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Geometry: Our Cultural Heritage de Audun Holme

Geometry: Our Cultural Heritage

Autor Audun Holme
en Limba Engleză Paperback – 28 noi 2014
This is a revised edition of the ?rst printing which appeared in 2002. The book is based on lectures at the University of Bergen, Norway.Over the years these lectures have covered many different aspects and facets of the wonderful ?eld of geometry. Consequently it has never been possible to give a full and ?nal account of geometry as such, at an undergraduatelevel: A carefully consideredselection has always been necessary. The present book constitutes the main central themes of these selections. One of the groups I am aiming at, is future teachers of mathematics. All too oftenthe textsdealingwith geometrywhichgo intothe syllabusforteacher-students present the material in ways which appear pedantic and formalistic, suppressing the very powerful and dynamic character of this old ?eld, which at the same time so young. Geometry is a ?eld of mathematical insight, research, history and source of artistic inspiration. And not least important, an integral part of our common cultural heritage.
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Specificații

ISBN-13: 9783642423925
ISBN-10: 3642423922
Pagini: 540
Ilustrații: XVII, 519 p.
Dimensiuni: 155 x 235 x 28 mm
Greutate: 0.75 kg
Ediția:2nd ed. 2010
Editura: Springer Berlin, Heidelberg
Colecția Springer
Locul publicării:Berlin, Heidelberg, Germany

Public țintă

Lower undergraduate

Cuprins

Part I A Cultural Heritage: 1 Early Beginnings.- 2 The Great River Civilizations.- 3 Greek and Hellenic Geometry.- 4 Geometry in the Hellenistic Era.- 5 Arabic Mathematics and Geometry.- 6 The Geometry of Yesterday and Today.- 7 Geometry and the Real World.- Part II Introduction to Geometry: 8 Axiomatic Geometry.- 9 Axiomatic Projective Geometry.- 10 Models for Non-Euclidean Geometry.- 11 Making Things Precise.- 12 Projective Space.- 13 Geometry in the Affine and the Projective Plane.- 14 Algebraic Curves of Higher Degrees in the Affine Plane R2.- 15 Higher Geometry in the Projective Plane.- 16 Sharpening the Sword of Algebra.- 17 Constructions with Straightedge and Compass.- 18 Fractal Geometry.- 19 Catastrophe Theory.- 20 General Polyhedra and Tesselations, and their Groups of Symmetry.- 21 Hints and Solutions to some of the Excercises.- References.- Index

Recenzii

From the reviews of the second edition:
“Devised primarily for future teachers of mathematics, but to be enjoyed by all lovers of geometry, including professional geometers, who will likely find something new in the historical part, this book renders an essential service to the mathematical community by presenting the story of geometry in two equal halves, the first half surveying its history up to Descartes and the second one presenting the version of geometry that emerged from the axiomatic revolution of the late 19th century, with an emphasis on algebraic geometry.” (Victor V. Pambuccian, Zentralblatt MATH, Vol. 1202, 2011)

Textul de pe ultima copertă

This book contains selected topics from the history of geometry, with "modern" proofs of some of the results, as well as a fully modern treatment of selected basic issues in geometry. It is geared towards the needs of future mathematics teachers. All too often the geometry which goes into the syllabus for these students presents the material in a pedantic and formalistic style, suppressing its dynamic character and its role as part of the foundation of our common cultural heritage. As such, one of my goals is to open up these aspects of the field; another is to extend an invitation to mathematics in general. It is an unfortunate fact that today, at a time when mathematics and knowledge of mathematics are more important than ever, phrases like math avoidance and math anxiety are very much in the public vocabulary. Making a serious effort to heal these ills is an essential task. Thus the book also aims at an informed public, interested in making a new beginning in math.For the 2nd edition, some of the historical material giving historical context has been expanded and numerous illustrations have been added. The main difference is however the inclusion of a large number of exercises with some suggestions for solutions.For excerpts from reviews from the first edition have a look at http://www.springer.com/978-3-540-41949-5.

Caracteristici

A very readable short history of geometry No prerequisites required Easy to understand by beginners New edition with large number of exercises with some suggestions for solutions Includes supplementary material: sn.pub/extras