Overview
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.
Full Product Details
Author: Benno Artmann ,
B. Artmann
Publisher: Springer-Verlag New York Inc.
Imprint: Springer-Verlag New York Inc.
Edition: 1st ed. 1999. Corr. 2nd printing 2001
Dimensions:
Width: 15.50cm
, Height: 2.00cm
, Length: 23.50cm
Weight: 1.530kg
ISBN: 9780387984230
ISBN 10: 0387984232
Pages: 349
Publication Date: 10 June 1999
Audience:
College/higher education
,
Professional and scholarly
,
Undergraduate
,
Postgraduate, Research & Scholarly
Format: Hardback
Publisher's Status: Active
Availability: Out of print, replaced by POD
We will order this item for you from a manufatured on demand supplier.
Reviews
B. Artmann <p>Euclid - The Creation of Mathematics <p> The author invites the a ~lover of mathematicsa (TM) to have a peek, via a gentle introduction and presentation of Euclida (TM)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. a AMERICAN MATHEMATICAL SOCIETY
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
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
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
