The English edition is intended for those students, homeschooled or not, who want to achieve a good command of elementary geometry, and learn to appreciate for its intellectual depth and beauty. More information about the book and its author is available through the publisher's webpage: www. The book is currently available at: www.
I posted this note here because some of you might be interested - a classical Russian geometry book translated into English. You can browse quite many sample pages to get an idea of the book. It was first published in has been revised and published more than forty times altogether. The original author Kiselev wrote several math textbooks. The books held this status until when they got replaced in this capacity by less successful clones written by more Soviet authors. Yet "Planimetry" remained the favorite under-the-desk choice of many teachers and a must for honors geometry students.
In the last decade, Kiselev's "Geometry," which has long become a rarity, was reprinted by several major publishing houses in Moscow and St. In the post-Soviet educational market, Kiselev's "Geometry" continues to compete successfully with its own grandchildren. If you look at the type of exercises found in the book, I think you will easily see that there is a difference when comparing to modern American books this book is meant for th graders.
For example these are from the sample pages provided on the website Suppose that an angle, its bisector, and one side of this angle in one triangle are respectively congruent to an angle, its bisector, and one side of this angle in another triangle. Prove that such triangles are congruent.
Prove that if two sides and the median drawn to the first of them in one triangle are respectively congruent to two sides and the median drawn to the first of them in another triangle, then such triangles are congruent. Prove theorems: If a diagonal divides a trapezoid into two similar triangles, then this diagonal is the geometric mean between the bases.
If two disks are tangent externally, then the segment of an external common tangent between the tangency points is the geometric mean between the diameters of the disks. If a square is inscribed into a right triangle in such a way that one side of the square lies on the hypotenuse, then this side is the geometric mean between the two remaining segments of the hypotenuse.
The altitude dropped to the hypotenuse divides a given right triangle into smaller triangles whose radii of the inscribed circles are 6 and 8 cm. Compute the radius of the inscribed circle of the given triangle. Compute the sides of a right triangle given the radii of its circumscribed and inscribed circle. Compute the area of a right triangle if the foot of the altitude dropped to the hypotenuse of length c divides it in the extreme and mean ratio.
Personally, I feel they are interesting sounding problems! I will probably solve some in future blogposts, as examples. But how many US high school students would be willing and able to do them? Feel free to comment. Now, this book could serve for a high school geometry course for sure. It does have one big disadvantage though if you're a homeschooler: there is no answer key. But the book appears to possess intellectual depth and beauty, just like its subject matter!
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Tags: math , geometry , curriculum. US students, I don't know, but I'm a Norwegian high school student interested in it : Though I'm pretty jealous at my Russian classmate's planimetry book in Russian Zadachi po planimetrii. Looks aweseome, and though there is an English translation in the public domain, it just isn't as cool as a thick, problem-rich textbook. I find problem 79 difficult to understand. That is, I don't understand what figure being described should look like.
Kiselev's geometry, Book 2 Stereometry - PDF Free Download
Recently I have been reading Heath's translation of Euclid's Elements and the greatest difficulty for me has been to understand the convoluted language of the translation. This can be a large obstacle to understanding. There is a two fold task: to think geometrically, and to speak and read geometrically.
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The chapter also includes an introduction into other non-Euclidean geometries: spherical and hyperbolic. Each section of the book is accompanied by a judicious selection of exercises about of which have been added in the translation. Many problems are solved in the body of the book, but the exercises come without solutions. In the afterword, Givental offers his thoughts on the changing role of axiomatics with a reference to Chapter 4 in modern mathematics and the contemporary ideology of math education as related to the teaching of geometry.
His analysis of the van Hiele model and the supporting research is remarkable. The van Hiele model stipulates that the ability of a learner to process geometric knowledge is determined by the level of geometric abstraction achieved by the learner. The prerequisite for attempting the next level is the mastering of the previous one. The five levels are. Since it originated in , van Hiele's theory has been supported by research and numerous field studies. Givental observes that van Hiele's theory consists of four independent assertions about the possibility of four transitions between the five levels.
The claims regarding the last two transitions hold logically , from the definition, simply because many is more than one.
The ability to handle an axiomatic approach in general level 4 implies the ability to handle one of them level 3. Likewise, the ability to derive all properties of shapes from axioms level 3 implies the ability to derive some of them level 2. It is possible, perhaps, to justify the need for research regarding the first two transitions: what the theory claims is that the ability to abstract can be achieved only after the two preliminary stages. Givental gives several convincing examples to illustrate this point. I wish to end the review with a general remark. Although we owe the English edition of Kiselev's Geometry to the private initiative of a single individual, its appearance should be considered in a broader context of the changes in school programs that are shaking the US math education establishment once more.
However good or theoretically justified a particular reform might be, its failure is practically a foregone conclusion if forced en masse on the unprepared population of students and teachers. The history of math education reform in the US in the 20 th century is a sequence of failed innovations. So much so that US educators have begun to look elsewhere for successful practices. Singapore textbooks are now commonly used by individual tutors and crowds of teachers at independent schools.
For generations, it influenced geometry teaching in the Eastern Europe and China. Its appearance in the US should be embraced by every single teacher and teacher college: the text worked well for generations of Soviet boys and girls and their teachers. Its introduction to the American user does not come too soon. Alex Bogomolny is a business and educational software developer who lives with his wife and a little son in East Brunswick, NJ.
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Geometry Book 1 Planimetry
Kiselev, adapted from Russian by Alexander Givental. Publication Date:. Number of Pages:.
BLL Rating:. The five levels are Visualization : student identifies shapes. Analysis : student attributes properties to shapes. Abstraction : student derives relationships between the properties of shapes. Deduction : student develops an appreciation of the logical structure that tracks the properties of shapes to axioms.