John Stillwell

eBook, PDF

The Four Pillars of Geometry (eBook, PDF)

Beschreibung

Geometry has something for everyone, and students will find themselves building on their strengths at times, and working to overcome weaknesses at other times. This new textbook demonstrates that geometry can be developed in four fundamentally different ways, and that all should be used if the subject is to be shown in all its splendor. Two chapters are devoted to each approach, the first being concrete and introductory, while the second is more abstract. The book contains more than 100 figures, and a large selection of exercises in each chapter.

Technische Details

• Geräte: PC
• ohne Kopierschutz
• Größe: 3.4MB

Barrierefreiheit

• Text-to-Speech

Autor

Geometry has something for everyone, and students will find themselves building on their strengths at times, and working to overcome weaknesses at other times. This new textbook demonstrates that geometry can be developed in four fundamentally different ways, and that all should be used if the subject is to be shown in all its splendor. Two chapters are devoted to each approach, the first being concrete and introductory, while the second is more abstract. The book contains more than 100 figures, and a large selection of exercises in each chapter.

Produktdetails

• Verlag: Springer US
• Seitenzahl: 229
• Erscheinungstermin: 29. Dezember 2005
• Englisch
• ISBN-13: 9780387290522
• Artikelnr.: 43728673

Rezensionen

From the reviews:

"This is an introductory book on geometry, easy to read, written in an engaging style. The author's goal is ... to increase one's overall understanding and appreciation of the subject. ... Along the way, he presents elegant proofs of well-known theorems ... . The advantage of the author's approach is clear: in a short space he gives a brief introduction to many sides of geometry and includes many beautiful results, each explained from a perspective that makes it easy to understand." (Robin Hartshorne, SIAM Review, Vol. 48 (2), 2006)

"The pillars of the title are ... Euclidean construction and axioms, coordinates and vectors, projective geometry, and transformations and non-Euclidean geometry. ... The

writing style is both student-friendly and deeply informed. The pleasing brevity of the book ... makes the book especially suitable as an instruction to geometry for the large and critically important population of undergraduate mathematics majors ... . Each chapter concludes with a well-written discussion section that combines history with glances at further results. There is a good selection of thought-provoking exercises." (R. J. Bumcrot, Mathematical Reviews, Issue 2006 e)

"The author acts on the assumption of four approaches to geometry: The axiomatic way, using linear Algebra, projective geometry and transformation groups. ... Each of the chapters closes with a discussion giving hints on further aspects and historical remarks. ... The book can be recommended to be used in undergraduate courses on geometry ... ." (F. Manhart, Internationale Mathematische Nachrichten, Issue 203, 2006)

"Any new mathematics textbook by John Stillwell is worth a serious look. Stillwell is the prolific author of more than half a dozen textbooks ... . I would not hesitate to recommend this text to any professor teaching a course in geometry who is more interested in providing a rapid survey of topics rather than an in-depth,semester-long, examination of any particular one." (Mark Hunacek, The Mathematical Gazette, Vol. 91 (521), 2007)

"The title refers to four different approaches to elementary geometry which according to the author only together show this field in all its splendor: via straightedge and compass constructions, linear algebra, projective geometry and transformation groups. ... the book can be recommended warmly to undergraduates to get in touch with geometric thinking." (G. Kowol, Monatshefte für Mathematik, Vol. 150 (3), 2007)

"This book presents a tour on various approaches to a notion of geometry and the relationship between these approaches. ... The book shows clearly how useful it is to use various tools in a description of basic geometrical questions to find the simplest and the most intuitive arguments for different problems. The book is a very useful source of ideas for high school teachers." (EMS Newsletter, March, 2007)

"The four pillars of geometry approaches geometry in four different ways, devoting two chapters to each, the first chapter being concrete and introductory, the second more abstract. ... The content is quite elementary and is based on lectures given by the author at the University of San Francisco in 2004. ... The book of Stillwell is a very good first introduction to geometry especially for the axiomatic and the projective point of view." (Yves Félix, Bulletin of the Belgian Mathematical Society, Vol. 15 (1), 2008)

Aus den Rezensionen: "... das macht dieses Buch ... wertvoll - umfasst das Buch das Wissen, das ein Gymnasiallehrer von Geometrie ... haben sollte. ... so profitieren nicht nur Studierende ... sondern auch ... Lehrer und ... Schüler der höheren Klassenstufen. ... An jeder Stelle erkennen wir, dass dem Autor die Geometrie ... ans Herz gewachsen ist, und dass er diese Freude an den Leser weitergeben möchte. ... Und so erklärt sich ... meine Begeisterung für dieses Buch, das man ... jedem mathematisch interessierten Abiturienten, auf jeden Fall ... jedem Mathematiklehrer in die Hand geben möge."(Harald Löwe, in: Mathematische Semesterberichte, 2007, Vol. 54, S. 128 f.)