# Half a Century of Pythagoras Magazine

Share this page *Edited by *
*Alex van den Brandhof; Jan Guichelaar; Arnout Jaspers*

MAA Press: An Imprint of the American Mathematical Society

Half a Century of Pythagoras Magazine
is a selection of the best and most inspiring articles from this Dutch
magazine for recreational mathematics. Founded in 1961 and still
thriving today, Pythagoras has given generations of high school
students in the Netherlands a perspective on the many branches of
mathematics that are not taught in schools. The book contains a mix of
easy yet original puzzles, more challenging and at least as original
problems, as well as playful introductions to a plethora of subjects
in algebra, geometry, topology, number theory, and more. Concepts like
the sudoku and the magic square are given a whole new dimension.

One of the first editors was a personal friend of world famous
Dutch graphic artist Maurits Escher, whose “impossible objects” have
been a recurring subject over the years. Articles about his work are
part of a special section on Mathematics and Art. While many books
on recreational mathematics rely heavily on folklore, a reservoir of
ancient riddles and games that are being recycled over and over again,
most of the puzzles and problems in Half a Century of Pythagoras
Magazine are original, invented for this magazine by Pythagoras'
many editors and authors over the years. Some are no more than cute
little brainteasers which can be solved in a minute, others touch on
profound mathematics and can keep the reader entranced
indefinitely. Smart high school students and anyone else with a sharp
and inquisitive mind will find in this book a treasure trove which is
rich enough to keep his or her mind engaged for many weeks and
months.

#### Reviews & Endorsements

… One appeal of the book for a student or novice mathematician is that the reader can start directly into these articles with very little mathematical background. But the articles have other strengths. The historical details provide a wonderful frame of reference for the reader and give a depth of human interest to the mathematics. Numerous mathematicians, artists, and craftsmen are discussed in conjunction with their mathematical interests. Overall, Half a Century of Pythagoras Magazine is very readable and appropriate for students and recreational puzzlers as well as for teachers looking for interesting historical examples for the classroom. The English translation is well done and just enough background is provided to allow readers to understand the problems without referring to external sources.

-- Tricia Muldoon Brown, MAA Reviews

# Table of Contents

## Half a Century of Pythagoras Magazine

- Cover cov11
- Half title i2
- Copyright ii3
- Title iii4
- Series iv5
- Contents ix10
- Preface xiii14
- 1 Brainteasers 118
- 2 Puzzles, Games, and Strategies 2138
- A game with graphs 2138
- Dudeney's hinge puzzle 2239
- Prime stuffer 2441
- Date cubes 2542
- Two "impossible" figures 2643
- Sangakus 2643
- Key ring puzzle 2744
- Matchboxes 2845
- Connector 2946
- Close the door! 3249
- An ugly picture 3552
- Superdokus 3855
- Geomagic squares 4057
- The 16 holes puzzle 4360
- A mathematical card trick 4461
- The Penrose triple star 4663
- Come loose and change 4865
- The Black game 4966
- Complex balancing 5269
- Fiddling with identical twins 5673
- The divisor game 6279
- The rotating cube 6582
- Three is too many 6683
- Problem 59 from the Scottish Book 6784
- One hundred prisoners 7087
- Pygram 7592
- The liar's guessing game 7693

- 3 Mathematics and Art 83100
- 4 Geometry 117134
- Pythagoras by folding ix10
- Ann's smart proof 118135
- Square of squares 120137
- Imprisoned squares 123140
- The pancake 130147
- Fagnano's problem 132149
- Keep rolling 135152
- Beauty contest winning theorem 137154
- Alexander's horned sphere 142159
- How big is the earth? 145162
- A rope around the earth 148165
- It seems improbable, but 153170
- Integrating by hats 154171
- A proof returned 157174
- Euler's formula 159176
- The platonic system 164181
- Platonic-like solids 168185
- Penrose tiles and the golden ratio 172189
- Brouwer's fixed point theorem 179196
- Windmill wings 187204

- 5 Numbers 191208
- Weighing letters 191208
- The snail and the elastic band 194211
- Clever pruning in infinity 197214
- Proof by rotation? 199216
- An awkward mathematical problem 202219
- Nines, nines, more nines 204221
- Is π normal? 207224
- Coster numbers 209226
- Continued fractions 212229
- The IQ formula 215232
- Primal fractions 219236
- The abc conjecture 222239
- The money machine 225242

- 6 Dionigmas 231248
- 7 Solutions 245262
- Bibliography 295312
- About the Editors 301318