Geometry in Our Three-dimensional World

The book presents a comprehensive overview of various aspects of three-dimensional geometry that can be experienced on a daily basis. By covering the wide range of topics — from the psychology of spatial perception to the principles of 3D modelling and printing, from the invention of perspective by Renaissance artists to the art of Origami, from polyhedral shapes to the theory of knots, from patterns in space to the problem of optimal packing, and from the problems of cartography to the geometry of solar and lunar eclipses ― this book provides deep insight into phenomena related to the geometry of space and exposes incredible nuances that can enrich our lives.

The book is aimed at the general readership and provides more than 420 color illustrations that support the explanations and replace formal mathematical arguments with clear graphical representations.

Readership: All people interested in geometry and science. General audience with a basic knowledge of high-school math. Teachers seeking ideas for a modern approach to teaching geometry with applications.

Alfred S Posamentier is currently Distinguished Lecturer at New York City College of Technology of the City University of New York. He is also Professor Emeritus of Mathematics Education at The City College of the City University of New York, and former Dean of the School of Education, where he was tenured for 40 years. He is the author and co-author of more than 75 mathematics books for teachers, secondary school students, and the general readership. Dr Posamentier is also a frequent commentator in newspapers and journals on topics relating to mathematics and education. He is still involved in working with mathematics teachers and supervisors, nationally and internationally, to help them maximize their effectiveness.

Bernd Thaller is Professor of Mathematics Education at the Institute of Mathematics and Scientific Computing of the University of Graz, Austria. After studying mathematics and physics in Graz at which he earned his doctorate, he did further studies at the University of Vienna and the Free University of Berlin. He became a mathematical physicist, making some important research contributions to relativistic quantum mechanics and quantum mechanical spectral and scattering theory. He has written a monograph about the Dirac equation and two books on Visual Quantum Mechanics.

He was coordinator of two large-scale European projects of research and development in educational math (Socrates 2005–2008 and Erasmus+ 2015–2017) and has been supervisor of more than 140 diploma theses and dissertations. In 2008 he founded and is currently head of the regional educational competence center for mathematics and geometry, whose main task is the coordination of activities of the teacher training institutions in Styria and the organization of in-service teacher training events, seminars, and workshops. He was coordinator of two large-scale European projects of research and development in educational math (Socrates 2005–2008 and Erasmus+ 2015–2017) and has been supervisor of more than 140 diploma theses and dissertations. In 2008 he founded and is currently head of the regional educational competence center for mathematics and geometry, whose main task is the coordination of activities of the teacher training institutions in Styria and the organization of in-service teacher training events, seminars, and workshops.

hristian Dorner is a member of the faculty in the Mathematics Department at the University of Vienna. His research focuses on stochastic thinking, financial mathematics for secondary school mathematics classes, procedural knowledge of students and research-based design of video-vignettes (short video clips) to be used for developing the practical didactic skills of prospective mathematics teachers. He has published research papers in peer-reviewed journals on mathematics education and gave several talks at international conferences on mathematics education.

Robert Geretschläger is currently a mathematics teacher at Bundesrealgymnasium Keplerstraβe (BRG) in Graz, Austria and a lecturer at the University of Graz. He is also actively involved in the production of challenging and entertaining mathematical problem-solving material for the Mathematik macht Freu(n)de project at the University of Vienna, Austria. He is involved in the organization of many mathematics competitions on a local, regional and national level. Among other duties, he has been the leader of the Austrian team at the International Mathematical Olympiad since 2007 and president of the organizing committee of the Mathematical Kangaroo in Austria since 1998.