European Mathematical Society - Dover Publications
https://euro-math-soc.eu/publisher/dover-publications
enNumbers: Histories, Mysteries, Theories
https://euro-math-soc.eu/review/numbers-histories-mysteries-theories
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
This booklet is the English translation of the German original from 2013: <em>Zahlen, Geschichte, Gesetze, Geheimnisse</em> The book starts and ends with the question: What is a number? Beutelspacher gives answers by sketching the historical evolution of the concept of numbers from counting one-two-three-many up to complex numbers.</p>
<p>
The author is a popularizer of mathematics, well known in Germany through his columns, and his many books. He is also the founder of the <em>Mathematikum</em>, a math museum in Giessen. The present book, his most recent, tells the evolution of the concept of numbers, and their representation through the centuries. The idea is that the text should be accessible for anyone with no or just a minimal knowledge of mathematics. This subject has been covered by many other authors before. For example Havil's <a href="/review/irrationals-story-numbers-you-cant-count"><em>The irrationals</em></a> or Stewart's <a href="/review/professor-stewarts-incredible-numbers"><em>Professor Stewart's incredible numbers</em></a> or Ifrah's monumental <em>The Universal History of Numbers</em>, and there are of course many more. So what is new here? Well, it is short, and yet nothing essential has been left out and it is truly explaining all that is needed for the layman to understand what is going on. However, it certainly is not a flat executive summary because it still has details and anecdotes to keep the attention of the reader.</p>
<p>
The content is organized in five chapters. That it should start with the integers is obvious. In fact the first chapter starts from counting in a primitive society. Gradually the concept of a natural number emerges and the early mathematicians investigated number patterns like even and odd numbers, square and triangular numbers, magic squares, and Pythagorean triples, but also prime numbers. A brief excursion is made to Fermat's last theorem and the ultimate proof by Wiles. Some cryptography and the basic idea of RSA coding are explained. This shows how important natural numbers still are in our modern society.</p>
<p>
The second chapter deals with the representation of numbers. The origin is of course tallying, and different notations and number systems. There were the Egyptian and Roman systems, which were not so useful for computing. The Babylonians had a place value sexagesimal system, which was much more useful. We inherited our 60 minutes in an hour and 60 seconds in a minute. For example their number 234 could for example denote 2 hours, 3 minutes and 4 seconds. It is however via the Arabic mathematicians that the Indian decimal system as we know it, including the zero, was introduced in Europe. The chapter also gives a good explanation of how the abacus was used for computing. Also some divisibility rules are explained. Division by 2, 5 and 10 are trivial of course, but still, the check digit at the end of our EAN barcodes is based on the remainder modulo 10 of the weighted sum of the digits in the code. Finally, there is obviously the binary system. It was described by Shannon in 1948 as the basis for communication, although Leibniz envisioned already a binary computer, but he did not elaborate on it.</p>
<p>
The story of the rationals and irrationals is told in the next chapter. The step to be made from the geometric concept of proportion to the ratio of two integers and then to the rational number that this ratio represents is not so obvious. The Egyptians had an ingenious system of unit fractions to compute with, but the true concept comes again from the Indians and it can be connected with decimal representation of numbers (containing a finite number of digits). But rationals had their limitations and gradually, starting with the incommensurability problem of the Greek, the irrationals conquer their way into the minds of mathematicians. The golden ratio which appears in the pentagram, was already scrutinized by the Greek. The marvelous proof of the irrationality of the square root of 2 is included. It is also pointed out that there are algebraic irrationals and transcendental irrationals.</p>
<p>
Chapter 4 prolongateso this idea and continues the dissection of the transcendentals. That requires the introduction of limits of number sequences. The rational numbers are now extended with the limits of these sequences. This gives for example the result that 0.999... represents a limit that is actually the same as 1, a fact not so easily accepted by a general reader. We are further instructed about the approximations to pi by the Greek, the introduction of Euler's number e and we are introduced to Cantor's theory of the infinite and how his diagonal technique could prove that there are infinitely many transcendental numbers</p>
<p>
The imaginary and complex numbers became necessary when one wanted to solve polynomial equations. We learn how al-Khwārizmī solved quadratic equations with geometric constructions, while Cardano had a formula which made him believe that a solution to such an equation can also be a negative number. In a geometric context, numbers are lengths, and then a negative solution is not acceptable. The algebra made possible what geometry could not deliver. For the cubic equation, we get the story of the Tartaglia-Fior duel and how Cardano pilfered Tartaglia's formula so that he could publish it and that is how today it gets Cardano's name attached to it. The quintic equation bears the dramatic story of Abel and Galois who both died at a young age. Abel from pulmonary tuberculosis and Galois from the consequences of a physical duel over a love affair. This stopped the race to find algebraic formulas for the solution a polynomial equation of higher degree. This doesn't mean that there are no solutions to the equation. Already quadratic equations required complex numbers, but they were not recognized. A quadratic with complex roots was considered to have none. It was Cardano who first used complex numbers implicitly, but without recognizing them in his computations for the cubic. After complex numbers were accepted, the fundamental theorem of algebra stating that every polynomial equation of degree <em>n</em> has <em>n</em> real or complex roots was soon formulated. It was however Gauss who finally proved it almost two centuries after Roth had given a first hint.</p>
<p>
The conciseness of the text and the objective of readability for laymen, necessitates some loose formulations that are strictly speaking not a hundred percent correct when isolated from the context. For example `Every equation can be solved!' (p.85) means actually `Every polynomial equation has a complex solution', or '[The binary system] is the representation of numbers used by modern computers' (p.37) which is only partially true since they work mostly with the hexadecimal number system with a lot of bells and whistles attached. And there are more such examples. But these are of course nitpicking and clearly, when seen in context, the lay reader will certainly have no problem with such formulations. To make every sentence unambiguous would only harm readability. It is only when they are used as a section title (like the one on page 85) that makes a mathematician frown.</p>
<p>
The text is pleasant to read and is well illustrated. The reader is gently guided through number wonderland, avoiding any abstraction or complexity that could deter the innocent reader. And yet, in all its simplicity such a reader is still challenged to follow the author in some of his scratching the surface of algebraic equations or some other true mathematical issues that are a bit more technical. Let me end by noting that the translators (A. Bruder, A. Easterday, J.J. Watkins) did an excellent job. In fact they have added an appendix with additional notes that contain sometimes more details (e.g. they give a proof of the nine test), often they refer to other (mostly recent) books or even websites where more information can be found. A useful addition because it is quite acceptable that this guided tour gets some readers hooked who want to read more about this fascinating world of numbers.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Adhemar Bultheel</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
This booklet is a translation of the German original of 2013 including some additional notes. It introduces the reader with a minimum of mathematical knowledge to the story of how the concept of a number evolved through the historical development of mathematics. From the counting numbers to the integers, rationals, irrationals, transcendentals, and complex numbers. </p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/albrecht-beutelspacher" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Albrecht Beutelspacher</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/dover-publications" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Dover Publications</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2016</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-0486803487 (pbk)</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">US$12.95 (pbk)</div></div></div><div class="field field-name-field-review-pages field-type-number-integer field-label-inline clearfix"><div class="field-label">Pages: </div><div class="field-items"><div class="field-item even">112</div></div></div><span class="vocabulary field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/imu/mathematics-education-and-popularization-mathematics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematics Education and Popularization of Mathematics</a></li><li class="vocabulary-links field-item odd"><a href="/imu/number-theory" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Number Theory</a></li></ul></span><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="http://store.doverpublications.com/0486803481.html" title="Link to web page">http://store.doverpublications.com/0486803481.html</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/11-number-theory" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">11 Number theory</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/11-03" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">11-03</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-other field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/01-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">01-01</a></li></ul></span>Sun, 13 Mar 2016 13:41:44 +0000Adhemar Bultheel46796 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/numbers-histories-mysteries-theories#comments100 Geometric Games
https://euro-math-soc.eu/review/100-geometric-games
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
Pierre Berloquin is a French engineer who graduated form the Ecole Nationale Supérieur des Mines, Paris in 1962. He is a freelance writer and had like Martin Gardner a regular science columns in French magazines. He has a special interest in games and logic puzzles and published many books on these topics.</p>
<p>
The present collection appeared originally around 1973, was collected and translated by Pierre Berloquin and first published in this form in 1976. It is now reproduced by Dover in 2015 together with a similar collection <a href="/review/100-numerical-games"><em>100 Numerical Games</em></a>. Martin Gardner in his foreword announces this booklet is one of a collection of four, the other two dealing with logical and alphabetical puzzles as they were originally published by Charles Scribner's Sons, New York. For a copy of the latter two one should try to find an original most probably to be found in antiquarian or second hand book shops, unless Dover has plans to also republish those in the future.</p>
<p>
Technically speaking these are puzzles, not games, so that the title can be a bit misleading. In practice, each puzzle is printed on a separate page with an illustration by Denis Dugas. There are few exceptions when two puzzles fit on the same page. Since the puzzles in this case are geometric, the drawings are essential in almost all the cases. There is some repetition in the type of puzzles. For example several mazes are included where the question is to fnd a path from A to B. There are also several match-stick puzzles: how to rearrange a pattern of matches to obtain a different pattern replacing only a specified number of matches. Also variations of the 8 queens problem on a chessboard do appear, or finding the one figure that differs from the others in a set of replicas.</p>
<p>
The puzzles are not very difficult so that the reader does not need any mathematical training to solve them. They are the kind of mild brain teasers that one finds in the puzzle corner of a newspaper. They are called geometric because they involve patterns and graphs, but they never require a theorem from geometry to solve them. All the solutions are collected at the end of the booklet. An easy going puzzle book that, thanks to Dover, is saved from oblivion.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Adhemar Bultheel</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
This is a collection of short single-page puzzles that appeared first in French magazines and that were collected and translated by the author in 1976. The illustrations by Denis Dugas form an integral, sometimes essential, part of the problem. This is an unaltered Dover edition of the original from 1976.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/pierre-berloquin" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Pierre Berloquin</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/dover-publications" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Dover Publications</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2015</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-0486789569 (pbk)</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">US$ 8.95</div></div></div><div class="field field-name-field-review-pages field-type-number-integer field-label-inline clearfix"><div class="field-label">Pages: </div><div class="field-items"><div class="field-item even">154</div></div></div><span class="vocabulary field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/imu/mathematics-education-and-popularization-mathematics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematics Education and Popularization of Mathematics</a></li></ul></span><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="http://store.doverpublications.com/048678956x.html" title="Link to web page">http://store.doverpublications.com/048678956x.html</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/00-general" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00 General</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/00a08" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00a08</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-other field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/00a07" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00a07</a></li></ul></span>Mon, 16 Nov 2015 09:41:48 +0000Adhemar Bultheel46531 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/100-geometric-games#comments100 Numerical Games
https://euro-math-soc.eu/review/100-numerical-games
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
Pierre Berloquin is a French engineer who graduated form the Ecole Nationale Supérieur des Mines, Paris in 1962. He is a freelance writer and had like Martin Gardner regular science columns in French magazines. He has a special interest in games and logic puzzles and published many books on these topics.</p>
<p>
The present collection appeared originally around 1973, was collected and translated by Pierre Berloquin and first published in this form in 1976. It is now reproduced by Dover in 2015 together with a similar collection <a href="/review/100-geometric-games"><em>100 Geometric Games</em></a>. Martin Gardner in his foreword announces this booklet as one of a collection of four, the other two dealing with logical and alphabetical puzzles as they were originally published by Charles Scribner's Sons, New York. For a copy of the latter two one should try to find an original most probably to be found in antiquarian or second hand book shops, unless Dover has plans to also republish those in the future.</p>
<p>
Technically speaking these are puzzles, not games, so that the title can be a bit misleading. In practice, each puzzle is printed on a separate page with an illustration by Denis Dugas. Some of the drawings are just illustrative for the puzzle, like in ``How many times do the hand of a clock form a right angle in 24 hours'', but sometimes they are an essential and are part of the problem formulation as for partially filled magic squares that have to be completed. There is some repetition in the type of puzzles, like several variants of magic squares. You also see several multiplications or divisions of large numbers written out as one would perform it by hand with pencil and paper but most of the digits are replaced by stars, and one has to fill in the missing digits. Classical are also the problems where you have to give different ways to form for example some number by using only one digit, parenthesis, and standard arithmetic operations. The challenge is clearly to find the most compact form. For example 20 = 5 × 5 − 5. Another recurrent type is the following. Given a diamond shape filled up with letters or numbers and the question is how many times can a certain pattern be found along rows, columns or diagonals.</p>
<p>
The puzzles are not very difficult so that the reader does not need any mathematical training to solve them. They are the kind of mild brain teasers that one finds in the puzzle corner of a newspaper. All the solutions are collected at the end of the booklet. An easy going puzzle book that, thanks to Dover, is saved from oblivion.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Adhemar Bultheel</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
This is a collection of short single-page puzzles that appeared first in French magazines and that were collected and translated by the author in 1976. The illustrations by Denis Dugas form an integral, sometimes essential, part of the problem. This is an unaltered Dover edition of the original from 1976.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/pierre-berloquin" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Pierre Berloquin</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/dover-publications" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Dover Publications</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2015</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-0486789586 (pbk)</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">US$ 8.95</div></div></div><div class="field field-name-field-review-pages field-type-number-integer field-label-inline clearfix"><div class="field-label">Pages: </div><div class="field-items"><div class="field-item even">160</div></div></div><span class="vocabulary field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/imu/mathematics-education-and-popularization-mathematics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematics Education and Popularization of Mathematics</a></li></ul></span><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="http://store.doverpublications.com/0486789586.ht" title="Link to web page">http://store.doverpublications.com/0486789586.ht</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/00-general" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00 General</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/00a08" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00a08</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-other field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/00a07" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00a07</a></li></ul></span>Mon, 16 Nov 2015 09:33:14 +0000Adhemar Bultheel46529 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/100-numerical-games#commentsFigures for Fun: Stories, Puzzles and Conundrums
https://euro-math-soc.eu/review/figures-fun-stories-puzzles-and-conundrums
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
Yakov Isidorovich Perelman (1882-1942) was a USSR science writer who wrote many popular physics and mathematics books. He died of starvation in Leningrad during the German siege. He is not related to the Fields Medal winner Grigori Perelman for solving the Poincaré conjecture. But the latter claims that he got interested in mathematics because his father gave him a book by Yakov Perelman.</p>
<p>
His books <em>Physics for Entertainment</em> and <em>Astronomy for Entertainment</em> and some others are freely available on the <a href="https://archive.org/" target="_blank">Internet Archive</a>. Also his <em>Mathematics Can be Fun</em> is available there. The latter consists of two parts: <em>Figures for fun. Stories, puzzles and conundrums</em>, and <em>Algebra Can Be Fun</em>. Although in a different edition in the Archive, the first part corresponds to the present booklet. This Dover publication of 2015 is an unabridged reproduction of the Frederik Ungar edition of 1965.</p>
<p>
The booklet consists of some hundred witty tricks, puzzles and stories. Few are classics but most of them are originals that I did not see before. The problems are most often presented in a story telling form complete with dialogues and surprised characters when the ending turns out to be unexpected. The stories are very diverse. There are stories to make it clear to an unexperienced reader how amazingly fast exponential growth is. Starting with a small number, doubling it in every step soon leads to dazzling large numbers. Similarly factorials and combinatorics easily lead to a quite large number of possibilities. Other tricks are based on counting and explain to the reader how he or she can perform some act and amaze the public with what seems to be clairvoyance. But there are also very simple and practical guidelines to count for example the number of different species in a large mixture, or how to count using your fingers or measuring using body parts. The geometrical puzzles probably require some more thinking. For example, a fly sitting on the outside of a cylindrical glass spots a drop diametrically across the glass but on the inside. What is the shortest path the fly should run to get to the drop? Others have a physical flavour: can one compute the number of raindrops in an amount of water or the water level resulting from snow melting, or how impossible is the deluge as it is described in the bible?</p>
<p>
The solutions and explanations are all included, sometimes following in a separate section, and sometimes they are part of the story. This a very entertaining booklet that will probably make you look for other books by Yakov Perelman. His physics book has a similar flavour and is certainly as pleasant to read as this one.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Adhemar Bultheel</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
This is a collection of puzzles, tricks, stories and practical hints that have all some mathematical flavour. They are brought in a most entertaining form. Dover brings this as an unaltered reprint of the Frederik Ungar version of 1965.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/yakov-perelman" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Yakov Perelman</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/dover-publications" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Dover Publications</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2015</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-0486795683 (pbk)</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">US$ 8.95</div></div></div><div class="field field-name-field-review-pages field-type-number-integer field-label-inline clearfix"><div class="field-label">Pages: </div><div class="field-items"><div class="field-item even">144</div></div></div><span class="vocabulary field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/imu/mathematics-education-and-popularization-mathematics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematics Education and Popularization of Mathematics</a></li></ul></span><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="http://store.doverpublications.com/0486795683.html" title="Link to web page">http://store.doverpublications.com/0486795683.html</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/00-general" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00 General</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/00a08" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00a08</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-other field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/00a07" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00a07</a></li></ul></span>Mon, 16 Nov 2015 09:28:24 +0000Adhemar Bultheel46528 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/figures-fun-stories-puzzles-and-conundrums#comments