Geometric symmetry (book)

Last updated
Geometric symmetry
Geometric symmetry front cover 1978.jpg
Cover page of the first edition
AuthorE.H. Lockwood and R.H. Macmillan
LanguageEnglish
SubjectGeometry, symmetry
Publisher Cambridge University Press
Publication date
1978
Publication placeUnited Kingdom
Media typePrint
Pages228
ISBN 978-0-521-21685-2
516.1
LC Class QA447.L63
Text Geometric symmetry at Internet Archive

Geometric symmetry is a book by mathematician E.H. Lockwood and design engineer R.H. Macmillan published by Cambridge University Press in 1978. The subject matter of the book is symmetry and geometry.

Contents

Structure and topics

The book is divided into two parts. The first part (chapters 1-13) is largely descriptive and written for the non-mathematical reader. The second part (chapters 14-27) is more mathematical, but only elementary geometrical knowledge is assumed.

In the first part the authors describe and illustrate the following topics: symmetry elements, frieze patterns, wallpaper patterns, and rod, layer and space patterns. The first part also introduces the concepts of continuous, dilation, dichromatic and polychromatic symmetry.

In the second part the authors revisit all of the topics from the first part; but in more detail, and with greater mathematical rigour. Group theory and symmetry are the foundations of the material in the second part of the book. A detailed analysis of the subject matter is given in the appendix below.

The book is printed in two colours, red and black, to facilitate the identification of colour symmetry in patterns.

Audience

In the preface the authors state: "In this book we attempt to provide a fairly comprehensive account of symmetry in a form acceptable to readers without much mathematical knowledge [...] The treatment is geometrical which should appeal to art students and to readers whose mathematical interests are that way inclined." However, Joseph H. Gehringer in a review in The Mathematics Teacher commented "Clearly not intended as a popular treatment of symmetry, the style of the authors is both concise and technical [...] this volume will appeal primarily to those devoting special attention to this field," [1]

Reception

The reception of the book was mixed.

Editions

Appendix: Subject coverage

Geometric symmetry subject coverage
Subject coverage
#ChapterTopics
1Reflexions and rotations Reflection, rotation, central inversion
2Finite patterns in the plane Cyclic symmetry, dihedral symmetry
3Frieze patterns Motif, frieze pattern, frieze group, glide reflection, translation
4Wallpaper patterns Wallpaper pattern, net
5Finite objects in three dimensions Rotary inversion, polyhedra, crystallographic point symmetry
6Rod patterns Rod pattern, helix, screw motion, enantiomorphic
7Layer patterns Layer pattern
8Space patterns Lattice, triclinic, monoclinic, orthorhombic, tetragonal, hexagonal, rhombohedral, cubic, Bravais lattice
9Patterns allowing continuous movement Continuous movement, continuous symmetry of a circle, continuous symmetry of a sphere
10Dilation symmetry Dilation symmetry, On Growth and Form
11Colour symmetry Dichromatic symmetry, polychromatic symmetry, M. C. Escher
12Classify and identifying plane patterns Cell, pattern analysis
13Making patterns Tessellation, regular and semi-regular tessellations, Schläfli symbol
14Movements in the plane Isometry, symmetry movement, symmetry element, direct and opposite isometries, transform of a movement
15Symmetry groups. Point groups Point group, point groups in two dimensions, point groups in three dimensions, crystallographic restriction theorem, Abelian group
16Line groups in two dimensions Line group, translational symmetry
17Nets Net
18Plane groups in two dimensions Plane group
19Movements in three dimensions Rotation in three dimensions, screw rotation
20Point groups in three dimensions Point groups in three dimensions
21Line groups in three dimensions Line groups in three dimensions
22Plane groups in three dimensions Layer group
23Lattices Lattice, Bravais lattice
24Space groups I Diad and tetrad rotations
25Space groups II Triad and hexad rotations, list of space groups
26Limiting groups Limiting groups
27Colour symmetry Dichromatic symmetry, polychromatic symmetry, antisymmetry

References

  1. Gehringer, Joseph H. (1979). "Review". The Mathematics Teacher. 72 (6): 472. doi:10.5951/MT.72.6.0465. JSTOR   27961735.
  2. Firey, W.J. (1978). "Review of Geometric symmetry". zbMATH Open . FIZ Karlsruhe. Zbl   0389.51008 . Retrieved 11 March 2024.
  3. Coxeter, H.S.M. (1978). "Review of Geometric symmetry" . MathSciNet . American Mathematical Society. MR   0514015.
  4. Cundy, H. Martyn (1979). "Review". The Mathematical Gazette . 63 (425): 212–214. doi:10.2307/3617910. JSTOR   3617910.
  5. Grünbaum, Branko; Shephard, Geoffrey Colin (1987). Tilings and patterns . p. 466. ISBN   978-0-716-71193-3. OCLC   13092426.
  6. Lockwood, E.H.; Macmillan, R.H. (1978). Geometric symmetry. Cambridge University Press. p. 228. ISBN   978-0-521-21685-2.
  7. Lockwood, E.H.; Macmillan, R.H. (2008). Geometric symmetry. Cambridge University Press. p. 228. ISBN   978-0-521-09301-9.