 Translations and Rotations.- 6.2 Fixed Points and Involutions.- 6.3 Exercises.- 7 Even Isometries.- 7.1 Parity.- 7.2 The Dihedral Groups.- 7.3 Exercises.- 8 Classification of Plane Isometries.- 8.1 Glide Reflections.- 8.2 Leonardo's Theorem.- 8.3 Exercises.- 9 Equations for Isometries.- 9.1 Equations.- 9.2 Supplementary Exercises (Chapter 1-8).- 9.3 Exercises.- 10 The Seven Frieze Groups.- 10.1 Frieze Groups.- 10.2 Frieze Patterns.- 10.3 Exercises.- 11 The Seventeen Wallpaper Groups.- 11.1 The Crystallographic Restriction.- 11.2 Wallpaper Groups and Patterns.- 11.3 Exercises.- 12 Tessellations.- 12.1 Tiles.- 12.2 Reptiles.- 12.3 Exercises.- 13 Similarities on the Plane.- 13.1 Classification of Similarities.- 13.2 Equations for Similarities.- 13.3 Exercises.- 14 Classical Theorems.- 14.1 Menelaus, Ceva, Desargues, Pappus, Pascal.- 14.2 Euler, Brianchon, Poncelet, Feuerbach.- 14.3 Exercises.- 15 Affine Transformations.- 15.1 Collineations.- 15.2 Linear Transformations.- 15.3 Exercises.- 16 Transformations on Three-space.- 16.1 Isometries on Space.- 16.2 Similarities on Space.- 16.3 Exercises.- 17 Space and Symmetry.- 17.1 The Platonic Solids.- 17.2 Finite Symmetry Groups on Space.- 17.3 Exercises.- Hints and Answers.- Notation Index.

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この本の情報

書名 Transformation geometry : an introduction to symmetry
著作者等 Martin, George Edward
Martin G.E. (State University of New York Albany USA)
Martin George E.
シリーズ名 Undergraduate texts in mathematics
出版元 Springer-Verlag
刊行年月 c1982
版表示 1st ed. 1982. Corr. 4th printing 1996
ページ数 xii, 237 p.
大きさ 25 cm
ISBN 3540906363
0387906363
NCID BA01218048
※クリックでCiNii Booksを表示
言語 英語
出版国 アメリカ合衆国
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