Benno Artmann

Euclid-The Creation of Mathematics (eBook, PDF)

• Format: PDF

Produktbeschreibung

Euclid presents the essential of mathematics in a manner which has set a high standard for more than 2000 years. This book, an explanation of the nature of mathematics from its most important early source, is for all lovers of mathematics with a solid background in high school geometry, whether they be students or university professors.

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Produktdetails

• Verlag: Springer New York
• Seitenzahl: 349
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9781461214120
• Artikelnr.: 44058121

Inhaltsangabe

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.

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