Thalia.de

The Four Pillars of Geometry

Many people think there is only one “right” way to teach geometry. For two millennia, the “right” way was Euclid’s way, and it is still good in many respects. But in the 1950s the cry “Down with triangles!” was heard in France and new geometry books appeared, packed with linear algebra but with no diagrams. Was this the new “right” way, or was the “right” way something else again, perhaps transformation groups? In this book, I wish to show 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. Euclid-style construction and axiomatics seem the best way to start, but linear algebra smooths the later stages by replacing some tortuous arguments by simple calculations. And how can one avoid projective geometry? It not only explains why objects look the way they do; it also explains why geometry is entangled with algebra. Finally, one needs to know that there is not one geometry, but many, and transformation groups are the best way to distinguish between them. Two chapters are devoted to each approach: The ?rst is concrete and introductory, whereas the second is more abstract. Thus, the ?rst chapter on Euclid is about straightedge and compass constructions; the second is about axioms and theorems. The ?rst chapter on linear algebra is about coordinates; the second is about vector spaces and the inner product.
Rezension
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)
Portrait
John Stillwell is a professor of mathematics at the University of San Francisco. He is also an accomplished author, having published several books.
… weiterlesen
In den Warenkorb
Filialabholung

Versandkostenfrei

Bezahlung bei Abholung

Beschreibung

Produktdetails


Einband gebundene Ausgabe
Seitenzahl 228
Erscheinungsdatum 09.08.2005
Sprache Englisch
ISBN 978-0-387-25530-9
Verlag Springer
Maße (L/B/H) 235/155/19 mm
Gewicht 532
Abbildungen 138 schwarzweisse Abbildungen,
Auflage 2005.
Buch (gebundene Ausgabe, Englisch)
39,99
inkl. gesetzl. MwSt.
Versandfertig in 3 - 5 Tagen
Versandkostenfrei
In den Warenkorb
Filialabholung

Versandkostenfrei

Bezahlung bei Abholung

Andere Kunden interessierten sich auch für

  • 15365119
    Thirteen Reasons Why
    von Jay Asher
    (13)
    Buch (Taschenbuch)
    8,29
  • 43564382
    Milk and Honey
    von Rupi Kaur
    (2)
    Buch (Taschenbuch)
    12,99 bisher 14,99
  • 47566547
    Good Night Stories for Rebel Girls
    von Francesca Cavallo
    Buch (gebundene Ausgabe)
    16,99 bisher 21,20
  • 54619015
    Thirteen Reasons Why. TV Tie-In
    von Jay Asher
    Buch (Taschenbuch)
    7,79 bisher 8,99
  • 17283460
    Thirteen Reasons Why
    von Jay Asher
    (13)
    Buch (Taschenbuch)
    8,99
  • 34910866
    The Life List
    von Lori Nelson Spielman
    (5)
    Buch (Taschenbuch)
    6,99 bisher 9,70
  • 54193482
    Thirteen Reasons Why
    von Jay Asher
    Buch (Taschenbuch)
    8,99
  • 1719784
    The Giver
    von Lois Lowry
    (1)
    Schulbuch (Taschenbuch)
    9,99
  • 23361882
    Thirteen Reasons Why
    von Jay Asher
    Schulbuch (Taschenbuch)
    9,60
  • 17345365
    Cornelsen Senior English Library - Literatur / Ab 10. Schuljahr - Looking for Alaska
    von John Green
    (22)
    Schulbuch (Taschenbuch)
    10,25
  • 38930428
    We Were Liars
    von E. Lockhart
    (11)
    Buch (Taschenbuch)
    7,99 bisher 10,49
  • 46576306
    The Hate U Give
    von Angie Thomas
    (1)
    Buch (gebundene Ausgabe)
    9,99 bisher 13,49
  • 4593954
    Cornelsen Senior English Library - Literatur / Ab 10. Schuljahr - The Perks of Being a Wallflower
    von Stephen Chbosky
    (25)
    Schulbuch (Taschenbuch)
    10,25
  • 40670892
    Perfect
    von Cecelia Ahern
    Buch (Taschenbuch)
    8,69 bisher 9,99
  • 45243079
    Fantastic Beasts and Where to Find Them. The Original Screenplay
    von Joanne K. Rowling
    (17)
    Buch (gebundene Ausgabe)
    14,95 bisher 21,99
  • 14751780
    Cornelsen Senior English Library - Literatur / Ab 10. Schuljahr - The Curious Incident of the Dog in the Night-Time
    von Mark Haddon
    (11)
    Schulbuch (Taschenbuch)
    10,25
  • 43831163
    A Court of Thorns and Roses 3
    von Sarah J. Maas
    Buch (Taschenbuch)
    8,19
  • 46297446
    Court of Wings and Ruin
    von Sarah J. Maas
    Buch (gebundene Ausgabe)
    17,99
  • 45795728
    Norse Mythology
    von Neil Gaiman
    (1)
    Buch (gebundene Ausgabe)
    11,59 bisher 12,89
  • 4570744
    The Curious Incident of the Dog in the Night-Time
    von Mark Haddon
    (11)
    Buch (Taschenbuch)
    6,89

Kundenbewertungen


Es wurden noch keine Bewertungen geschrieben.