The Method of Coordinates

Gelfand Correspondence Program in Mathematics

by Israel M. Gelfand, E.G. Glagoleva, A.A. Kirillov

This introductory text explores the translation of geometric concepts into the language of numbers in order to define the position of a point in space (the orbit of a satellite, for example). The two-part treatment begins with discussions of the coordinates of points on a line, coordinates of points in a plane, and the coordinates of points in space.
Part 2 examines geometry as an aid to calculation and the necessity and peculiarities of four-dimensional space. Written for systematic study, it features a helpful series of "road signs" in the margins, alerting students to passages requiring particular attention, and an abundance of ingenious problems — with solutions, answers, and hints — promote habits of independent work

Genres: Mathematics, Textbooks, Reference, Geometry

80 pages, Paperback

First published January 1, 1967

About the author

Israel Moiseevich Gelfand, also written Israïl Moyseyovich Gel'fand, or Izrail M. Gelfand (Yiddish: ישראל געלפֿאַנד‎, Russian: Израиль Моисеевич Гельфанд ; 2 September [O.S. 20 August] 1913 – 5 October 2009) was a prominent Soviet mathematician. He made significant contributions to many branches of mathematics, including group theory, representation theory and functional analysis. The recipient of many awards, including the Order of Lenin and the Wolf Prize, he was a Fellow of the Royal Society and professor at Moscow State University and, after immigrating to the United States shortly before his 76th birthday, at Rutgers University.

Reviews

[Kate · Rating 5 out of 5]

I read the Dover edition of this book. It did take getting used to the cheaper printing and there were a few errors, but on the whole it was an acceptable publication.

I'm not sure how I would have fared without a bit of a math background. I think these books were originally written for high schoolers, but there's no way I could have waded through Method of Coordinates in high school. (I was not a particularly good math student, though.)

The first chunk of this book handled absolute value which was a challenge for me, but Gelfand gave superior explanations and problems to any other math text that I've seen cover absolute value. Next Gelfand covered coordinates in two dimensions and the distance formula. Gelfand spends a few pages on polar coordinates before he handles everything again in three dimensions and then finally in four dimensions. And then it's all over on page 69.

This is my second book in this series. I started with Trigonometry. These books really do give the student a deeper understanding of the material presented in high school and the problems give a much better preparation for Calculus.

[Bruno Oliveira · Rating 5 out of 5]

Uma obra prima que por aliar simplicidade e precisão deveria ser incorporada ao ensino básico. Merecedor de uma resenha mais detalhada que infelizmente agora não posso escrever.

[Maxim Perepelitsyn · Rating 5 out of 5]

Yet another great booklet from Gelfand, nice introduction to 4d space and cube.