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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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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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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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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