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Descripción Buch. Condición: 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. Nº de ref. del artículo: 9780792341451
Descripción Hardcover. Condición: new. Nº de ref. del artículo: 9780792341451
Descripción Gebunden. Condición: 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. Nº de ref. del artículo: 5967839
Descripción Condición: New. Nº de ref. del artículo: ABLIING23Feb2416190182237
Descripción Buch. Condición: 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. Nº de ref. del artículo: 9780792341451
Descripción Condición: New. PRINT ON DEMAND Book; New; Fast Shipping from the UK. No. book. Nº de ref. del artículo: ria9780792341451_lsuk
Descripción Condición: 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. . . . . Nº de ref. del artículo: V9780792341451
Descripción Condición: 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. Nº de ref. del artículo: V9780792341451