Kiselev's Geometry

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. . .

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/

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.