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Geometry for Entertainment (1950)

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

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