Mistakes in Geometric Proofs – Dubnov

In this post, we will see the book Mistakes in Geometric Proofs by Ya. S. Dubnov.

About the book

THIS BOOKLET presents examples of faulty geometric proofs, some of which illustrate mistakes in reasoning that a student might make, while others are classic sophisms. Chapters 1 and 3 present these faulty proofs, and then Chapters 2 and 4 give detailed analyses of the mistakes.

Naturally, in order to read this booklet, the reader must be
acquainted with plane geometry. Only an acquaintance with theorems concerning parallel and perpendicular lines and polygons is needed for Chapters 1 and 2. Chapters 3 and 4 contain more advanced material and presuppose some knowledge of the simpler properties of circles, the concept of limit, trigonometry, and some solid geometry.

lt is suggested that the reader first examine the examples of
incorrect proofs given in Chapters 1 and 3. He should attempt to discover the mistakes in these examples by himself before reading Chapters 2 and 4. Portions of the text appearing in fine print, as well as many of the footnotes, may be omitted on first reading; these are intended primarily for the more advanced reader.

The book was translated from Russian by Alfred K. Henn and Olga A. Titelbaum and was published in 1963 under the Topics in Mathematics series.

Credits to original uploader.

You can get the book here.

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Contents

Introduction 1
CHAPTER 1. Mistakes in Reasoning within the Grasp of the Beginner 5
CHAPTER 2. Analysis of the Examples Given in Chapter 1 19
CHAPTER 3. Mistakes in Reasoning Connected with the Concept of Limit 34
CHAPTER 4. Analysis of the Examples Given in Chapter 3 50

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