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WORK TITLE: The Evolution of the Eye
WORK NOTES: with Hannes F. Paulus
PSEUDONYM(S):
BIRTHDATE: 1955
WEBSITE:
CITY: Vienna
STATE:
COUNTRY: Austria
NATIONALITY: Austrian
http://www.springer.com/us/book/9783319174754#aboutAuthors
RESEARCHER NOTES:
PERSONAL
Born 1955, in St. Johann im Pongau, Austria.
ADDRESS
CAREER
Mathematician and educator. Professor of mathematics and geometry, University of Applied Arts, Vienna, Austria, 1998—. Visiting professor, Princeton University, 1986-87.
WRITINGS
SIDELIGHTS
University of Vienna professor of mathematics and geometry Georg Glaeser’s works range from books that deal with ways of creating geometric models through computer modelling (Fast Algorithms for 3D-graphics, Open Geometry: OpenGL + Advanced Geometry, Handbook of Geometric Programming using Open Geometry GL) to books that deal with the wonders of geometry in the natural world (Der mathematische Werkzeugkasten: Anwendungen in Natur und Technik, Bilder der Mathematik—which was translated under the title A Mathematical Picture Book—and The Universe of Conics: From the Ancient Greeks to 21st Century Developments) to works that celebrate his fascination with nature and animal photography (Nature and Numbers: A Mathematical Photo Shooting, Die Evolution des Auges—ein Fotoshooting, translated as The Evolution of the Eye, and Die Evolution des Fliegens—ein Fotoshooting).
Geometry and Its Applications in Arts, Nature, and Technology and Nature and Number
In Geometry and Its Applications in Arts, Nature, and Technology, Glaeser explores the relationship between his field and the natural world, but he does so in a less scientific context than might be expected. “This picture book is more than just a coffee-table book, unless it is a table in the coffee room of a math department, because it contains not only many pictures but also gives theorems and proofs(!),” enthused Adhemar Bultheel in a review for the Web site of the European Mathematical Society. “If the reader is not interested in these proofs, there is no harm done or discontinuity in the appreciation of the global story.” Geometry and its Applications in Arts, Nature, and Technology, said M.D. Sanford, writing in Choice, “feeds into the author’s intent for readers to use their imagination to see proofs.”
Reviewers have remarked that Glaeser also brings an artist’s eye to the study of mathematics. In Nature and Number, for instance, he looks at the relationship between mathematical form and nature. “Mathematics is more than mere calculation,” he wrote in the introduction to the first chapter of Nature and Number. “It is an artificial construct created by humans, employing a strict set of rules…. It would seem that nature is different from such absolute approaches, and yet, more than any other discipline, mathematics is capable of modelling natural processes and providing deeper insights into its underlying mechanisms.”
The Universe of Conics
The Universe of Conics is profusely illustrated with diagrams and pictures that illuminate the history and study of conics, along with the requisite mathematical formulae, and it places the study of the geometry of conics in the context of our understanding of the universe. “Our universe is full of conics, even if we cannot always see them—like the orbits of the planets,” Glaeser and his coauthors wrote in the introduction to The Universe of Conics. “It needed very accurate observations to detect … and a great physicist … to prove that. Conics play a substantial role in the whole universe. On a large scale, the orbits of planets look like conics. Astronomers have recognized this fact and physicists have provided it. Many older and newer visualisations clearly show the ellipses as orbits of planets of our solar system with the Sun as the common focus.”
“I hope that the text will be taken up by the community of K–12 researchers and educators here in the U.S. and abroad,” stated Tushar Das in a review for the Web site of the Mathematical Association of America. “if only to aid the return of younger minds to this lush area of classical mathematics that plays `a fundamental role in numerous fields of mathematics and physics, with applications to mechanical engineering, architecture, astronomy, design and computer graphics.’” “Knowledge about conics and quadrics probably reached its culmination point at the beginning of the twentieth century,” Glaeser and his coauthors concluded. “Since then there seems to be an increasing loss of knowledge. This book will help to sum up and preserve more or less known properties of these fascinating curves.”
BIOCRIT
BOOKS
Glaeser, Georg, and Hannes F. Paulus, Die Evolution des Auges—ein Fotoshooting, Springer Spektrum (Berlin, Germany), 2014, translation published as The Evolution of the Eye, Springer Berlin Heidelberg (New York, NY), 2015.
Glaeser, Georg, Nature and Numbers: A Mathematical Photo Shooting, Ambra (Vienna, Austria), 2014.
Glaeser, Georg, Hellmuth Stachel, and Boris Odehnal, The Universe of Conics: From the Ancient Greeks to 21st Century Developments, Springer Berlin Heidelberg (New York, NY), 2016.
PERIODICALS
Choice, September, 2013, M.D. Sanford, review of Geometry and Its Applications in Arts, Nature, and Technology, p. 119; April, 2016, T.A. Franz-Odendaal, review of The Evolution of the Eye, p. 1191.
ONLINE
European Mathematical Society, http://euro-math-soc.eu/ (February 13, 2013), Adhemar Bultheel, review of Geometry and its Applications in Arts, Nature, and Technology.
Mathematical Association of America, http://www.maa.org/ (March 14, 2017), Tushar Das, review of The Universe of Conics: From the Ancient Greeks to 21st Century Developments.
LC control no.: n 94023591
Descriptive conventions:
rda
Personal name heading:
Glaeser, Georg
Place of origin: Vienna (Austria)
Affiliation: Universität für Angewandte Kunst Wien
Profession or occupation:
Mathematicians College teachers
Found in: His Fast algorithms for 3D graphics, 1994: CIP t.p. (Georg
Glaser) pub. info (Dr. Georg Glaser, Lehrkanzel für
Geometrie, Hochschule für Angewandte Kunst)
Nature and numbers, 2013: page 4 of cover (Georg Glaeser is
an Austrian mathematician and has been a professor of
mathematics and geometry at the University of Applied
Arts, Vienna since 1998)
Associated language:
eng
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Georg Glaeser has been professor of mathematics and geometry at the University of Applied Arts Vienna since 1998. As an author of numerous books on the topics of mathematics, geometry, computer graphics and photography, he simultaneously indulges a deep passion for animal photography. He specializes in a unique synthesis that bridges mathematics and biology through the prism of popular science. His latest book on this topic – Nature and Numbers – was published by Birkhauser in 2014.
Glaeser, Georg. Geometry and its applications in arts, nature and technology
M.D. Sanford
51.1 (Sept. 2013): p119.
Copyright: COPYRIGHT 2013 American Library Association CHOICE
http://www.ala.org/acrl/choice/about
51-0333
QA447
MARC
Glaeser, Georg. Geometry and its applications in arts, nature and technology, [tr.] by Peter Calvache and George Campbell. Springer, 2013 (c2012). 510p index alp ISBN 9783709114506, $59.95
The title of this book might lead readers to believe it is a textbook for an applied geometry class. In fact, it is more like a coffee-table book that readers with no special mathematical background can browse through, and whose sections can be read in no particular order. However, some mathematical knowledge and previous experience would be useful since Glaeser (Univ. of Applied Arts, Vienna, Austria) occasionally delves into analytical geometry and calculus to flush out explanations of certain topics. The book is visually appealing and feeds into the author's intent for readers to use their imagination to see proofs and descriptions. Readers will also enjoy the variety of applied topics from Euclidean and non-Euclidean geometry that Glaeser presents, for example, planetary orbits, DaVinci's use of perspective in The Last Supper, and Klein bottles. Summing Up: Recommended. ** Lower- and upper-division undergraduates and general readers.--M. D. Sanford, Felician College
Sanford, M.D.
Source Citation (MLA 8th Edition)
Sanford, M.D. "Glaeser, Georg. Geometry and its applications in arts, nature and technology." CHOICE: Current Reviews for Academic Libraries, Sept. 2013, p. 119. General OneFile, go.galegroup.com/ps/i.do?p=ITOF&sw=w&u=schlager&v=2.1&id=GALE%7CA343155857&it=r&asid=b375ef6a78dda040a8f73747420d4815. Accessed 3 Mar. 2017.
Gale Document Number: GALE|A343155857
Glaeser, Georg. The evolution of the eye
T.A. Franz-Odendaal
53.8 (Apr. 2016): p1191.
Copyright: COPYRIGHT 2016 American Library Association CHOICE
http://www.ala.org/acrl/choice/about
Glaeser, Georg. The evolution of the eye, by Georg Glaeser and Hannes F. Paulus. Springer, 2015. 214p bibl index afp ISBN 9783319174754 cloth, $34.99; ISBN 9783319174761 ebook, $19.99
53-3509
QP475
MARC
Mathematician Glaeser (Univ. of Applied Arts Vienna, Austria), author of Geometry and Its Applications in Arts, Nature and Technology (CH, Sep'13, 51-0333), and biologist Paulus (formerly, Univ. of Vienna, Austria) have written a valuable work about various intriguing aspects of the eye. The book's ten chapters cover topics such as types of eyes, seeing in a 3-D world, seeing above and below water, master genes, color, and more. Each chapter is about 20 pages long and contains both text and images. The high-resolution photographs are spectacular; the text sections present tidbits of fascinating facts such that both images and text provide insights into the essence of the adaptations of eyes over evolutionary time. The photographs have been carefully selected to be informative, not just complementary to the text. Images include species names and common names of the animals shown. An accompanying website supports the text. As a coffee-table-style book, this work will be very accessible to a diverse readership including the general public and high school and undergraduate students. Summing Up: *** Highly recommended. All library collections.--T. A. Franz-Odendaal, Mount Saint Vincent University
Source Citation (MLA 8th Edition)
Franz-Odendaal, T.A. "Glaeser, Georg. The evolution of the eye." CHOICE: Current Reviews for Academic Libraries, Apr. 2016, p. 1191. General OneFile, go.galegroup.com/ps/i.do?p=ITOF&sw=w&u=schlager&v=2.1&id=GALE%7CA449661640&it=r&asid=d04bfc4e3303eec9cad9892bc9ba530b. Accessed 3 Mar. 2017.
Gale Document Number: GALE|A449661640
What is immediately striking at first glance is the luxury of this publication: thick paper with hundreds of colorful glossy pictures and graphs. If you love books and geometry, this is one to fall in love with. Heavy stuff though: about 1.4 kg, it is a treasure that you would not like to take in your hand lugage on a plane.
In fact, the book has been available in German as Geometrie und ihre Anwendungen in Kunst, Natur und Technik (Elsevier, Spektrum Akademischer Verlag, 2005/2007). This is the English translation, extended with 60 pages and extra illustrations (there are about 900 of them). The author is professor at the Universität für angewandte Kunst in Vienna, and this might explain that this book, with geometry as the binding factor, has so many and very diverse applications. Moreover, this is not his first book on this kind of topic and he has also books on software for computer geometry (OpenGL®). Additional information about this book and links to other publications can be found at the book's website www.uni-ak.ac.at/geometrie.
This picture book is more than just a coffee-table book unless it is a table in the coffee room of a math department, because it contains not only many pictures, but also gives theorems and proofs(!). Although the proofs are not so very technical and are more descriptive geometrical than analytical with a minimum of formulas. If the reader is not interested in these proofs, there is no harm done or discontinuity in the appreciation of the global story told when they are just skipped.
The emphasis is clearly on the applications of geometry. In 13 chapters of increasing complexity, the reader is confronted with many expected but also with many unexpected applications. Sometimes, the application is more physics than geometry, but if it has an important geometrical component, it is reason enough to include it.
The author starts with points, lines, and elementary curves in the plane, to move on to projections. Already there the reader finds applications such as what can be learned from the shadows of objects or about the retro-reflector in a bicycle wheel. Entering the 3D world starts with polyhedra, then moves on to curves in 2D and 3D, to arrive at cones and cylinders as the simplest examples of what is further elaborated: developable surfaces, conic sections and surfaces of revolution. On a more advances level we find helical, spiral and minimal surfaces and an introduction to splines and NURBS for modeling general curved surfaces. All of this is amply illustrated with many applications from industrial design, architecture, cartography, connecting pipes, gear wheels, animal horns, DNA, and many more.
After that, the chapters start dealing with the more applied sciences. Chapter 9 is about optics: the human eye and photography and reflections and refraction. The next two chapters deal with the geometry of motion: curves generated by all sorts of mechanical devises, and orbits in astronomy. The last two chapters are about tilings of the plane and symmetry and other remarkable patterns appearing in nature. The latter two are are promoted from an appendix in the German edition to proper chapters in this one. There are also two appendices left in the form of short courses. One is about free hand drawing. As the author rightfully claims, in this computer age where pictures and graphs are rendered digitally by computer software, generating a result that is unnaturally close to perfection, free hand drawing becomes a rare skill while it should be a basic one for communication. The second course is about photography: the rules of perspective brought in practice. Both of these can be read independent from the rest of the text.
Reviewer:
A. Bultheel
Affiliation:
KU Leuven
Book details
A marvelous book, abundantly illustrated. It contains many applications in art science and technology, all with an underlying geometric flavour. There are some theorems and proofs, but these can be just skipped without harming the overall reading in case the reader is not interested in the technicalities.
Author:
georg glaeser
Publisher:
springer verlag
Published:
2012
ISBN:
978-3-7091-1450-6
Price:
42.35 € (hardcover)
Pages:
520
http://www.degruyter.com/view/product/212233
Categorisation
51 Geometry
51-01
Submitted by Adhemar Bultheel | 13 / Feb / 2013
[Reviewed by
Tushar Das
, on
03/14/2017
]
Conics may well be on the verge of becoming an endangered species in a variety of mathematical curricula around the world. At a time firmly implanted in the heartland of high-school and undergraduate mathematics (and physics), conics could easily find themselves relegated to the fringes of courses nowadays. We may be more certain regarding the decline and near-obliteration of projective geometry within undergraduate curricula.
If you are an undergraduate in the U.S. today, you may have seen conics either in high school, or possibly in a (remedial) entry-level college course in your freshman year. Some readers may remember them from multivariable calculus if their instructor had time to demonstrate that the orbits of planets are ellipses. And perhaps a handful of linear algebra instructors return their students to (either dreams or nightmares of) conics via quadratic forms, while struggling to fit whatever else makes the last week or two of a first, and sadly often only, course. A fortunate few may study an upper-level course or an independent study in undergraduate classical algebraic geometry and may have there (re)discovered conics as examples of affine varieties. That may well be the extent of it.
The text being reviewed — The Universe of Conics: From the ancient Greeks to 21st century developments — was written and beautifully illustrated by conical connoisseurs Georg Glaeser, Hellmuth Stachel and Boris Odehnal. The authors are Viennese geometers who have published extensively in computational geometry, computer graphics and allied areas. Their book is a visual delight. The hundreds of meticulously crafted and beautifully rendered figures (that adorn almost three out of every four pages) form the most attractive component of the book. In the authors’ words: “The book has been written for people who love geometry and it is mainly based on figures and synthetic conclusions rather than on pure analytic calculations. In many proofs, illustrations help to explain ideas and to support the argumentation, and in a few cases, the picture can display a theorem at a glance together with its proof.”
After a brief historical introduction, Chapter 2 begins with the classical definitions of conics and describes a variety of mechanical linkages that generate conics. Chapter 3 discusses differential geometric properties, and Chapter 4 studies conics as generated by the planar intersection of a surface in Euclidean 3-space. There is a shift in sophistication in Chapters 5 through 7 that study conics in the framework of projective geometry, followed by an affine perspective in Chapter 8. There appears to be an implicit demand for “more mathematical maturity” for this set of chapters. The last two chapters are a compendium of more esoteric results. Chapter 9 presents a potpourri of special problems such as pedal points and Poncelet porisms. The book ends with a final Chapter 10 on conics in non-Euclidean geometries.
The writing is uneven with regard to detail, and there could have been some more hand-holding through the more sophisticated portions of the text. Though my preferences are biased in favor of the strongly geometric and visual approach taken by the authors in explaining the bulk of the material, plenty of (our?) students who lack basic visualization skills and an aptitude for geometric reasoning will struggle with the book.
Sadly, the reader is left completely in the dark regarding the production of the beautiful and instructive figures that adorn almost every page. A separate resource on how to create such figures may be extremely well-received, and poised to revitalize classes on geometry, especially those aimed at training teachers at the elementary, middle and high school levels. Such a text/course may radically enhance the creation and use of manipulative materials and technology in the setting of geometry education. We hope that the authors will provide some documentation and further aids (perhaps on their websites) to empower readers to create and manipulate such figures on their own.
Higher eduction aside, I hope that the text will be taken up by the community of K–12 researchers and educators here in the US and abroad, if only to aid the return of younger minds to this lush area of classical mathematics that plays “a fundamental role in numerous fields of mathematics and physics, with applications to mechanical engineering, architecture, astronomy, design and computer graphics”.
Tushar Das is an Assistant Professor of Mathematics at the University of Wisconsin–La Crosse.