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Kiselev's Geometry / Book I. Planimetry Hardcover – December 31, 2006


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Product Details

  • Hardcover: 248 pages
  • Publisher: Sumizdat (December 31, 2006)
  • Language: English
  • ISBN-10: 0977985202
  • ISBN-13: 978-0977985203
  • Product Dimensions: 8.6 x 5.6 x 0.8 inches
  • Shipping Weight: 15.2 ounces (View shipping rates and policies)
  • Average Customer Review: 4.4 out of 5 stars  See all reviews (14 customer reviews)
  • Amazon Best Sellers Rank: #163,207 in Books (See Top 100 in Books)

Editorial Reviews

Review

Beware the code words "quantitative reasoning" often bandied about by the secret enemies of geometry who would suppress that subject like some sort of pagan religion or foolish luxury. In fact, most high schools, for various reasons, bypass rigorous geometry for weak calculus; as a result, many college students now hit a brick wall trying to follow any precise logical argument, or worse, construct one. Plato warned us! In the book by Kiselev, translator Givental, himself a very distinguished mathematician, aims to rescue geometry for our time by bringing into English a classic of Russian pedagogy, a book with a track record extending back more than a century. Indeed, under the Soviets, an era of prodigious mathematical achievement, Kiselev's book actually attained the status of stable, meaning it was the entire nation's official book for classroom use, and it held that status for decades, remaining popular still. SUMIZDAT (the name evidently a portmanteau of sum and samizdat) calls itself a publisher promoting nonsense-free mathematics and science curricula. Givental's excellent and concise Linear Algebra and Differential Equations (2001), albeit published by the AMS, also nicely fits this category. Certainly library shelves must make a place for Kiselev's classic! By D. V. Feldman, University of New Hampshire. From November'07 issue of --Choice (book review magazine for academic libraries)

I highly recommend (...) Kiselev's Planimetry. I can claim that no geometry textbook in history of Western civilization was printed in more copies than Kiselev. By Alexandre Borovik, the author of ''Mathematics under the microscope" --Homeschoolmath blog.

The book under review is an expanded translation of a unique phenomenon in the Russian mathematical literature. First published in 1892 by A. P. Kiselev as Elementary Geometry, by 1940 it underwent more than 40 revisions and eventually became a measuring rod for geometry education in Russia against which all other textbooks had to be judged. If nothing else, this book's staying power may serve as an enticement to anyone interested in, or involved with, high school geometry. Its introduction to the English speaking student and teacher is thus more than welcome. The effort by A. Givental, who translated the book from Russian and combined pieces of the many editions of the original, deserves wholehearted recognition and sincere praise. (...) The book was originally written in a clear, no-nonsense style which has been polished over its many editions and revisions. The style was well preserved in the translation. There is nothing in the book that will even occasionally distract from the subject. (...) In the Translator's Foreword, Professor Givental mentions three virtues of a good textbook (precision, simplicity, conciseness) formulated yet by Kiselev himself, and adds a fourth one competence in the subject. Thinking specifically of Kiselev's Geometry, one other feature must be mentioned: autonomy of the discourse. Every textbook is created for a particular audience which is usually characterized by the level of preparedness to absorb the material, both in terms of the requisite knowledge and the ability to do so. The requirements are usually set up in the introduction and are commonly violated in the text. This is either done tacitly or with a reference to the imposed limitations on the size or the scope of the book. One salient virtue of Kiselev's Geometry is that, throughout, the author remains faithful to his intended audience, viz., middle and junior high school students taking up geometry for the first time. (...) The full review is found here --Mathematical Association of America Online Book Reviews. --Mathematical Association of America Online Book Reviews<br /><br /> --Mathematical Association of America Online Book Reviews

The book under review is an expanded translation of a unique phenomenon in the Russian mathematical literature. First published in 1892 by A. P. Kiselev as Elementary Geometry, by 1940 it underwent more than 40 revisions and eventually became a measuring rod for geometry education in Russia against which all other textbooks had to be judged. If nothing else, this book's staying power may serve as an enticement to anyone interested in, or involved with, high school geometry. Its introduction to the English speaking student and teacher is thus more than welcome. The effort by A. Givental, who translated the book from Russian and combined pieces of the many editions of the original, deserves wholehearted recognition and sincere praise. (...) The book was originally written in a clear, no-nonsense style which has been polished over its many editions and revisions. The style was well preserved in the translation. There is nothing in the book that will even occasionally distract from the subject. (...) In the Translator's Foreword, Professor Givental mentions three virtues of a good textbook (precision, simplicity, conciseness) formulated yet by Kiselev himself, and adds a fourth one competence in the subject. Thinking specifically of Kiselev's Geometry, one other feature must be mentioned: autonomy of the discourse. Every textbook is created for a particular audience which is usually characterized by the level of preparedness to absorb the material, both in terms of the requisite knowledge and the ability to do so. The requirements are usually set up in the introduction and are commonly violated in the text. This is either done tacitly or with a reference to the imposed limitations on the size or the scope of the book. One salient virtue of Kiselev's Geometry is that, throughout, the author remains faithful to his intended audience, viz., middle and junior high school students taking up geometry for the first time. (...) The full review is found here --Mathematical Association of America Online Book Reviews

I highly recommend (...) Kiselev's Planimetry. I can claim that no geometry textbook in history of Western civilization was printed in more copies than Kiselev. By Alexandre Borovik, the author of ''Mathematics under the microscope" --Homeschoolmath blog

From the Back Cover

"Those reading these lines are hereby summoned to raise their children to a good command of Elementary Geometry, to be judged by the rigorous standards of the ancient Greek mathematicians."

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Customer Reviews

All pictures are clear.
Natalia Smirnova
This book should be on the reference desk of every secondary school teacher of geometry.
Charles Ashbacher
Actually, when I choose a geometry book, the first thing I check is "two-column proof".
JS

Most Helpful Customer Reviews

44 of 45 people found the following review helpful By Lilia T on February 23, 2007
Format: Hardcover
This is a unique book that not only introduces the students to the world of 2-D Geometry, but teaches them fundamental concepts of mathematical logic and rigorous proof.

All the definitions and theorems are very well illustrated and discussed in a thought-provoking way. All pictures are intuitive and simple, and in many instances show different ways of thinking about the same concept, or problem, or idea.

The book achieves an extraordinary goal - using only elementary concepts it opens the world of real mathematics.

This goal is achieved by a combination of the time-proved approach to introducing the concepts of axioms, theorems, and proofs and an exceptionally rich set of well-tested exercises and problems of various levels of difficulty.

Kiselev's Geometry will greatly benefit every middle-school and high-school student who will study it carefully and thoughtfully. The benefits will go far beyond Geometry, as the students will gain ability to think about new concepts, approaches, ideas, and these skills are applicable to every single domain of the modern human knowledge.

The instruction of a competent and enthusiastic teacher is definitely needed for most students studying this book, as the material has to be discussed and played with.

This is not a self-study manual.
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28 of 29 people found the following review helpful By Natalia Smirnova on April 11, 2008
Format: Hardcover
There is no such person in Russia who never heard anything about "Geometry" by A. Kiselev. Usually students quickly forget names printed on covers of their school textbooks, but the name "Kiselev" became a legend. Several generations of Russian school students learned to think mathematically by studying this book.
Kiselev's Geometry is written in a plain language. Material is organized in a very logical way. All definitions, axioms and theorems are formulated in an absolutely precise mathematical style. All pictures are clear. All proofs are straightforward. This gives students an opportunity to understand everything in this book even after first reading and helps to build solid knowledge in geometry.
For people who wants to form their own opinion I would also recommend to read Translator's Foreword and take a look on sample pages (there are 49 of them) at the publisher's website: [...]
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10 of 10 people found the following review helpful By JS on December 27, 2013
Format: Hardcover Verified Purchase
Thirty five years ago when I was at school in China, I learned Euclidean geometry (both plane and solid) from my excellent math teachers. I enjoyed spending hours solving and proving hard problems. I had great pleasure from working on these problems - although a child, I felt capable of deducing something new based on a few simple definitions, axioms and theorems. More importantly, it enriched my life by making me appreciate the elegance of math and physical sciences.

Fast forward to the time when my child started grade 8 in Canada, to my great disappointment, the geometry education in North America has deteriorated to merely some formulas for simple calculations and sporadic geometrical facts without justifications. At the same time, the math textbooks are stuffed with some strange "innovations": mindless tessellation, confusing figure rotation, invalid "proof" by measurement, etc.

After shaking my head too many times, I decided to take matters into my own hands and to introduce my child to the beauty of Euclidean geometry. After browsing a few geometry books, I fell in love with this book. It has contents and styles almost identical to what I learned before. I even found many problems I solved decades ago. (In his preface, Prof. Givental mentioned that Kiselev had a great influence on geometry education in Eastern Bloc and China.) We had a slow start but we managed to finish the book in one year. For each worked theorem in the book, I explained the proof to my child first, and then asked her to read it and finally prove it in her language. This way, she studied and proved every worked theorem in the book. She also proved most of the proof problems and solved about 75% of the computation problems in the exercises.
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7 of 7 people found the following review helpful By CC on August 6, 2013
Format: Hardcover Verified Purchase
Warning: This book is a translation and has not been edited to make it easy to read. Part of why the book is hard to read is that all the given geometric information is presented in the order necessary to construct the corresponding figure (an important skill in geometry is to draw what you are proving! Geometry is visual, after all).

Unfortunately, common core and most other existing state standards screw up otherwise great books like this. These days, most geometry courses include too much material on co-ordinate geometry (useful in say the sciences at lower levels but not so useful for mathematicians and research scientists, especially when they have entire fields and courses dedicated to making everything co-ordinate-less), applications (again, leave this to the science courses. We do poorly in international rankings because we focus too little on learning the mathematical ideas), and misc. topics that get thrown in (e.g. the combined algebra and geometry courses now common in some districts).

This book stands out as one of the few remaining pure synthetic geometry textbooks. Synthetic simply refers to using axioms and definitions and proving theorems from them. Instead of calculations, the field, and this book, rely on logic. Every step must be and is justified. Classical proofs (alternative proofs are usually not given) are presented for all of the essential theorems, with none but the most specialized (usually contest and olympiad level material) left out. Note that this book only covers 2D geometry. For 3D geometry and vectors, use the second book, also by this author.
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