Euclid's treatment of mathematics and the presentation of its essential features has set the standard which remains today, and which every mathematician should know
Artmann reveals many pieces of beautiful mathematics from the Elements, which are easily accessible and can be studied in detail by anyone with a minimal training in math
Each book of the Elements is clearly described in detail, and proofs are given for important results
Modernized language is used to make the material more accessible to the reader
Includes general remarks about typical mathematical procedures of the day, subjects of historical interest, and connections to philosophy
Euclid's treatment of mathematics and the presentation of its essential features has set the standard which remains today, and which every mathematician should know
Artmann reveals many pieces of beautiful mathematics from the Elements, which are easily accessible and can be studied in detail by anyone with a minimal training in math
Each book of the Elements is clearly described in detail, and proofs are given for important results
Modernized language is used to make the material more accessible to the reader
Includes general remarks about typical mathematical procedures of the day, subjects of historical interest, and connections to philosophy
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.
|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.|This is a book for all lovers of mathematics with a solid background in high school geometry, from teachers and students to university professors. For each of Euclid's thirteen Books, the author has given a general deillegalscription of the contents and structure of the Book, plus one or two sample proofs.
Preface *Notes to the reader *General historical remarks *The Origins of Mathematics I: 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 Defiinitions *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 *Notes *Bibliography *Index
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
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.
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.
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
Inhaltsverzeichnis
Preface *Notes to the reader *General historical remarks *The Origins of Mathematics I: 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 Defiinitions *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 *Notes *Bibliography *Index
Klappentext
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.
This is a book for all lovers of mathematics with a solid background
in high school geometry, from teachers and students to university
professors. For each of Euclid's thirteen Books, the author has given
a general deillegalscription of the contents and structure of the Book, plus
one or two sample proofs.
