Publikationen
Perspectives on Projective Geometry
Projective geometry is one of the most fundamental and at the same time most beautiful branches of geometry. It can be considered the common foundation of many other geometric disciplines like Euclidean geometry, hyperbolic and elliptic geometry or even relativistic space-time geometry. This book offers a comprehensive introduction to this fascinating field and its applications. In particular, it explains how metric concepts may be best understood in projective terms. One of the major themes that appears throughout this book is the beauty of the interplay between geometry, algebra and combinatorics. This book can especially be used as a guide that explains how geometric objects and operations may be most elegantly expressed in algebraic terms, making it a valuable resource for mathematicians, as well as for computer scientists and physicists. The book is based on the author’s experience in implementing geometric software and includes hundreds of high-quality illustrations.
1st Edition., 2011, XXII, 571 p. 380 illus., 250 in color., Hardcover ISBN: 978-3-642-17285-4
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Geometriekalküle
Wie kann man geometrische Objekte und Operationen so darstellen, dass sie durch möglichst einfache algebraische Manipulationen verarbeitet werden können? Dies ist die Leitfrage dieses Buches, welche im Verlauf von insgesamt 12 Kapiteln von verschiedenen Seiten beleuchtet wird. Unter diesem Blickwinkel werden Einführungen in projektive Geometrie, geometrische Invariantentheorie, Euklidische Geometrie (unter besonderer Berücksichtigung komplexer Zahlen) Möbiusgeometrie, und Lie‘sche Kreisgeometrie gegeben. Hierbei liegt der Schwerpunkt auf Eleganz der Methoden, welche nicht selten automatisch zu eleganten algorithmischen Ansätzen führen. Für den Leser stellt das Buch eine Brücke vom Grundwissen in der Linearen Algebra zu modernen (und klassischen) Ansätzen der Geometrie dar. Neben zahlreichen Übungsaufgaben, Abbildungen und im Internet verfügbaren interaktiven Visualisierungen wird jedes Kapitel durch einen „Exkurs" ergänzt, der Einblicke in Anwendungen oder weiterführende Themen gibt. Das Buch richtet sich an Studierende und Dozenten der Mathematik, Informatik und Physik ab dem dritten Semester.
2009, XI, 224 S. 141 Abb., 46 in Farbe., Softcover ISBN: 978-3-642-02529-7
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The Cinderella.2 Manual
Cinderella.2, the new version of the well-known interactive geometry software, has become an even more versatile tool than its predecessor. It now consists of three connected parts: An enhanced geometry component with new features like transformations and dynamic fractals, a simulation laboratory to explore basic laws of Newton mechanics, and an easy to use scripting language that enables any user to quickly extend the software even further. Cinderella.2 Manual is the first book to offer complete instruction and techniques for using Cinderella.2. It contains a wealth of examples, in particular for the Cindy-Script language which interacts smoothly with the geometry and simulation components, and a complete reference. Cinderella.2 is Math in Motion all the way, and this book provides comprehensive documentation from start to finish
2011, X, 470 p. 600 illus., Hardcover ISBN: 978-3-540-34924-2
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Cinderella User Manual
Cinderella is a unique, technically very sophisticated teachware for geometry. It will be used as a tool by students learning Euclidean, projective, spherical and hyperbolic geometry, as well as in geometric research by scientists. Moreover, it can also serve as an authors' tool to design web pages with interactive constructions or even complete geometry exercises.
2000, X, 143 p. 126 illus., Softcover ISBN: 978-3-540-67139-8
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Realization Spaces of Polytopes
The book collects results about realization spaces of polytopes. It gives a presentation of the author's "Universality Theorem for 4-polytopes". It is a comprehensive survey of the important results that have been obtained in that direction. The approaches chosen are direct and very geometric in nature. The book is addressed to researchers and to graduate students. The former will find a comprehensive source for the above mentioned results. The latter will find a readable introduction to the field. The reader is assumed to be familiar with basic concepts of linear algebra.
1996, XI, 187 p., Softcover ISBN: 978-3-540-62084-6
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Automated Deduction in Geometry
Jürgen Richter-Gebert, Dongming Wang (Eds.)
The book collects results about realization spaces of polytopes. It gives a presentation of the author's "Universality Theorem for 4-polytopes". It is a comprehensive survey of the important results that have been obtained in that direction. The approaches chosen are direct and very geometric in nature. The book is addressed to researchers and to graduate students. The former will find a comprehensive source for the above mentioned results. The latter will find a readable introduction to the field. The reader is assumed to be familiar with basic concepts of linear algebra.
1996, XI, 187 p., Softcover ISBN: 978-3-540-62084-6
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Pi und Co: Kaleidoskop der Mathematik
Behrends, Ehrhard; Gritzmann, Peter; Ziegler, Günter M. (Hrsg.)
Mathematik ist eine äußerst vielseitige, lebendige Wissenschaft. Von ihren großen Themen wie Zahlen, Unendlichkeiten, Dimensionen und Wahrscheinlichkeiten spannen die Autoren einen Bogen bis hin zu aktuellen Anwendungen in der Logistik, der Finanzwelt, der Kryptographie, der Medizin und anderen Gebieten.
Breit gefächert wie die Mathematik ist auch das Spektrum der Beiträge. Leicht verständliche, unterhaltsame Texte finden sich ebenso wie anspruchsvollere mathematische Herausforderungen.
Das Buch ist also eine Einladung an jeden, seinen eigenen Zugang zu dieser spannenden und abenteurreichen Wissenschaft zu finden.
Buchkapitel: U. Kortenkamp & J. Richter-Gebert: Zusammenspiel Mathematik und Architektur
1. Aufl. 2008. Korr. Nachdruck, 2008, X, 391 S., Geb. ISBN: 978-3-540-77888-2
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Alles Mathematik: Von Pythagoras zum CD-Player
Martin Aigner, Ehrhard Behrends (Hrsg.)
Das Buch umfasst etwa zwanzig sorgfältig ausgearbeitete Beiträge renommierter Referenten, die mit den gängigen Vorurteilen "Mathematik ist zu schwer, zu trocken, zu abstrakt, zu abgehoben" aufräumen. Denn Mathematik ist überall in den Anwendungen gefragt, weil sie das oft einzige Mittel ist, praktische Probleme zu analysieren und zu verstehen. Vom CD-Player zur Börse, von der Computertomographie zur Verkehrsplanung, alles ist (auch) Mathematik. Wer hätte gedacht, dass die Primzahlen, die schon seit der Antike die Mathematiker beschäftigen, heute ganz wesentlich zu unserer Datensicherheit beitragen?Es ist die Hoffnung der Herausgeber, dass zwei wesentliche Aspekte der Mathematik deutlich werden : Einmal ist sie die reinste Wissenschaft - Denken als Kunst - , und andererseits ist sie durch eine Vielzahl von Anwendungen in allen Lebensbereichen gegenwärtig.
Buchkapitel: J. Richter-Gebert: Blicke in die Unendlichkeit
3., überarb. Aufl. 2009. X, 386 S. Mit einem Prolog von Gero von Randow. ISBN: 978-3-8348-0416-7
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Mathematics Everywhere
Martin Aigner, Ehrhard Behrends (Hrsg.)
Mathematics is all around us. Often we do not realize it, though. Mathematics Everywhere is a collection of presentations on the role of mathematics in everyday life, through science, technology, and culture. The common theme is the unique position of mathematics as the art of pure thought and at the same time as a universally applicable science. The authors are renowned mathematicians; their presentations cover a wide range of topics. From compact discs to the stock exchange, from computer tomography to traffic routing, from electronic money to climate change, they make the "math inside" understandable and enjoyable. An additional attractive feature is the leisurely treatment of some hot topics that have gained prominence in recent years, such as Fermat's Theorem, Kepler's packing problem, and the solution of the Poincaré Conjecture. Or maybe you have heard about the Nash equilibrium (of "A Beautiful Mind" fame), or the strange future of quantum computers, and want to know what it is all about? Well, open the book and take an up-to-date trip into the fascinating world of the mathematics all around us.
Chapter: J. Richter-Gebert: Reflections on Reflections
AMS, 2010; 330 pp; softcover ISBN-10: 0-8218-4349-4
The Coxeter Legacy: Reflections and Projections
Chandler Davis, Erich W. Ellers (Eds.)
Donald Coxeter infused enthusiasm, even passion, for mathematics in people of any age, any background, any profession, any walk of life. Enchanted by Euclidean geometry, he was interested in the beauty, the description, and the exploration of the world around us. His involvement in art and with artists earned him admiration and friends in the intellectual community all over the globe. Coxeter's devotion to polytopes and his interest in the theory of configurations live on in his students and followers. Coxeter groups arise in various subjects in applied mathematics, and they have a permanent place in some of the most demanding and fascinating branches of abstract mathematics, such as Lie algebras, algebraic groups, Chevalley groups, and Kac-Moody groups. This collection of articles by outstanding researchers and expositors is intended to capture the essence of the Coxeter legacy. It is a mixture of surveys, up-to-date information, history, storytelling, and personal memories; and it includes a rich variety of beautiful illustrations.
Chapter: J. Richter-Gebert: Meditations on Cevas Theorem
AMS, 2006; 320 pp; hardcover ISBN-10: 0-8218-3722-2
Foundations of Computational Mathematics
Felipe Cucker, J Maurice Rojas (Eds.)
This invaluable book contains 19 papers selected from those submitted to a conference held in Hong Kong in July 2000 to celebrate the 70th birthday of Professor Steve Smale. It may be regarded as a continuation of the proceedings of SMALEFEST 1990 (”From Topology to Computation”) held in Berkeley, USA, 10 years before, but with the focus on the area in which Smale worked more intensively during the '90's, namely the foundations of computational mathematics.
Chapter: U. Kortenkamp & J. Richter-Gebert: Complexity Issues in Dynamaic Geometry
World Scientific, 2002; 480pp, ISBN: 978-981-02-4845-1
Innovationsprojekt Frühpädagogik: Professionalität im Verbund von Praxis, Forschung, Aus- und Weiterbildung
Eva Hammes-DiBernardo, Sabine Hebenstreit-Müller (Hrsg.)
Neue Bündnisse und Strukturen sind notwendig, um die Qualität der Kitas als Lern- und Lebensorte für Kinder und ihre Familien nachhaltig zu sichern. Das Buch stellt nationale Modelle und internationale Forschung vor, die zeigen, wie solche Verbundsysteme funktionieren können und neue Lösungen ermöglichen.
Buchkapitel: J. Richter-Gebert: Mathematik spielend lernen
Schneider Verlag Hohengehren, 2005; 228 Seiten, ISBN: 3896769901
Journal Papers
Kombinatorische Geometrie
- Nonrealizability Proofs in Computational Geometry (with J. Bokowski and B. Sturmfels)
- On the Classification of Non-Realizable Oriented Matroids (Part I: Generation) (with J. Bokowski)
- On the Classification of Non-Realizable Oriented Matroids (Part II: Properties) (with J. Bokowski)
- On the Distribution of Order Types (with J. Bokowski and W. Schindler)
- On the Finding of Final Polynomials (with J. Bokowski)
- Zonotopal Tilings and the Bohne-Dress Theorem (with G.M. Ziegler)
- Euclideaness and Final Polynomials in Oriented Matroid Theory
- Mnëv's Universality Theorem Revisited
- Two interesting oriented matroids
- Oriented matroids (with G. M. Ziegler)
- Universality theorems for oriented matroids and polytopes
- Orientability of matroids is NP-complete
- First steps in tropical geometry» (with B. Sturmfels, Th. Theobald)
Projektive Geometrie und andere geometrische Arbeiten
- Complex Matroids - phirotopes and their realizations in rank 2 (with A. Below and V. Krummeck)
- Aschenputtel und Perlenketten: so etwas wie eine Buchbesprechung
- Meditations on Ceva's Theorem
- Diagrams, Tensors and Geometric reasoning (with Peter Lebmeir)
- Rotations, Translations and Symmetry Detection for Complexified Curves (with Peter Lebmeir)
- Hyperbolization of Euclidean Ornaments» (with Martin von Gagern)
- Geometry of Numerical Complex Time Integration (with Thorsten Orendt and Michael Schmid)
- Geometriekalküle» (with Thorsten Orendt)
Polytope
- Realization Spaces Polytopes (Springer Lecture Notes 1643)
- Realization spaces of 4-polytopes are universal (Research report with G. M. Ziegler)
- Basic properties of convex polytopes (with M. Henk and G. M. Ziegler)
- Extremal properties of 0/1-Polytopes (with U, Hund, A. Sarangarajan and G.M. Ziegler)
- Finding small triangulations of polytope boundaries is hard
- Minimal simplicial dissections and triangulations of convex 3-polytopes (with A. Below, U. Brehm and J. de Loera)
- The complexity of finding small triangulations of convex 3-polytopes (with A. Below and J. de Loera)
Dynamische Geometrie
- Euklidische und nicht-euklidische Geometrie in Cinderella (with U. Kortenkamp)
- Geometry education in the internet age (with U. Kortenkamp)
- Shrink wrapped Java in education (with U. Kortenkamp)
- Dynamische Geometrie: Grundlagen und Möglichkeiten (with U. Kortenkamp)
- Dynamic Aspects in Computational Geometry (with U. Kortenkamp)
- A dynamic setup for elementary geometry (with U. Kortenkamp)
- Complexity issues in dynamic geometry (with U. Kortenkamp)
- Grundlagen dynamischer Geometrie (with U. Kortenkamp)
- Decision complexity in dynamic geometry (with U. Kortenkamp)
- Recognition of computationally constructed loci (with Peter Lebmeir)
- Cinderella.2 – Geometrie und Physik im Dialog (with U. Kortenkamp)
- The power of scripting: DGS meets programming (with U. Kortenkamp)
- Blended Experimentation with DGS (with U. Kortenkamp)
- Cinderella» (with U. Kortenkamp)
- The Cinderella Documentation» (with U. Kortenkamp)
Mathematikvermittlung
- Zusammenspiel: Mathematik und Architektur (with U. Kortenkamp)
- Mathematik spielend Lernen
- Mathematik be-greifen (with V. Krummeck)
- Ein Drunter und Drüber, Mathematik von statischen Konstruktionen spielerisch erfahren
- Blicke in die Unendlichkeit
- Mikrolaboratorien und virtuelle Modelle im universitären Mathematikunterricht
- Der Reiz des Haptischen – Modelle und ihre vielfältigen Aufgaben