Euclid. The Creation of Mathematics - Artmann, Benno
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Even if the material covered by Euclid may be considered elementary for the most part, the way in which he presents essential features of mathematics in a much more general sense, has set the standards for more than 2000 years. He displays the axiomatic foundation of a mathematical theory and its conscious development towards the solution of a specific problem. We see how abstraction works and how it enforces the strictly deductive presentation of a theory. We learn what creative definitions are and how the conceptual grasp leads to the classification of the relevant objects.…mehr

Produktbeschreibung
Even if the material covered by Euclid may be considered elementary for the most part, the way in which he presents essential features of mathematics in a much more general sense, has set the standards for more than 2000 years. He displays the axiomatic foundation of a mathematical theory and its conscious development towards the solution of a specific problem. We see how abstraction works and how it enforces the strictly deductive presentation of a theory. We learn what creative definitions are and how the conceptual grasp leads to the classification of the relevant objects.
  • Produktdetails
  • Verlag: Springer / Springer New York / Springer, Berlin
  • 1st ed. 1999. Corr. 2nd printing 2001
  • Erscheinungstermin: Januar 1999
  • Englisch
  • Abmessung: 241mm x 161mm x 20mm
  • Gewicht: 634g
  • ISBN-13: 9780387984230
  • ISBN-10: 0387984232
  • Artikelnr.: 08032793
Autorenporträt
Benno Artmann, Göttingen, Germany
Inhaltsangabe
Preface Notes to the reader General historical remarks The Origins of Mathematics I: The Testimony of Eudemus Euclid: Book I Origin of Mathematics 2: Parallels and Axioms Origins of Mathematics 3: Pythagoras of Samos Euclid: Book II Origin of Mathematics 4: Squaring the Circle Euclid: Book III Origin of Mathematics 5: Problems and Theories Euclid: Book IV Origin of Mathematics 6: The Birth of Rigor Origin of Mathematics 7: Polygons after Euclid Euclid: Book V Euclid: Book VI Origin of Mathematics 8:Be Wise, Generalize Euclid: Book VII Origin of Mathematics 9: Nicomachus and Diophantus Euclid:Book VIII Origins of Mathematics 10: Tools and Theorems Euclid: Book IX Origin of Mathematics 11: Math is Beautiful Euclid: Book X Origins of Mathematics 12: Incommensurability and Irrationality Euclid: Book XI Origins of Mathematics 13: The Role of Defiinitions Euclid: Book XII Origins of Mathematics 14: The Taming of the Infinite Euclid: Book XIII Origin of Mathematics 15: Symmetry Through the Ages Origin of Mathematics 16: The Origin of the Elements Notes Bibliography Index
Rezensionen
B. Artmann

Euclid - The Creation of Mathematics

"The author invites the 'lover of mathematics' to have a peek, via a gentle introduction and presentation of Euclid's Elements, with detours to previous Greek geometers, whose work has been incorporated in the Elements. The contents of the Elements are presented book by book . . . with full statements of the definitions, axioms, propositions, and proofs involved. There are . . . notes to subsequent development of Euclidean themes . . . justifications of steps of proof and of the sequence in which results appear . . . An original and pleasing feature of the book consists in the references to Greek architecture, which emphasize the pervasiveness of the concern for proportion in Greek culture, as well as the references to archaeological finds of dodecahedra- and icosahedra-shaped objects."-AMERICAN MATHEMATICAL SOCIETY