Euclid The Creation of Mathematics

Benno Artmann

348 pages, parution le 05/02/2002

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Résumé

The philosopher Immanuel Kant writes in the popular introduction to his philosophy: "There is no single book about metaphysics like we have in mathematics. 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 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. 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 appendix, the reader will find items of general interest for mathematics, such as the question of parallels, squaring the circle, problem and theory, what rigour 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.

Contents

Notes to the reader.
General historical remarks.
The Origins of Mathematics 1: 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 Definitions.

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.

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Benno Artmann
Parution	05/02/2002
Nb. de pages	348
Format	16 x 24
Couverture	Relié
Poids	655g
Intérieur	Noir et Blanc
EAN13	9780387984230
ISBN13	978-0-387-98423-0