Euclid, The Creation of Mathematics (Relié)

  • Springer

  • Paru le : 21/07/1999
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The philosopher Immanuel Kant writes in the popular introduction to his philosophy: "There is no single book about metaphysics like we have in mathernatics.... > Lire la suite
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The philosopher Immanuel Kant writes in the popular introduction to his philosophy: "There is no single book about metaphysics like we have in mathernatics. If you want to know what mathematics is, just look at Euclid's Elements" (Prolegomena, Paragraph 4). Even if the material covered by Euclid may be considered elementary for its most parts, 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 toward 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. For each of Euclid's thirteen Books, the author has given a general description of the contents and structure of the Book, plus one or two sample proofs. In an accompanying section, the reader will find items of general interest for mathematics, such as the question of parallels, squaring the circle, problem and theory, what rigor is, the history of the platonic polyhedra, irrationals, the process of generalization, and more. This is a book for all lovers of mathematics with a solid background in high school geometry, from teachers and students to University professors. It is an attempt to understand the nature of mathematics from its most important early source.
    • General Historical Remarks
    • The Contents of the Elements
    • The Origin of Mathematics 1: The Testimony of Eudemus
    • Euclid Book I
    • The Origin of Mathematics 2: Parallels and Axioms
    • The Origin of Mathematics 3: Pythagoras of Samos
    • Euclid Book II
    • The Origin of Mathematics 4: Squaring the Circle
    • Euclid Book III
    • The Origin of Mathematics 5: Problems and Theories
    • Euclid Book IV
    • The Origin of Mathematics 6: The Birth of Rigor
    • The Origin of Mathematics 7: Polygons After Euclid
    • Euclid Book V
    • Euclid Book VI
    • The Origin of Mathematics 8: Be Wise, Generalize
    • Euclid Book VII
    • The Origin of Mathematics 9: Nicomachus and Diophantus
    • Euclid Book VIII
    • The Origin of Mathematics 10: Tools and Theorems
    • Euclid Book IX
    • The Origin of Mathematics 11: Math Is Beautiful
    • Euclid Book X
    • The Origin of Mathematics 12: Incommensurability and Irrationality
    • Euclid Book XI
    • The Origin of Mathematics 13: The Rôle of Definitions
    • Euclid Book XII
    • The Origin of Mathematics 14: The Taming of the Infinite
    • Euclid Book XIII
    • The Origin of Mathematics 15: Symmetry Through the Ages
    • The Origin of Mathematics 16: The Origin of the Elements.
  • Date de parution : 21/07/1999
  • Editeur : Springer
  • ISBN : 0-387-98423-2
  • EAN : 9780387984230
  • Présentation : Relié
  • Nb. de pages : 343 pages
  • Poids : 0.655 Kg
  • Dimensions : 16,2 cm × 24,3 cm × 2,2 cm
Benno Artmann - Euclid, The Creation of Mathematics.
Euclid, The Creation of Mathematics
85,59 €
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