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About This Book xv
been a tightly interwoven process and I am quite convinced that without our
mathematical discussions on the software several sections of this book would
never have been written. In Section 26.5 you will see beautiful pictures of
hyperbolic ornaments. They have been produced with the software project
morenaments by Martin von Gagern (using hand-drawn sketches of myself as
input). Also this project was essential for shaping some of the mathematics
presented in this book.
I cannot count the mathematical discussions I have had with colleagues
and students on various topics in this book. Many students who attended my
classes on Projective Geometry helped to clarify several mathematical and
stylistic issues, and many of them definitely helped to clarify the exposition. I
am especially grateful to those of them who encouraged me to leave the book
in its present, rather explanatory style. They convinced me that even today
students are willing to read fat books and that it is worse to approach the
same topic from very different directions. Discussions with colleagues were
also essential; here I would like to mention a few of the main players who have
consciously or unconsciously contributed to the book in its present form (i.e.
I learned a lot from them): G¨unter Ziegler, Jim Blinn, J¨urgen Bokowski,
Bernd Sturmfels, Henry Crapo, Walter Whiteley, Tim Hoffmann, Ulrich Ko-
rtenkamp, AleXX Below, and Martin von Gagern. A special thank you goes
to Anders Bj¨orner, who in the earliest stages of this project encouraged me
to write this book. Perhaps here I should also mention two other mathemati-
cians from whom I learned a lot although I will here on earth unfortunately
never have the chance to meet them: Julius Pl¨ucker and Felix Klein.
Publishing this book with Springer Verlag means a lot to me. I am very
happy to be able to collaborate with Martin Peters and Ruth Allewelt. They
were always friendly and remained patient, even though writing this book
took much longer than promised.
My greatest, warmest, and foremost thanks go to the one person who has
influenced me most throughout my entire life. Without the love, encourage-
ment, faith in me, patience, and deep understanding of my wife, Ingrid, all
else would mean nothing at all. Thank you!
A special thank you also goes to my daughter Angie. I am surprised that
she is still willing to give stylistic advice on so many fine points. Her fresh and
modern look on things helped to improve the layout and graphical appearance
in many points. A final thanks goes to Jimmy, our new “family member.” He
helped me to stay grounded in the very final stages of the manuscript.
J¨urgen Richter-Gebert
Garching, October 2010