Lunda Geometry: Mirror Curves, Designs, Knots, Polyominoes, Patterns, Symmetries

Lunda Geometry: Mirror Curves, Designs, Knots, Polyominoes, Patterns, Symmetries
Author: Paulus Gerdes
Publisher: Lulu.com
Total Pages: 204
Release: 2008-06-26
Genre: Art
ISBN: 1435726294
GET BOOK

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 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), 'Visual Mathematics' (Belgrade), and 'Mathematics in School' (UK).

Modularity

Modularity
Author: Werner Callebaut
Publisher: MIT Press
Total Pages: 480
Release: 2005
Genre: Computers
ISBN: 9780262033268
GET BOOK

Modularity—the attempt to understand systems as integrations of partially independent and interacting units—is today a dominant theme in the life sciences, cognitive science, and computer science. The concept goes back at least implicitly to the Scientific (or Copernican) Revolution, and can be found behind later theories of phrenology, physiology, and genetics; moreover, art, engineering, and mathematics rely on modular design principles. This collection broadens the scientific discussion of modularity by bringing together experts from a variety of disciplines, including artificial life, cognitive science, economics, evolutionary computation, developmental and evolutionary biology, linguistics, mathematics, morphology, paleontology, physics, theoretical chemistry, philosophy, and the arts. The contributors debate and compare the uses of modularity, discussing the different disciplinary contexts of "modular thinking" in general (including hierarchical organization, near-decomposability, quasi-independence, and recursion) or of more specialized concepts (including character complex, gene family, encapsulation, and mosaic evolution); what modules are, why and how they develop and evolve, and the implication for the research agenda in the disciplines involved; and how to bring about useful cross-disciplinary knowledge transfer on the topic. The book includes a foreword by the late Herbert A. Simon addressing the role of near-decomposability in understanding complex systems. Contributors: Lee Altenberg, Lauren W. Ancel-Meyers, Carl Anderson, Robert B. Brandon, Angela D. Buscalioni, Raffaele Calabretta, Werner Callebaut, Anne De Joan, Rafael Delgado-Buscalioni, Gunther J. Eble, Walter Fontana, Fernand Gobet, Alicia de la Iglesia, Slavik V. Jablan, Luigi Marengo, Daniel W. McShea, Jason Mezey, D. Kimbrough Oller, Domenico Parisi, Corrado Pasquali, Diego Rasskin-Gutman, Gerhard Schlosser, Herbert A. Simon, Roger D. K. Thomas, Marco Valente, Boris M. Velichkovsky, Gunter P. Wagner, Rasmus G. Winter Vienna Series in Theoretical Biology

Puzzle Fun with BiLLies

Puzzle Fun with BiLLies
Author: paulus gerdes
Publisher: Lulu.com
Total Pages: 78
Release: 2009-11-02
Genre: Games & Activities
ISBN: 055713482X
GET BOOK

Who of us does not like a pastime that can divert and educate at the same time? The puzzles in this book are accessible to teenagers and adults alike, and may be explored individually or in clubs, either in leisure time, or at school.This book "More puzzle fun with biLLies" presents one hundred puzzles, which you can solve using all fourteen 'biLLies', the pieces of the game. For instance, you can make the happy puppet on the front cover using the fourteen 'biLLies'.You will be asked to make certain symmetrical patterns.Have fun with the intriguing and tantalizing 'biLLies'! (76 pp.)

Linknot: Knot Theory By Computer

Linknot: Knot Theory By Computer
Author: Slavik Vlado Jablan
Publisher: World Scientific
Total Pages: 497
Release: 2007-11-16
Genre: Mathematics
ISBN: 9814474037
GET BOOK

LinKnot — Knot Theory by Computer provides a unique view of selected topics in knot theory suitable for students, research mathematicians, and readers with backgrounds in other exact sciences, including chemistry, molecular biology and physics.The book covers basic notions in knot theory, as well as new methods for handling open problems such as unknotting number, braid family representatives, invertibility, amphicheirality, undetectability, non-algebraic tangles, polyhedral links, and (2,2)-moves.Hands-on computations using Mathematica or the webMathematica package LinKnot and beautiful illustrations facilitate better learning and understanding. LinKnot is also a powerful research tool for experimental mathematics implementation of Caudron's ideas. The use of Conway notation enables experimenting with large families of knots and links.Conjectures discussed in the book are explained at length. The beauty, universality and diversity of knot theory is illuminated through various non-standard applications: mirror curves, fullerens, self-referential systems, and KL automata.

Geometry from Africa

Geometry from Africa
Author: Paulus Gerdes
Publisher: Cambridge University Press
Total Pages: 236
Release: 1999-09-30
Genre: Juvenile Nonfiction
ISBN: 9780883857151
GET BOOK

This book draws on geometric ideas from cultural activities from Subsaharan Africa to develop mathematical reasoning.

More Puzzle Fun with BiLLies

More Puzzle Fun with BiLLies
Author: paulus gerdes
Publisher: Lulu.com
Total Pages: 78
Release: 2009-11-02
Genre: Games & Activities
ISBN: 0557134846
GET BOOK

Who of us does not like a pastime that can divert and educate at the same time? The puzzles in this book are accessible to teenagers and adults alike, and may be explored individually or in clubs, either in leisure time, or at school. This book More puzzle fun with biLLies presents one hundred puzzles, which you can solve using all fourteen 'biLLies', the pieces of the game. For instance, you can make the happy puppet on the front cover using the fourteen 'biLLies'. You will be asked to make certain symmetrical patterns. Have fun with the intriguing and tantalizing 'biLLies' (76 pp.)

Otthava

Otthava
Author: Paulus Gerdes
Publisher: Lulu.com
Total Pages: 294
Release: 2010-01-01
Genre: History
ISBN: 0557382904
GET BOOK

In the book "Otthava: Making Baskets and Doing Geometry in the Makhuwa Culture in the Northeast of Mozambique" I reflect on practices in the Makhuwa culture, which provide evidence of the geometric considerations operating in basket weaving, and are suitable and appropriate for mathematical and educational exploration. A proper scientific understanding of this knowledge, and the educational value of these manifestations may lead to a better appreciation of the Makhuwa culture. The practices I present in this book belong to the cultural sphere of 'otthava' - weaving, plaiting, interweaving, interlacing, braiding - that is, to basket- and mat- weaving. The topics which are analysed are the making of funnels, hats, fish traps, containers, trays, dance rattles, purses, decorated braids, baskets and handbags, knots and circular mats (292 pp.) Colour versions of the photographs in the book are published in a separate supplement.

African Pythogoras

African Pythogoras
Author: Paulus Gerdes
Publisher: Lulu.com
Total Pages: 126
Release: 2011
Genre: Education
ISBN: 1257161008
GET BOOK

"AFRICAN PYTHAGORAS: A study in culture and mathematics education" shows how diverse African ornaments and artefacts may be used to create an attractive context for the discovery and the demonstration of the Pythagorean Theorem and of related ideas and propositions. (first full colour edition, 124 pp.)

TINHLÈLÒ

TINHLÈLÒ
Author: Paulus Gerdes
Publisher: Lulu.com
Total Pages: 134
Release: 2010
Genre: Art
ISBN: 0557486254
GET BOOK

The books "TINHLÈLÒ, Interweaving Art and Mathematics: Colourful Basket Trays from the South of Mozambique" exhibits and analyses coloured circular winnowing baskets collected by the author since the end of the 1970s (132 pp. colour).