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The Method of Coordinates Paperback – January 1, 1990

ISBN-13: 978-0817635336 ISBN-10: 0817635335 Edition: 1990th

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The Method of Coordinates + Functions and Graphs (Dover Books on Mathematics) + Algebra
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Product Details

  • Paperback: 74 pages
  • Publisher: Birkhäuser; 1990 edition (January 1, 1990)
  • Language: English
  • ISBN-10: 0817635335
  • ISBN-13: 978-0817635336
  • Product Dimensions: 6 x 0.2 x 9 inches
  • Shipping Weight: 4.8 ounces (View shipping rates and policies)
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Best Sellers Rank: #1,763,903 in Books (See Top 100 in Books)

Editorial Reviews

Review

"All through both volumes [‘Functions & Graphs’ and ‘The Methods of Coordinates’], one finds a careful description of the step-by-step thinking process that leads up to the correct definition of a concept or to an argument that clinches in the proof of a theorem. We are ... very fortunate that an account of this caliber has finally made it to printed pages... Anyone who has taken this guided tour will never be intimidated ever again... High school students (or teachers) reading through these two books would learn an enormous amount of good mathematics. More importantly, they would also get a glimpse of how mathematics is done."

--- H. Wu, The Mathematical Intelligencer

"This book is a concise and compact treatment of the essential ideas of coordinate geometry.  The authors demonstrate powerfully how geomtric ides may be communicated and studied effectively without the aid of pictures.  Graphics are of course of vital importance int he methods of Euclidean geometry. However, the methods of coordinate geometry are able to transform pure geometric ideas into algebraic manipulations where the meaning is very clear once the formalism is learnt. In particular the book demonstrates the value of conveying information in the form of images embedded in formulas.  This is very useful in the transmission of information by electronic means. . . This book is a valuable tool for teaching the redimentary concepts of analytical geometry.  It contains a number of excellent examples and exercises which go further than a mere introductory programme.  the exercises, while not numerous, are very thought-provoking and are bound to pose a serious challenge to the interested student."

---The Mathematical Gazette

Language Notes

Text: English (translation)
Original Language: Russian

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22 of 23 people found the following review helpful By N. F. Taussig on July 15, 2004
Format: Paperback
The authors of this slim volume demonstrate the power of coordinate geometry, which they describe as a means of translating geometric figures into algebraic formulas, through their lucid exposition, interesting examples, and well-chosen exercises.

The authors begin with the coordinate geometry of the real line. They discuss absolute value and define what distance means. Next the authors examine the coordinate geometry of the plane. They define distance in the plane, show how relations among the coordinates define geometric figures, and discuss different coordinate systems that can be used in the plane. Their examples illustrate how algebraic methods developed by Rene Descartes make it possible to solve geometric problems efficiently that would be quite difficult to solve using synthetic geometry. The authors then treat the coordinate geometry of three-dimensional space in a similar manner.

The second part of the book begins with a problem concerning lattice points in the plane. The authors use this example and its generalizations to justify exploring the coordinate geometry of four-dimensional space. They carefully treat the example of a four-dimensional unit hypercube, examining its properties by considering its analogues in lower dimensions: the segment [0, 1] of the real number line, the unit square in the coordinate plane, and the unit cube in space.

Since the book was initially written for a correspondence course for high school students in the Soviet Union, it is designed for self-study and accessible to students who have had high school courses in algebra and geometry.
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Format: Paperback
To succeed in mathematics, it is necessary to understand the different coordinate systems. The Cartesian coordinate system, where algebra and geometry are combined into a single synergistic operation, is one of the greatest of all mathematical achievements. Most students at the lower levels are exposed to the Cartesian system, but unfortunately not to the other coordinate systems.

The authors develop a full explanation of the basic Cartesian system by starting with the linear coordinate system. They then expand it out to two, three and four dimensions. The transition is easy and understandable. They also briefly cover the various forms of polar coordinates in two and three dimensions. With thorough and complete explanations of the basic coordinate systems, this book is an excellent primer on this fundamental concept of mathematics. All students should be exposed to coordinate systems other than the Cartesian, humans use the three-dimensional coordinate system more than we use the two dimensional coordinate system.
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