Articles liés à Approaches to Algebra: Perspectives for Research and...
Synopsis
In Greek geometry, there is an arithmetic of magnitudes in which, in terms of numbers, only integers are involved. This theory of measure is limited to exact measure. Operations on magnitudes cannot be actually numerically calculated, except if those magnitudes are exactly measured by a certain unit. The theory of proportions does not have access to such operations. It cannot be seen as an "arithmetic" of ratios. Even if Euclidean geometry is done in a highly theoretical context, its axioms are essentially semantic. This is contrary to Mahoney's second characteristic. This cannot be said of the theory of proportions, which is less semantic. Only synthetic proofs are considered rigorous in Greek geometry. Arithmetic reasoning is also synthetic, going from the known to the unknown. Finally, analysis is an approach to geometrical problems that has some algebraic characteristics and involves a method for solving problems that is different from the arithmetical approach. 3. GEOMETRIC PROOFS OF ALGEBRAIC RULES Until the second half of the 19th century, Euclid's Elements was considered a model of a mathematical theory. This may be one reason why geometry was used by algebraists as a tool to demonstrate the accuracy of rules otherwise given as numerical algorithms. It may also be that geometry was one way to represent general reasoning without involving specific magnitudes. To go a bit deeper into this, here are three geometric proofs of algebraic rules, the frrst by Al-Khwarizmi, the other two by Cardano.
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(eds.) Approaches to Algebra. Perspectives for Reasearch and Teaching.
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Kluwer, Dordrecht, 1996
ISBN 10 : 0792341457
ISBN 13 : 9780792341451
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Hardcover. Etat : Wie neu. Dordrecht, Kluwer (1996). gr.8°. Some figs. XV, 345 p. Hardbound. Mathematics Education Library, volume 18.- Incl. bibliography. N° de réf. du vendeur 95220
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Approaches to Algebra: Perspectives for Research and Teaching. Mathematics Education Library, Band 18;
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gebundene Ausgabe. Etat : Gut. 345 Seiten; Das hier angebotene Buch stammt aus einer teilaufgelösten wissenschaftlichen Bibliothek und trägt die entsprechenden Kennzeichnungen (Rückenschild, Instituts-Stempel.); Schnitt und Einband sind etwas staubschmutzig; der Buchzustand ist ansonsten ordentlich und dem Alter entsprechend gut. Text in ENGLISCHER Sprache! Sprache: Englisch Gewicht in Gramm: 800. N° de réf. du vendeur 1574995
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Approaches to Algebra
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Springer Netherlands Jun 1996, 1996
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ISBN 13 : 9780792341451
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Buch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -In Greek geometry, there is an arithmetic of magnitudes in which, in terms of numbers, only integers are involved. This theory of measure is limited to exact measure. Operations on magnitudes cannot be actually numerically calculated, except if those magnitudes are exactly measured by a certain unit. The theory of proportions does not have access to such operations. It cannot be seen as an 'arithmetic' of ratios. Even if Euclidean geometry is done in a highly theoretical context, its axioms are essentially semantic. This is contrary to Mahoney's second characteristic. This cannot be said of the theory of proportions, which is less semantic. Only synthetic proofs are considered rigorous in Greek geometry. Arithmetic reasoning is also synthetic, going from the known to the unknown. Finally, analysis is an approach to geometrical problems that has some algebraic characteristics and involves a method for solving problems that is different from the arithmetical approach. 3. GEOMETRIC PROOFS OF ALGEBRAIC RULES Until the second half of the 19th century, Euclid's Elements was considered a model of a mathematical theory. This may be one reason why geometry was used by algebraists as a tool to demonstrate the accuracy of rules otherwise given as numerical algorithms. It may also be that geometry was one way to represent general reasoning without involving specific magnitudes. To go a bit deeper into this, here are three geometric proofs of algebraic rules, the frrst by Al-Khwarizmi, the other two by Cardano. 372 pp. Englisch. N° de réf. du vendeur 9780792341451
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Approaches to Algebra: Perspectives for Research and Teaching (Mathematics Education Library, 18)
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Springer, 1996
ISBN 10 : 0792341457
ISBN 13 : 9780792341451
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Etat : Good. Your purchase helps support Sri Lankan Children's Charity 'The Rainbow Centre'. Ex-library, so some stamps and wear, but in good overall condition. Our donations to The Rainbow Centre have helped provide an education and a safe haven to hundreds of children who live in appalling conditions. N° de réf. du vendeur Z1-W-007-02269
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Approaches to Algebra
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Gebunden. Etat : New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. In Greek geometry, there is an arithmetic of magnitudes in which, in terms of numbers, only integers are involved. This theory of measure is limited to exact measure. Operations on magnitudes cannot be actually numerically calculated, except if those magnit. N° de réf. du vendeur 5967839
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Approaches to Algebra: Perspectives for Research and Teaching (Mathematics Education Library, 18)
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Approaches to Algebra : Perspectives for Research and Teaching
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Buch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - In Greek geometry, there is an arithmetic of magnitudes in which, in terms of numbers, only integers are involved. This theory of measure is limited to exact measure. Operations on magnitudes cannot be actually numerically calculated, except if those magnitudes are exactly measured by a certain unit. The theory of proportions does not have access to such operations. It cannot be seen as an 'arithmetic' of ratios. Even if Euclidean geometry is done in a highly theoretical context, its axioms are essentially semantic. This is contrary to Mahoney's second characteristic. This cannot be said of the theory of proportions, which is less semantic. Only synthetic proofs are considered rigorous in Greek geometry. Arithmetic reasoning is also synthetic, going from the known to the unknown. Finally, analysis is an approach to geometrical problems that has some algebraic characteristics and involves a method for solving problems that is different from the arithmetical approach. 3. GEOMETRIC PROOFS OF ALGEBRAIC RULES Until the second half of the 19th century, Euclid's Elements was considered a model of a mathematical theory. This may be one reason why geometry was used by algebraists as a tool to demonstrate the accuracy of rules otherwise given as numerical algorithms. It may also be that geometry was one way to represent general reasoning without involving specific magnitudes. To go a bit deeper into this, here are three geometric proofs of algebraic rules, the frrst by Al-Khwarizmi, the other two by Cardano. N° de réf. du vendeur 9780792341451
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Approaches to Algebra
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Springer Netherlands, Springer Netherlands Jun 1996, 1996
ISBN 10 : 0792341457
ISBN 13 : 9780792341451
Neuf
Couverture rigide
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Buch. Etat : Neu. This item is printed on demand - Print on Demand Titel. Neuware -In Greek geometry, there is an arithmetic of magnitudes in which, in terms of numbers, only integers are involved. This theory of measure is limited to exact measure. Operations on magnitudes cannot be actually numerically calculated, except if those magnitudes are exactly measured by a certain unit. The theory of proportions does not have access to such operations. It cannot be seen as an 'arithmetic' of ratios. Even if Euclidean geometry is done in a highly theoretical context, its axioms are essentially semantic. This is contrary to Mahoney's second characteristic. This cannot be said of the theory of proportions, which is less semantic. Only synthetic proofs are considered rigorous in Greek geometry. Arithmetic reasoning is also synthetic, going from the known to the unknown. Finally, analysis is an approach to geometrical problems that has some algebraic characteristics and involves a method for solving problems that is different from the arithmetical approach. 3. GEOMETRIC PROOFS OF ALGEBRAIC RULES Until the second half of the 19th century, Euclid's Elements was considered a model of a mathematical theory. This may be one reason why geometry was used by algebraists as a tool to demonstrate the accuracy of rules otherwise given as numerical algorithms. It may also be that geometry was one way to represent general reasoning without involving specific magnitudes. To go a bit deeper into this, here are three geometric proofs of algebraic rules, the frrst by Al-Khwarizmi, the other two by Cardano.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 372 pp. Englisch. N° de réf. du vendeur 9780792341451
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Approaches to Algebra
Edité par
Kluwer Academic Publishers, 1996
ISBN 10 : 0792341457
ISBN 13 : 9780792341451
Neuf
Couverture rigide
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Etat : New. Aims at understanding the functioning of algebraic reasoning, its characteristics, the difficulties students encounter in making the transition to algebra, and the situations conducive to its favorable development. This book provides an introduction to generalization, problem solving, modeling, and functions. Editor(s): Bednarz, Nadine; Kieran, Carolyn (Universite du Quebec a Montreal, Canada); Lee, L. (Universite de Quebec a Montreal, Canada). Series: Mathematics Education Library. Num Pages: 364 pages, biography. BIC Classification: JNU; PBF. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 235 x 155 x 22. Weight in Grams: 698. . 1996. Hardback. . . . . N° de réf. du vendeur V9780792341451
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Approaches to Algebra
Edité par
Kluwer Academic Publishers, 1996
ISBN 10 : 0792341457
ISBN 13 : 9780792341451
Neuf
Couverture rigide
Vendeur : Kennys Bookstore, Olney, MD, Etats-Unis
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Etat : New. Aims at understanding the functioning of algebraic reasoning, its characteristics, the difficulties students encounter in making the transition to algebra, and the situations conducive to its favorable development. This book provides an introduction to generalization, problem solving, modeling, and functions. Editor(s): Bednarz, Nadine; Kieran, Carolyn (Universite du Quebec a Montreal, Canada); Lee, L. (Universite de Quebec a Montreal, Canada). Series: Mathematics Education Library. Num Pages: 364 pages, biography. BIC Classification: JNU; PBF. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 235 x 155 x 22. Weight in Grams: 698. . 1996. Hardback. . . . . Books ship from the US and Ireland. N° de réf. du vendeur V9780792341451
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