Approaches to Algebra - Perspectives for Research and Teaching (Hardcover, 1996 ed.)

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.

General

Imprint:	Springer
Country of origin:	Netherlands
Series:	Mathematics Education Library, 18
Release date:	June 1996
First published:	June 1996
Editors:	N. Bednarz • C. Kieran • L. Lee
Dimensions:	235 x 155 x 22mm (L x W x T)
Format:	Hardcover
Pages:	348
Edition:	1996 ed.
ISBN-13:	978-0-7923-4145-1
Categories:	Books > Social sciences > Education > Teaching of a specific subject Books > Science & Mathematics > Mathematics > General
LSN:	0-7923-4145-7
Barcode:	9780792341451

Is the information for this product incomplete, wrong or inappropriate? Let us know about it.

Does this product have an incorrect or missing image? Send us a new image.

Is this product missing categories? Add more categories.

Review This Product

No reviews yet - be the first to create one!