We now come to Algebra can be fun by Yakov Perelman. This book has been translated into many Indian Languages. As with other Perelman books this book also has many editions.

From the Preface

This is not an easy-reading text on algebra for beginners.

Neither is it a manual. It is a book for free reading. It is

designed for a reader with some knowledge of algebra, even

though half mastered and perhaps half forgotten. The

present text hopes to help the reader recall such haphazard

knowledge and polish it up, the aim being to fix certain

facts in his mind. It is meant to develop in the reader a

taste for algebra and problem-solving, and also excite him

to dip into algebra textbooks and fill in the blanks in his

knowledge.To make the subject more attractive I have made use of

a variety of tools: problems with intriguing plots to excite

the reader’s curiosity, amusing excursions into the history

of mathematics, unexpected uses that algebra is put to in

everyday affairs, and more.

This particular edition was edited and supplemented by *V. G. Boltyansky* and rranslated

from the thirteenth Russian edition by *George Yankovsky* ans was published by Mir in 1979.

You can get the book here.

Update: Added Internet Archive Link 07 December 2015

Contents

From the Author’s Preface to

the Third Edition 5

**Chapter I. The Fifth Operation of Mathematics 11
**

The Fifth Operation 11

Astronomical Numbers 12

How Much does the Earth’s Atmosphere Weigh? 14

Combustion Without Flames or Heat 15

The Changing Weather 16

A Combination Lock 17

The Superstitious Cyclist 19

The Results of Repeated Doubling 20

Millions of Times Faster 21

Ten Thousand Operations per Second 25

The Number of All Possible Chess Games 28

The Secret of the Chess Machine 29

The Biggest Number Using Only Three Twos 32

Three Threes 33

Three Fours 33

Three Identical Digits 34

The Biggest Number Using Four Ones 35

Four Twos to Make the Biggest Number 36

**Chapter II. The Language of Algebra 38 **

The Art of Setting up Equations 38

The Life of Diophantus 39

The Horse and the Mule 41

Four Brothers 42

Two Birds by the Riverside 43

Out for a Stroll 45

Making Hay 46

Cows in the Meadow 50

Newton’s Problem 53

Interchanging the Hands of a Clock 55

The Hands of a Clock Come Together 58

Guessing Numbers 59

Imaginary Nonsense 63

The Equation Does the Thinking 63

Curios and the Unexpected 64

At the Barber’s 67

Tramcars and a Pedestrian 68

Rafts and a Steamboat 70

Two Cans of Coffee 71

A Question of Dancing 72

Reconnaissance at Sea 73

At the Cycle Track 75

A Competition of Motocyclists 76

Average Speeds 78

High-Speed Computing Machines 80

**Chapter III. As an Aid to Arithmetic 92 **

Instantaneous Multiplication 92

The Digits 1, 5 and 6 95

The Numbers 25 and 76 96

Infinite “Numbers” 96

Additional Payment 100

Divisibility by 11 101

A License Number 103

Divisibility by 19 105

A Theorem of Sophie Germain 106

Composite Numbers 107

The Number of Primes 109

The Largest Prime Discovered So Far HO

A Responsible Calculation 110

When It’s Easier Without Algebra 114

**Chapter IV. Diophantine Equations 116 **

Buying a Sweater 116

Auditing Accounts 120

Buying Stamps 123

Buying Fruit 124

Guessing a Birthday 126

Selling Chickens 128

Two Numbers and Four Operations 131

What Kind of Rectangle? 132

Two Two-Digit Numbers 133

Pythagorean Numbers 135

An Indeterminate Equation of the Third Degree 139

One Hundred Thousand for the Proof of a Theorem 143

**Chapter V. The Sixth Mathematical Operation 146 **

The Sixth Operation 146

Which Is Greater? 147

Solve It at a Glance 149

Algebraic Comedies 150

**Chapter VI. Second-Degree Equations 154 **

Shaking Hands 154

Swarms of Bees 155

A Troop of Monkeys 156

Farsighted Equations 157

Euler’s Problem 158

Loudspeakers 160

The Algebra of a Lunar Voyage 162

“A Hard Problem” 166

Finding Numbers 168

**Chapter VII. Largest and Smallest Values 170 **Two Trains 170

Planning the Site of a Flag Station 172

An Optimal Highway 175

When Is the Product a Maximum? 177

When Is the Sum a Minimum? 181

A Beam of Maximum Volume 181

Two Plots of Land 182

Making a Kite 183

Building a House 185

Fencing in a Lot 187

A Trough of Maximum Cross Section 188

A Funnel of Maximum

Capacity 190

The Brightest Illumination 192

**Chapter VIII. Progressions 195 **

The Most Ancient Problem Dealing with Progressions 195

Algebra on Squared Paper 196

Watering the Garden 198

Feeding Chickens . 198

A Team of Diggers 200

Apples 201

Buying a Horse 202

Paying for the Wounds of a Soldier 204

**Chapter IX. The Seventh Mathematical Operation 206
**

The Seventh Operation 206

Rivals of Logarithms 207

The Evolution of Logarithmic Tables 209

Logarithmic-Table Champions 210

Logarithms on the Stage 211

Logarithms on a Stock-Raising Farm 213

Logarithms in Music 215

The Stars, Noise and Logarithms 217

Logarithms in Electric Lighting 218

Making out a Will for Hundreds of Years 220

Constant Growth of Capital 222

The Number e 224

A Logarithmic Comedy 226

Any Number via Three Twos 227

Dear sir,

it is very nice that you are bringing out the brilliant works of Mr.Peralmann.

But the file when i downloaded is corrupted. Please look into it.

Thank you.

R.Krithivasan rkvasan2006ster@gmail.com

What do you mean by corrupted? Can you give details? Did you give the correct password?

D

what is the password for this book Sir.

sorry sir

i got it

mirtitles

thanks for your reply. Actually when i downloaded and saved and try to extract from winrar the file extension comes as djvu instead of pdf. when i still open it shows junk characters.

Corruptions while downloading are quite well-known.

You just have to re-download.

@ramani

You need a password to unzip , which is given in this webpage.

If your winzip / winrar doesnt work, try with 7zip or a different (latest) version of winzip/winrar

Thanks for uploading this book!

I have it in printed form but my copy is in bad shape & hence I did not scan it.

For those of you who don’t fancy DJVU format, I have converted the book to PDF with OCR and bookmarks.

You can download it from here:

http://www.mediafire.com/?2gw94jgj6mgb5sb

Thanks gnv64, actually your comment went into spam, hence some time to appear here. Will take care in the future.

D

Thanks for re-uploading the book.

I have uploaded a PDF version with OCR & bookmarks of 5.12 mb.

It can be downloaded from here:

http://www.mediafire.com/?2gw94jgj6mgb5sb

Thanks a lot. I had downloaded it.

Please re upload. Mediafire is blocked where I live

Million Thanks!!

@Mahoma, Updated the post with a 4shared link.

Update: Added Internet Archive Link 07 December 2015

https://archive.org/details/AlgebraCanBeFun