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Throughout the history of mathematics, maximum and minimum problems
have played an important role in the evolution of the field. Many
beautiful and important problems have appeared in a variety of
branches of mathematics and physics, as well as in other fields of
sciences. The greatest scientists of the past - Euclid, Archimedes,
Heron, the Bernoullis, Newton, and many others - took part in
seeking solutions to these concrete problems. The solutions
stimulated the development of the theory, and, as a result,
techniques were elaborated that made possible the solution of a
tremendous variety of problems by a single method. This book
presents fifteen 'stories' designed to acquaint readers with the
central concepts of the theory of maxima and minima, as well as
with its illustrious history.This book is accessible to high school
students and would likely be of interest to a wide variety of
readers. In Part One, the author familiarizes readers with many
concrete problems that lead to discussion of the work of some of
the greatest mathematicians of all time. Part Two introduces a
method for solving maximum and minimum problems that originated
with Lagrange. While the content of this method has varied
constantly, its basic conception has endured for over two
centuries. The final story is addressed primarily to those who
teach mathematics, for it impinges on the question of how and why
to teach. Throughout the book, the author strives to show how the
analysis of diverse facts gives rise to a general idea, how this
idea is transformed, how it is enriched by new content, and how it
remains the same in spite of these changes.
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Geometry (Paperback)
V. V. Prasolov, V.M. Tikhomirov
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R4,099
Discovery Miles 40 990
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Ships in 12 - 17 working days
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This book provides a systematic introduction to various geometries,
including Euclidean, affine, projective, spherical, and hyperbolic
geometries. Also included is a chapter on infinite-dimensional
generalizations of Euclidean and affine geometries. A uniform
approach to different geometries, based on Klein's Erlangen Program
is suggested, and similarities of various phenomena in all
geometries are traced. An important notion of duality of geometric
objects is highlighted throughout the book. The authors also
include a detailed presentation of the theory of conics and
quadrics, including the theory of conics for non-Euclidean
geometries. The book contains many beautiful geometric facts and
has plenty of problems, most of them with solutions, which nicely
supplement the main text. With more than 150 figures illustrating
the arguments, the book can be recommended as a textbook for
undergraduate and graduate-level courses in geometry.
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