This is a new English translation of the book from the original Russian published in 1950.
Geometry for Entertainment is written both for friends of mathematics and for those readers from whom many attractive aspects of mathematics have somehow been hidden.
More importantly, this book is intended for those readers who studied (or are currently studying) geometry only at the blackboard and therefore are not used to noticing familiar geometric relationships in the world of things and phenomena around us, have not learnt to use the acquired geometric knowledge in practise, in difficult cases of life, on a hike, in a bivouac or front-line situation.
To arouse the reader’s interest in geometry or, in the words of the author, “to inspire a desire and cultivate a taste for its study is the objective of this book.”
Release Notes
Yakov Perelman’s books always have had a special place in my heart. Several of his classic works are translated, though this one was not. This was a rather ambitious first project of translating an entire book, I was not sure if I could complete it in a reasonable time frame. To my own surprise the project got completed in little over a month: first commit on 25 April and last on 30 May 2024. I took help from several online translators for the translations. I did learn to read a bit of Russian in the process. 🙂
Hopefully there are no major blunders in the translation. Please do let me know if you find any errors either in the translation or the mathematics.
Though I have credited the link on the Internet Archive (IA user Philipp Zanko aka Russian Lutheran), I must thank the original scanner who made this file available (if it was not Russian Lutheran). The processing of these scans was done with GIMP (for selection and editing) and Inkscape (for vector pdf conversion). The final file size is slightly larger (~ 55 M) primarily due to the heavy illustrations. They were converted to vector pdf for the book from the original scans.
I have use LuaLaTeX engine for compilation and Linux Libertine font for the book. The typesetting in LaTeX also provided several challenges which were sorted through expert help at tex.stackexchange. I have used a square profile for the book with wide margin which allows for a nicer reading.
The book is released with an open but a restrictive license, CC By NC SA. We might go for a print version of the book (though others are still pending ikik), this step is towards that goal.
Overall, I am very satisfied with the outcome, and it gives me great pleasure to share it with you. I hope you enjoy reading it too. I am optimistic that this is first of many translations of to come. Do wish me luck!
Damitr Mazanav – “The Mitr”
PS: An electronic version of Astronomy for Entertainment updated with all the recent discoveries in astronomy is in the pipeline, hopefully we should see its release in next couple of months. Also, Irodov’s Fundamental Laws of Mechanicsand Basic Laws of Electromagnetism are about ready (figures remain to be redrawn).
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Translated from the Russian by Damitr Mazanav from Seventh Revised edition published in 1950.
This English edition first Published online in May 2024 by The Mir Titles Project.
Source files available here.
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Editor’s Preface xv
Translator’s Preface xix
I. Geometry In The Open Air 1
1. Geometry In The Forest 5
By the length of the shadow 5
Two More Methods 13
The Method of Jules Verne 15
How Sergeant Popov Acted 19
Using a Notebook 22
Without Approaching The Tree 23
Forest Rangers’ Altimeter 25
Using a Mirror 29
Two Pines 32
The shape of the tree trunk 33
Universal Formula 35
Volume and Weight of a Tree at the Root 38
Leaf Geometry 43
Six-legged heroes 45
2. Geometry By The River 51
Measuring the width of the river 51
Using a visor 58
The Length Of An Island 61
A pedestrian on the opposite bank 62
Simple Rangefinders 65
The energy of the river 69
The Flow Rate 71
How Much Water Flows In The River? 74
Water Wheel 80
Rainbow Film 81
Circles on the Water 83
Fantastic Shrapnel 86
The Keel Wave 87
Speed of Projectiles 91
Finding Pond Depth 93
Starry Sky in the River 95
Path Across the River 97
To Construct Two Bridges 99
3. Geometry In The Open Field 101
Visible sizes of the Moon 101
Angle of View 105
Plate and Moon 107
Moon and Copper Coins 108
Sensational Photographs 109
Reservoir Set Decoration 112
Living Protractor 114
Jacob’s Staff 118
Rake Angle Gauge 120
Artilleryman’s Angle 122
Your visual acuity 125
The Limiting Minute 127
The Moon and Stars at the Horizon 130
The length of the Moon’s Shadow 134
How high is the cloud above the ground? 136
Tower Height from Photograph 144
4. Geometry on the Road 149
The art of measuring by steps 149
Eye-meter 151
Slopes 157
Heap of Gravel 161
The Proud Hill 163
At a Road Curve 165
Radius of Curvature 167
The bottom of the ocean 170
Do water mountains exist? 173
5. Field Trigonometry Without Formulas and Tables 177
Calculation of the sine 177
Extraction of the square root 183
To find an angle from its sine 185
Height of the Sun Problem 187
Distance to the Island Problem 188
Lake Width Problem 190
Triangle Area Problem 192
Determining the Magnitude of an Angle without any Instruments 194
6. Where Heaven and Earth Converge 197
Horizon 197
Ship on the Horizon 201
The Distance to the Horizon 202
Gogol’s Tower Problem 210
Pushkin’s Hill 211
Where the Rails Meet 212
Lighthouse Problems 213
Lightning Problem 215
Sailboat Problem 216
Horizon on the Moon 217
In the Lunar crater 218
On Jupiter 219
7. The Geometry Of The Robinsons 221
The Geometry of the Starry Sky 221
The latitude of the ‘Mysterious island’ 227
Determining Geographic Longitude 231
Part 2 Between Seriousness And Joke In Geometry 235
8. Geometry In The Dark 239
Into the Depths of the Hold 239
Measuring the Barrel 240
Measuring ruler (The Mayne-Reid Problem) 242
What needed to be done 245
Verification of the Calculation 248
The Night Journey of Mark Twain 254
Mysterious Circumnavigation 257
Measuring with Bare Hands 269
Straight Angle in the Dark 272
9. Old And New About The Circle 275
Practical geometry of the Egyptians and Romans 275
“I know this and I remember it perfectly.” 277
Jack London’s Error 284
Dropping a Needle 285
Straightening a Circle Problem 288
Squaring the Circle 290
Triangle of Bing 296
Head or Feet 297
Wire Along the Equator Problem 299
Facts and Calculations 300
The Girl on the Tightrope 305
The Path through the Pole 309
For the drive belt 317
The Raven’s Cleverness 321
10. Geometry Without Measurements And Calculations 325
Building without a compass 325
Centre of Gravity of a Plate 327
Napoleon’s Task 328
Simple Trisector 330
Clock Trisector 332
Dividing a Circle 333
Billiard Ball Problem 336
The “Smart” Ball 339
In One Stroke 348
The Seven Bridges of Königsberg 353
Geometrical Joke 354
Form Verification Problem 356
Game 357
11. Big And Small In Geometry 361
In a Thimble 361
Volume and Pressure 364
Thinner than a spider web but stronger than steel 368
Two Jars 371
Gigantic Cigarette 372
Ostrich Egg Task 373
Elephant Bird Egg 374
Eggs of Russian Birds 375
Weight of the eggshell 377
The sizes of our coins 378
Coin worth a million roubles 379
Visual Representations 379
Our Normal Weight 384
Gulliver’s Geometry 386
12. Geometric Economy 395
How Did Pahom Buy Land 395
The Problem of Leo Tolstoy 400
Trapezoid or Rectangle 403
The Remarkable Property of a Square 405
Plots of Different Shapes 407
Figures with the Greatest Area 409
Nails 413
Body of Greatest Volume 413
Product of Equal Factors 414
Triangle with the Greatest Area 417
The Heaviest Beam 418
From a Cardboard Triangle 419
The Tinsmith’s Dilemma 421
The Turner’s Dilemma 424
How to Lengthen a Board? 427
The Shortest Path 430
