Customer Reviews

Kiselev's Geometry / Book I. Planimetry

5 star:		(5)
4 star:		(0)
3 star:		(1)
2 star:		(1)
1 star:		(0)

 

 

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.

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: http://www.sumizdat.org/

Being obsessed in creating "more accessible" learning material for the higher grades, boards of education around the globe tend to approved what can be best described as mediocre material in geometry and mathematics. Regretfully this has become the norm. Though more than a century old, Kiselev's Geometry stays current and teaches mid graders the structure and lucid reasoning of geometry. It further teaches the children proper mathematical rigor and serves as a proper introduction for higher mathematics in collage.

This is an incredible work. There may be a few, "better" textbooks. The educational community is on a pattern of creating new works every few years. In some cases, we don't need to revise - the older books are better. This may be one of those. . .

This work by Kiselev was first published in 1892 and it remained a staple of Russian mathematical education until 1955, when it was officially phased out. For some time it was formally designated a "staple", meaning that it was the textbook to be used throughout the Soviet Union. After it was demoted, even though it was not the official textbook, it was still widely used as an under-the-desk reference. When you read the work, there is no doubt in your mind why it held such a high status for so long. Targeted for what would be equivalent to 7th through 9th graders in America, the explanations of planar geometry are excellent. Each section ends with a large set of problems to answer and a few proofs to work through. Solutions to the exercises are not included.

Planar geometry is an area of mathematics that is abstract in foundation but concrete in practice as the student can always draw a figure for reference. This book should be on the reference desk of every secondary school teacher of geometry. The main chapter headings are:

*) The straight line

*) The circle

*) Similarity

*) Regular polygons & circumference

*) Areas

Published in Journal of Recreational Mathematics reprinted with permission

The geometric concepts are presented well, but the language is not clear. The topic requires not just an explanation of points, rays, lines, segments, circles, angles and other elements of planimetry, it also demands an authoritative command of the language to define the terms, theorems, and corollaries. I doubt that the authority of language was lost in the translation from Russian. This book is disappointing in the way it discusses the subject with the apparent assumption that the reader understands terms and concepts perfectly even though they have only been poorly explained in the author's words. It's like reading a badly written product manual. One can very well learn to operate the product, but it's so much more pleasant when the instructions are more perfectly lucid. Only with such definitive language could a book on geometry take the place of authority this one appears to have been given by others.

I am a homeschooler grandpa with EE educational background and retired from a career in industry doing computing,math & statistics. Geometry is not my expertise so my opinion needs to be understood in this context.

I was excited about this text book because of its reviews that said it was a very practical and widely revered textbook for decades in Russia. I purchased the book and chose to return it because it seemed lacking in modern instruction approaches. The book is small and does not use nice visual graphics to make learning easier. There are no separate teacher's resource materials to help an inexperienced teacher get up to speed on the topics. I am not an expert but I have purchased Ray C Jurgensen's textbook "Geometry" Publ by McDougal Littell 1990-2000. ISBN 0-395-97727-4. So far I am liking this text but I also found a teacher's edition ISBN 0-395-97728-2 which I find necessary and very helpful for this inexperienced geometry teacher. So far I give these Jurgensen Geometry books together a 5-star rating.