Yakov Perelman – Algebra Can Be Fun

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

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15 Responses to Yakov Perelman – Algebra Can Be Fun

  1. ramani krithivasan says:

    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

  2. mir_fan says:

    @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

  3. gnv64 says:

    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

  4. gnv64 says:

    I have uploaded a PDF version with OCR & bookmarks of 5.12 mb.
    It can be downloaded from here:
    http://www.mediafire.com/?2gw94jgj6mgb5sb

  5. Please re upload. Mediafire is blocked where I live
    Million Thanks!!

  6. The Mitr says:

    Update: Added Internet Archive Link 07 December 2015

    https://archive.org/details/AlgebraCanBeFun

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