First published in by A. Kiselev as Elementary Geometry, by 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. Its introduction to the English speaking student and teacher is thus more than welcome. The effort by A.

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Adapted From Russian by Alexander Givental The book under review is an expanded translation of a unique phenomenon in the Russian mathematical literature. If nothing else, its staying power may serve an enticement to anyone interested in, or involved with, high school geometry. First published in by A. Kiselev as Elementary Geometry, by 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.

Its introduction to the English speaking student and teacher is more than welcome. The effort by Professor A. Givental who translated the book from Russian and combined pieces of the many editions of the original deserves a wholehearted recognition and sincere praise. The early history of the book is murky. Its 23rd edition is available online.

The upheaval of brought an overhaul of the education system based more on revolutionary zeal than on evolutionary societal demands. But towards the early s the situation was ripe for a more rational attitude. On February 12, , the Central Party Committee has issued a directive that instructed the responsible organizations to replace the "working class books" used in schools until then with specially designated "stable" textbooks Math Education , n1 , p.

The temporary replacement kept the official title until the mid s. It appears that in the recognition has been awarded to the text authored by N. Nikitin and A. Izvolsky, V. Boltyansky and I. Yaglom, A. Kolmogorov, a translation of J. I do not know whether by that time any book has been assigned an official status, but in a booklet Proofs in Geometry, first published in , A.

Fetisov while illustrating an erroneous proof notes dejectedly that the diagram is similar to the one used in an officially "approved book". There is no doubt as to what book he referred to. There is no doubt that the wind of change in geometry education that began blowing in Europe at the end of the 19th century, has reached and influenced the Russian policy makers.

He accordingly split the theorem into two parts, the first of which did not require parallel lines. To a teacher a theorem of such significance provides a rich background for historical and philosophical discussion that most students are capable of appreciating. He does not follow Euclid blindly, though. Geometric objects are introduced each in its time, not at the beginning of the book. Their properties are defined when they become needed or are about to be proved.

Kiselev also goes to some length to clarify general notions, like theorem and axiom, explains the relation between a theorem and its converse, inverse, and contrapositive statements, and proof by contradiction.

Many sections are preceded by short introductions. Sometimes the divergence from the Elements is significant as, for example, in his treatment of the Pythagorean theorem. He proves the theorem only after the theory of proportions. And the proof p. Along with the full version of VI. 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 may even occasionally distract from the subject.

Circumference is defined p. Does not sound impressive? But consider then that Kiselev goes to a considerable length by preceding the definition with a reasonably developed theory of limits pp. For example, the book does prove that the limit which is the circumference exists p.

This comes after a thorough discussion of similarity pp. In particular, he proves p. Combining this with the theory of limits he derives p. For example, H. Jacobs Geometry, 3rd ed, p. And this after constructing a table for several polygons and observing the behavior of the ratio. Another topic that drew my attention is the irrationality of the square root of 2. The proof is then followed by articles on lengths of segments, approximation, irrational numbers and the number line.

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 commonly are violated in the text.

This is done tacitly or with a reference to the imposed limitations on the size or the scope of the book. Assuming only very basic knowledge of mathematics, Kiselev builds a geometry edifice from the bottom up supplying both bricks and mortar in the process. The book is very much self-contained. The book comes with nearly exercises distributed all over the book. Some are supplied with hints but none with a solution. I do not believe Kiselev had an intention or a pedagogical reason to conceal solutions from the student.

In the Introduction to the first edition, he mentions a then available problem collection from which he drew exercises. While I do think that the absence of a solution key in the first English edition may deter some potential users, I do not believe it should. On one hand, in the body of the book, Kiselev devotes considerable time to solving problems, paying special attention to a variety of basic constructions.

The text is interspersed with remarks on problem solving and methods of proof all of which come with practical demonstrations. On the other hand, at this time and day and access to the internet, an interested student can easily get a solution to a problem or two or an advice to help with a solution. There is a multitude of online forums that exist just to this end. The book will serve well geometry students and teachers, homeschoolers, student teachers and their instructors.

Book I. ISBN

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## KISELEV PLANIMETRY PDF

Adapted From Russian by Alexander Givental The book under review is an expanded translation of a unique phenomenon in the Russian mathematical literature. If nothing else, its staying power may serve an enticement to anyone interested in, or involved with, high school geometry. First published in by A. Kiselev as Elementary Geometry, by 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. Its introduction to the English speaking student and teacher is more than welcome.

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## Kiselev's Geometry, Book I: Planimetry

The book is also good for experience with proofs, another topic which is slowly disappearing in all but its simplest form from high school curricula. The book dominated in Russian math education for several decades, was reprinted in dozens of millions of copies, influenced geometry education in Eastern Europe and China, and is still active as a textbook for grades. Each section ends with a large set of problems to answer and a few proofs to work through. Competition Math for Middle School Paperback. BF is congruent to CG.