There
was a boom in symmetry related basic monographs in the years 2007-2009.
These publications together mark a milestone in
the process of
disciplinarization of symmetrology.
A Birkhäuser book (2007) on
Symmetry
by György Darvas
Flyer and Order form
(.pdf)
by Ian Stewart
Basic Books Inc. (2007)
From Summetria to Symmetry: The Making of a Revolutionary Scientific Concept
by Giora Hon and Bernard R. Goldstein
Series: ARCHIMEDES, New Studies in the History of Science and Technology, Vol. 20
Springer (2008)
How Science and Nature Are Founded on Symmetry
by Joe Rosen
Series:
The Frontiers Collection
Springer (2008)
by
John H. Conway,
Heidi Burgiel,
Chaim Goodman-Strauss
A K Peters, Ltd.
(2008)
Symmetrical Analysis Techniques for Genetic Systems and Bioinformatics:
Advanced Patterns and Applications
by Sergey V. Petoukhov and Matthew He
IGI Global (2009)
Configurations of Points and Lines
by Branko Grünbaum
American Mathematical Society (2009)
Over
the listed scientific monographs there were published a few further
books recently that made a good service for the popularization of
symmetry studies in the wide public and among pupils and undergraduate
students:
Avner Ash and Robert Gross:
Fearless Symmetry, Princeton University Press (2006)
Mark Ronan:
Symmetry and the Monster, Oxford University Press, New York (2006)
Mario Livio:
The golden ratio and aesthetics (2002)
Matrix Genetics, Algebras of
Genetic Code, Noise-immunity
by Sergey V. Petoukhov
(in Russian)
This book describes the utility of matrix methods to
represent and to analyze hierarchical systems of genetic encoding for
mathematical classification and for modeling natural forms of ordering these
systems. The work demonstrates a connection of forms of ordering genetic code
with special algebras, and also with a series of other well known mathematical
structures: Hadamard matrices, double numbers, transformations of hyperbolic turns,
the golden section, the Pythagorean musical scale, etc.These
algebras (e.g., that of quaternions) are related to special multidimensional
geometries. They
permit to develop new models in the fields of molecular genetics,
bioinformatics and mathematical biology in general.
The received data reveal adequacy of matrix
mathematics from the theory of discrete signal processing and noise-immunity
coding to investigate molecular systems of genetic encoding. They give
additional bases to think that structures of genetic code are determined in
many respects by demands of noise-immunity of genetic information.
There are some chapters in the book which refer explicitly to
symmetry: they are chapter VII (Symmetry in finite words and in
languages (p.219-250) and the section "Symmetry phenomena in infinite
words (p.365-372). But there are many other chapters referring to
symmetry phenomena under some specific forms, such as periodocity
and its extensions, (almost periodicity, quasiperiodicity),
attractors,etc.:chapter IV, Numbers as words (p.127-154), chapter IX,
Infinite words (p.337-380), chapter X, Biology and
languages(p.381-432), and chapter XI, Chemistry and languages
(p.433-448)are in this situation.The other chapters too have strong
links with symmetey phenomena.
by Paulus Gerdes
The book 'Lunda Geometry' presents new mathematical ideas
discovered in the context of analysing properties of 'sona' drawings from
Angola.
The book “Lunda Geometry” explains how the mathematical
concepts of mirror curves and Lunda-designs were discovered in the context of
the author’s research of ‘sona’, illustrations traditionally made in the sand by
Cokwe storytellers from eastern
Angola (a region
called Lunda) and neighboring regions of
Congo and
Zambia. Examples of mirror curves from several
cultures (Africa and ancient
Egypt,
South India, Celtic knots, …) are presented. Lunda-designs are aesthetically attractive and
display interesting symmetry properties. Examples of Lunda-patterns and
Lunda-polyominoes are presented. Some
generalizations of the concept of Lunda-design are discussed, like hexagonal
Lunda-designs, Lunda-k-designs, Lunda-fractals, and circular Lunda-designs.
Lunda-designs of Celtic knot designs are
constructed.
Several chapters were published in journals like ‘Computers &
Graphics’ (Oxford), and ‘Visual
Mathematics’ (Belgrade). The first edition of the book had been
published by the ‘Universidade Pedagógica’
(Maputo,
Mozambique) and is out of
print. The new edition is expanded with
two chapters, one published in the book “Symmetry 2000”.
Other books in English by Paulus Gerdes related to the theme of
“Lunda Geometry” are:
“Geometry from Africa” (The Mathematical
Association of America, Washington DC, 1999 (see chapter 4)), “Sona Geometry
from Angola:
Mathematics of an African Tradition” (Polimetrica,
Monza, 2006), “Drawings from
Angola: Living
Mathematics” (Lulu.com, 2007), and “Adventures in the World of Matrices” (Nova
Science Publishers, New York,
2007).
by Paulus Gerdes
From the Preface:
“Over
the years, Paulus Gerdes has established himself as the pre-eminent
expert on patterns in African weaving and basketry, and the broader
implications of these patterns.
<>… This new book is a broad gallery of plaited African designs.
<>
These range over much of the continent while concentrating on those parts of Africa that are closest to his Mozambique center,
including Kongo, Mbole and Mangbetu from Congo, Cokwe and Lunda from
Angola, Digo from Kenya, Soga from Uganda, Zulu from South Africa, and
Makhuwa in Mozambique itself, but including such distant peoples as
Bamileke in Cameroon. As well as careful illustrations of details that might
easily be overlooked by a casual observer, there is enlightening
information about the cultural meaning of particular designs and their
symmetries, both local and global. …
In Gerdes’ gallery we are shown the love of patterns and symmetries that are the result of centuries of exultant exploration.
