Overview
The final book in Israel Gelfand's internationally renowned correspondence course
Focuses on geometric constructions and includes over 400 figures in order to develop students' geometrical intuition
Contains a large number of exercises with answers, as well as problems suggested for further study
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Table of contents (4 chapters)
Keywords
About this book
Geometry takes a different approach to presenting basic geometry for high-school students and others new to the subject. Rather than following the traditional axiomatic method that emphasizes formulae and logical deduction, it focuses on geometric constructions. Illustrations and problems are abundant throughout, and readers are encouraged to draw figures and “move” them in the plane, allowing them to develop and enhance their geometrical vision, imagination, and creativity. Chapters are structured so that only certain operations and the instruments to perform these operations are available for drawing objects and figures on the plane. This structure corresponds to presenting, sequentially, projective, affine, symplectic, and Euclidean geometries, all the while ensuring students have the necessary tools to follow along.
Geometry is suitable for a large audience, which includes not only high school geometry students, but also teachers and anyone else interested in improving their geometrical vision and intuition, skills useful in many professions. Similarly, experienced mathematicians can appreciate the book’s unique way of presenting plane geometry in a simple form while adhering to its depth and rigor.
“Gelfand was a great mathematician and also a great teacher. The book provides an atypical view of geometry. Gelfand gets to the intuitive core of geometry, to the phenomena of shapes and how they move in the plane, leading us to a better understanding of what coordinate geometry and axiomatic geometry seek to describe.”
- Mark Saul, PhD, Executive Director, Julia Robinson Mathematics Festival
“The subject matter is presented as intuitive, interesting and fun. No previous knowledge of the subject is required. Starting from the simplest concepts and by inculcating in the reader the use of visualization skills, [and] after reading the explanations and working through the examples, you will be able to confidently tackle the interesting problems posed. I highly recommend the book to any person interested in this fascinating branch of mathematics.”
- Ricardo Gorrin, a student of the Extended Gelfand Correspondence Program in Mathematics (EGCPM)
Reviews
“This book is intended to engage the reader visually, tactilely, and kinesthetically. … It has a good set of material to enliven more traditional geometry instruction. … There are problems and exercises throughout. The exercises are accompanied by solutions.” (MAA Reviews, October 10, 2020)
Authors and Affiliations
About the authors
In 1964, he created the Correspondence School in Mathematics (ZMSH) in Moscow, and later on, the Gelfand Correspondence Program in Mathematics (GCPM) at Rutgers University, both of which made mathematics available to a broad range of students. His goal was to pass on to students his belief that mathematics is simple, beautiful, and a part of human culture which anyone can learn and enjoy, just like literature, poetry, art, and music.
Tatiana Alekseyevskaya (Gelfand) graduated from the Department of Cybernetics and Applied Mathematics at Kiev State University in Ukraine. She then received her PhD in Mathematics in Moscow for her research on systems of quasi-linear equations and related geometrical constructions describing isotachophoresis, a process used in biological studies of protein molecules. She has extensive experience teaching mathematics to undergraduate students in both Russia and the United States, and worked closely with Israel Gelfand at Rutgers University, preparing assignments to be used in the GCPM.
Bibliographic Information
Book Title: Geometry
Authors: Israel M. Gelfand, Tatiana Alekseyevskaya (Gelfand)
DOI: https://doi.org/10.1007/978-1-0716-0299-7
Publisher: Birkhäuser New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Authors 2020
Softcover ISBN: 978-1-0716-0297-3Published: 23 February 2020
eBook ISBN: 978-1-0716-0299-7Published: 22 February 2020
Edition Number: 1
Number of Pages: XXI, 420
Number of Illustrations: 467 b/w illustrations