Induction in Geometry

by ;
Format: Paperback
Pub. Date: 2019-10-16
Publisher(s): Dover Pubns
  • Free Shipping Icon

    Free Shipping on all Orders Over $35!*

    *excludes Marketplace items.

List Price: $14.95

Buy New

Special Order. We will make every effort to obtain this item but cannot guarantee stock or timing.

Rent Book

Select for Price
There was a problem. Please try again later.

Rent Digital

Online: 1825 Days access
Downloadable: Lifetime Access

Used Book

We're Sorry
Sold Out

This item is being sold by an Individual Seller and will not ship from the Online Bookstore's warehouse. The Seller must confirm the order within two business days. If the Seller refuses to sell or fails to confirm within this time frame, then the order is cancelled.

Please be sure to read the Description offered by the Seller.


Induction in Geometry discusses the application of the method of mathematical induction to the solution of geometric problems, some of which are quite intricate. The book contains 37 examples with detailed solutions and 40 for which only brief hints are provided. Most of the material requires only a background in high school algebra and plane geometry; chapter six assumes some knowledge of solid geometry, and the text occasionally employs formulas from trigonometry. Chapters are self-contained, so readers may omit those for which they are unprepared. 
To provide additional background, this volume incorporates the concise text, The Method of Mathematical Induction. This approach introduces this technique of mathematical proof via many examples from algebra, geometry, and trigonometry, and in greater detail than standard texts. A background in high school algebra will largely suffice; later problems require some knowledge of trigonometry. The combination of solved problems within the text and those left for readers to work on, with solutions provided at the end, makes this volume especially practical for independent study.

Author Biography

L. I. Golovina was on the faculty of Moscow State University.
I. M. Yaglom (1921–88) was affiliated with Moscow State Pedagogical Institute. He wrote several popular books on mathematics, including these Dover publications: Challenging Mathematical Problems with Elementary Solutions (with A. M. Yaglom) in two volumes, and The U.S.S.R. Olympiad Problem Book (with D. O. Shklarsky and N. N. Chentzov).
I. S. Sominskii was on the faculty of the Novgorod Pedagogical Institute.

Table of Contents

Tables of Contents:
The Method of Mathematical Induction:
1. The Method of Mathematical Induction
2. Examples and Exercises
3. Proofs of Some Theorems of Algebra
4. Solutions of Exercises in Chapter 2.

Induction in Geometry:
Introduction: What Is the Method of Mathematical Induction?
1.  Computation by Induction
2. Proof by Induction.
3. Construction by Induction
4. The Determination of Geometric Loci by Induction
5. Definitions by Induction
6. Induction on the Number of Dimensions

An electronic version of this book is available through VitalSource.

This book is viewable on PC, Mac, iPhone, iPad, iPod Touch, and most smartphones.

By purchasing, you will be able to view this book online, as well as download it, for the chosen number of days.

A downloadable version of this book is available through the eCampus Reader or compatible Adobe readers.

Applications are available on iOS, Android, PC, Mac, and Windows Mobile platforms.

Please view the compatibility matrix prior to purchase.