Euclid—The Creation of Mathematics

Benno Artmann (Autor)

Buch | Softcover

349 Seiten

2012 | Softcover reprint of the original 1st ed. 1999
Springer-Verlag New York Inc.
978-1-4612-7134-5 (ISBN)

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This book is for all lovers ofmathematics. It is an attempt to under stand the nature of mathematics from the point of view of its most important early source. Even if the material covered by Euclid may be considered ele mentary for the most part, the way in which he presents it has set the standard for more than two thousand years. Knowing Euclid's Elements may be ofthe same importance for a mathematician today as knowing Greek architecture is for an architect. Clearly, no con temporary architect will construct a Doric temple, let alone organize a construction site in the way the ancients did. But for the training ofan architect's aesthetic judgment, a knowledge ofthe Greek her itage is indispensable. I agree with Peter Hilton when he says that genuine mathematics constitutesone ofthe finest expressions ofthe human spirit, and I may add that here as in so many other instances, we have learned that language ofexpression from the Greeks. While presenting geometry and arithmetic Euclid teaches us es sential features of mathematics in a much more general sense. 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 enforces the strictly deductive presentation ofa theory. We learn what creative definitions are and v VI ----=P:. . :re:. ::::fa=ce how a conceptual grasp leads to toe classification ofthe relevant ob jects.

1 General Historical Remarks.- 2 The Contents of the Elements.- 3 The Origin of Mathematics 1: The Testimony of Eudemus.- 4 Euclid Book I: Basic Geometry.- 5 The Origin of Mathematics 2: Parallels and Axioms.- 6 The Origin of Mathematics 3: Pythagoras of Samos.- 7 Euclid Book II: The Geometry of Rectangles.- 8 The Origin of Mathematics 4: Squaring the Circle.- 9 Euclid Book III: About the Circle.- 10 The Origin of Mathematics 5: Problems and Theories.- 11 Euclid Book IV: Regular Polygons.- 12 The Origin of Mathematics 6: The Birth of Rigor.- 13 The Origin of Mathematics 7: Polygons After Euclid.- 14 Euclid Book V: The General Theory of Proportions.- 15 Euclid Book VI:Similarity Geometry.- 16 The Origin of Mathematics 8: Be Wise, Generalize.- 17 Euclid Book VII: Basic Arithmetic.- 18 The Origin of Mathematics 9: Nicomachus and Diophantus.- 19 Euclid Book VIII: Numbers in Continued Proportion, the Geometry of Numbers.- 20 The Origin of Mathematics 10: Tools and Theorems.- 21 Euclid Book IX: Miscellaneous Topics from Arithmetic.- 22 The Origin of Mathematics 11: Math Is Beautiful.- 23 Euclid Book X: Incommensurable Magnitudes 23.1 Commensurability and Its Relation to Other Notions 227.- 24 The Origin of Mathematics 12: Incommensurability and Irrationality.- 25 Euclid Book XI: Solid Geometry.- 26 The Origin of Mathematics 13: The Role of Definitions.- 27 Euclid Book XII: Volume by Limits.- 28 The Origin of Mathematics 14: The Taming of the Infinite.- 29 Euclid Book XIII: Regular Polyhedra.- 30 The Origin of Mathematics 15: Symmetry Through the Ages.- 31 The Origin of Mathematics 16: The Origin of the Elements.- Notes.

Illustrationen	B. Artmann
Zusatzinfo	XVI, 349 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Euclid • Euclid's elements • Geometry • History of Mathematics
ISBN-10	1-4612-7134-7 / 1461271347
ISBN-13	978-1-4612-7134-5 / 9781461271345
Zustand	Neuware