1997 hardcover edition:
2003 softcover (corrected) edition:
Michael Keller, the editor of
World Game Review,
wrote a short review that appeared in issue number 13
(February 1998), p. 30.
After noting Harry Lindgren's 1964 book Geometric Dissections
and my 1972 revision of it (Recreational Problem in Geometric Dissections
& How to Solve Them), Keller writes:
"Last October, Frederickson completed a new book on the subject,
called Dissections: Plane & Fancy.
It brings the field up to date with recent discoveries,
and like its predecessor is beautifully illustrated,
but the new volume makes much more interesting reading,
full of history, literary pastiches, biographies of nearly 50 contributors
to the field of dissections,
and Frederickson's accounts of his own discoveries and how he came to make them.
…
This is an essential book for anyone with interest in geometric dissections."
Sherman Stein, Professor Emeritus of Mathematics
at the University of California Davis, wrote
a very nice review for Math Reviews
that first appeared in May 1998.
Some excerpts from the review, which echo the spirit of the book:
"This book promises to serve as the bible of recreational dissections
for at least a generation, just as Harry
Lindgren's Recreational Problems in Geometric Dissections and How to Solve Them
was the classic source from
1964 to the present. Moreover, the two books are intimately connected,
for Frederickson edited the 1972 revision of
Lindgren's for Dover. In his preface to that revision he wrote,
`Several years ago I picked up the first edition of this
book. It immediately fascinated me ... I was just enticed by the diagrams.
Off and on I would pull the book down off
my bookshelf and spend an hour marveling at the beauty of the dissections.'
This is the reaction I expect people to
have to his own book."
"I hope every teacher of high school mathematics will use this book as a
source of enrichment in their algebra and
geometry classes. It even applies some trigonometry and is a
fine introduction to regular tilings of the plane, which
are put to use to make economical dissections."
"That the book is a monumental labor of love is proved not only
by the enthusiastic style, the abundance of clear
diagrams, the lengthy list of references, the thorough index,
but also by the biographies of 48 contributors to the field
(among whom are architects, a chemist, an astronomer, a banker,
a businessman, in addition to engineers and mathematicians)."
"The biographies raise three questions: Why are no women to be found
among the contributors? Why do recreational
dissectors tend to live to a ripe old age? Could geometry be therapeutic?"
"It is clear by browsing through the book and the web page that the field of recreational dissections is alive and well.
Frederickson's book will lead it well into the next century."
Jan de Geus wrote a nice review in
the June 1998 issue (#46) of Cubism For Fun,
a newsletter in English published by the Nederlandse Kubus Club NKC (Dutch Cubists Club).
Follow this link to the homepage
of the newsletter.
Excerpting from the review,
which appears on page 29:
"Since 1991 Frederickson is fanatically collecting ALL DISSECTIONS from
all over the world.
With the help of many contributors he has now published in these 310 pages
all dissections from puzzle-books and (sometimes) very old magazines.
Apart from a lot of history,
the majority of the book is however filled with new dissections
from Frederickson."
- "Which dissection-puzzle has Dudeney made ? And Sam Loyd ?
- You'll find them in this marvelous book."
"Very special is the biographical information of all dissectologists.
The bibliography of 9 pages is very valuable."
Paul Gailiunas,
a chemistry teacher at Gosforth High School in Tyne and Wear, England,
wrote "Cutting a Fine Figure", a nice review in
the September 1998 issue (#164) of Mathematics Teaching,
a quarterly journal published by the
Association of Teachers of Mathematics, in England.
Excerpting from the review,
which appears on page 43:
"... this is more than just a book of puzzles.
It is organized around the main strategies that have been used to find new dissections,
and makes interesting reading simply for the insights it gives into
mathematical thinking."
"Frederickson has done extensive research into the history of dissections
and he is able to put many discoveries in a wider context,
as well as establishing who deserves recognition
for prior discovery in most cases.
Where possible he gives a short biography of the more important contributors,
some well known (Abu'l Wafa, Cardano, Sam Loyd), others less so."
"This book is clearly a must for any dissection enthusiast,
and anyone interested in recreational mathematics generally
will find it valuable.
It is extremely well researched, copiously illustrated with line drawings,
and gives clear and generally entertaining explanations
of a huge range of dissections.
It provides a useful source of ideas for developing various aspects of geometry,
and also makes some contribution to the history of mathematics.
It would be a useful addition to any library."
Jan de Geus,
at the Hague in the Netherlands,
wrote a column based on my book for
the September 1998 issue (volume 74, number 1) of
Euclides,
a monthly trade paper published by the
Nederlandse Vereniging an Wiskundeleraren
(Dutch Organization of Mathematics Teachers).
The column ``Recreatie'' was a normal feature involving puzzles,
and can be found online in:
enkele artikelen uit EUCLIDES
On page 34, in "Opgave 687,"
after some discussion of my book, readers are left to solve the puzzle
of dissecting hexagrams for 32 + 42 = 52.
Excerpting from the column:
"In de loop van een jaar verschijnen er vele (wiskundige) puzzelboeken.
Vaak is het een herhaling van bestaand materiaal of het zijn te kinderlijke opgaven.
Maar soms verschijnt er een juweeltje met veel oorspronkelijk materiaal.
Ik heb het over Dissections: Plane & Fancy ..."
Translation (with the assistance of Anton Hanegraaf throughout):
"In the course of a year many (mathematical) puzzle books appear.
Often they involve merely the repetition of existing material
or the problems are too childish.
But sometimes there appears a gem, full of original material.
I refer to Dissections: Plane & Fancy ..."
"Meetkundige verdeelspuzzels zijn altijd al onderwerp
geweest van recreatieve wiskunde. Velen kennen de
scharnierpuzzel van Dudeney: draai je de vier stukken
de ene kant op, dan ontstaat er een gelijkzijdige driehoek.
Draai je de andere kant op, dan ontstaat er een
vierkant! Eindelijk weet ik nu de bron: de puzzelrubriek
in de `Weekly Dispatch' van 6 April 1902.
Zo kan ik nog wel uren doorgaan: sla een willekeurig
hoofdstuk op en geniet van de soms zeer slimme verdelingen,
en als het een bekende opgave is: in de uitgebreide
bibliografie vinden we de bron."
Translation:
"Geometric dissection puzzles have always been a subject
of recreational mathematics. Many people know Dudeney's
hinged dissection puzzle: turn the pieces one way and an
equilateral triangle appears. Turn them the other way
and a square appears! At last I know its source:
the puzzle column of April 6, 1902 in the `Weekly Dispatch'.
I can continue like this for hours. Turn to an arbitrary
chapter and enjoy the - sometimes very clever - dissections.
And in case it concerns a known problem, its source can
always be found back in the extensive bibliography."
"Uniek voor dit puzzelboek zijn de kaders,
waarin de levensbeschrijving staat van de bedenker van de besproken verdeling.
Zo komt dit boek ook werkelijk tot leven."
Translation:
"Unique to this puzzle book are the frames,
which contain biographies of the inventors
of the dissections that are discussed.
In this way the book really comes to life."
My dissection of hexagrams for 32 + 42 = 52
was given as the solution in the January 1999 (volume 74, number 4) issue.
Excerpting from Jan de Geus's comments, which appear on page 143:
"Steeds groter wordt mijn bewondering voor Greg N. Frederickson
als de oplossingen van Recreatie 687 binnenstromen.
Greg heeft een oplossing gevonden voor
32 + 42 = 52 m.b.h.
hexagrammen in slechts 9 stukken!
Alleen de bezitters van zijn boek `Dissections, Plane & Fancy'
zonden zo'n minimale oplossing in. (Ter controle
heb ik deze inzenders opgebeld.)"
Translation:
"Ever greater becomes my admiration for Greg N. Frederickson
as the solutions to Recreation 687 stream in.
Greg had found a solution for
32 + 42 = 52
hexagrams in only 9 pieces!
Only those who possess his book `Dissections, Plane & Fancy'
sent in such a minimal solution. (I telephoned these people
to check this.)"
"De Recreatie-lezers hadden slechts één maand de tijd,
terwijl Greg al jaren verdeelspuzzels verzamelt. Daarom neemt
uw puzzelredacteur eerbiedig zijn petje af voor inzenders,
die slechts 11 of 12 stukjes nodig hadden. ...
Het kan dus écht, zonder te spiegelen, in slechts
NEGEN stukjes.
Begrijpt u nú de waarde van dit fantastische boek?
Het is 310 bladzijden lang genieten."
Translation:
"The readers of this column had only one month,
while Greg has been collecting dissection problems for years.
So your puzzle editor respectfully takes off his hat
for those competitors who needed only 11 or 12 pieces. ...
Indeed, it can really be done in only NINE pieces,
with none turned over.
Do you now understand the value of this fantastic book?
It is 310 pages full of enjoyment."
Paul Scott,
a professor in the Department of Pure Mathematics
at the University of Adelaide,
and Cheryl Glenie, a teacher at Evanston Primary School in Adelaide,
wrote a very nice review in the third issue for 1998 (volume 54, number 3) of the
Australian Mathematics Teacher,
a publication of
The Australian Association of Mathematics Teachers.
(Follow this link to the
homepage
for the periodical.)
Excerpting from the review,
which appears on page 40:
"This is a delightful book which will undoubtedly replace Lindgren's
Geometric Dissections (1964) as the authoritative work on the subject."
"The 24 chapters cover the material in a style which is interesting and easy to read.
The text is liberally sprinkled with diagrams and short histories
of people who have been involved with dissections."
"I recommend this as a good book for the dedicated geometer or puzzelist,
and a `must' for all with an interest in dissections."
Andy Liu,
book review editor and professor of mathematics at the University of Alberta,
wrote a very nice review in the November 1998 issue (volume 24, number 7) of
Crux Mathematicorum with Mathematical Mayhem,
the Canadian Mathematical Society's problem solving journal.
(Follow this link to the homepage of the on-line
supplement
to the journal.)
Excerpting from the review,
which appears on pages 396-397:
"This is a much awaited sequel to Harry Lindgren's 1964 classic work,
Geometric Dissections, which the author (G.N.F.) revised and
augmented in the 1972 Dover edition. Actually, the current volume is much
more than just a sequel. It is the most comprehensive treatise on the
subject of geometric dissections. It may be enjoyed on at least three levels."
"First and foremost, this book is a collection of interesting dissection
puzzles, old and new. Only some background in high school geometry is needed
to fully enjoy these problems."
"This book is also an instructive manual on the art and science of geometric
dissections. While one may admire the ingenuity which produced the
spectacular solutions, the author probes into the underlying fabric which
might have led to such incisive insight."
"Finally, this book is an important historical document, detailing the
inter-cultural development of the subject. ...
Biographical sketches of Wafa, Dudeney, Loyd and Lindgren are provided,
along with those of over forty other people who have made significant
contributions to geometric dissections. The writing style is very engaging,
and the book is good reading even if one skips over some of the more
complicated technical details."
"In conclusion, the reviewer echoes Martin Gardner that this book will be a
classic. It comes with the highest recommendation."
George Garfield Hall, a fellow of the IMA and longtime member of the faculty
at the University of Nottingham,
wrote a very nice review in the December 1998 issue (volume 34, number 6) of
Mathematics Today,
the bulletin of The Institute of Mathematics and its Applications.
(Follow this link to the homepage
for the bulletin.)
He earned a Ph.D. from Cambridge University in 1950, and became a Professor of Mathematics at the University of Nottingham in 1962. He was Emeritus Professor and Senior Research Fellow in the Shell Centre for Mathematical Education at the University of Nottingham. He has a Sc. D. degree from Cambridge University and an Honorary D. Eng. degree from Kyoto University. He was a member of the International Academy of Quantum Molecular Science. George Hall passed away in 2018.
Excerpting from the review,
which appears on page 189:
"The author has produced a beautiful book replete with many examples
and giving biographical sketches of the principal originators.
He even includes problems which the reader can attempt.
The book starts simply enough to challenge the absolute novice
but eventually introduces 3-dimensional dissections
which can pose serious problems for the most sophisticated reader."
"If you are lucky enough to see a copy, do read it.
Your life will be enriched!"
Katharina Huber,
then a postdoctoral fellow in Mathematics at Massey University,
wrote a very nice review in the December 1998 issue (number 74) of the
New Zealand Mathematical Society Newsletter,
a periodical published by the New Zealand Mathematical Society.
(Follow this link to the homepage
for the periodical.)
Dr. Huber became a Senior Lecturer in the School of Computing Sciences
at the University of East Anglia in 1998, and by 2019 was an Associate Professor there.
Excerpting from the review:
"Dissections (e.g.in the disguise of tessellations) are a well
studied area of modern mathematics. However, dissection problems need
not only interest the expert working in the field, but can also be
fascinating to the interested amateur. Dissections: plane &
fancy is a book which admirably addresses these problems. Its
declared aim to contribute to the area of recreational mathematics has
been more then reached. The way in which fairly complicated techniques
and dissections (e.g. Theobald's dissection of a hexagon to a
square p.129) are developed and presented turn it into an easy to
digest and enjoyable book to read."
"A great number of biographical notes and
anecdotes of the people involved in the development of the theory
such as H.Lindgren and S.Loyd are spread through the whole text which adds an
interesting touch."
"Summing up, the material is very well presented. This together with
the agreeable writing style made the book a pleasure to read."
Loren Larson, Professor Emeritus of Mathematics at St. Olaf College,
in Minnesota,
wrote a very nice telegraphic review in the April 1999 issue (volume 106, number 4) of the
American Mathematical Monthly,
a publication of the
Mathematical Association of America.
(Follow this link to the homepage
for the periodical.)
Quoting from the review,
which appears on page 381:
"A beautiful book that entices, entertains, fascinates, and instructs.
Collects, organizes, and presents 2000+ years of discovery alongside exciting
new contributions.
Complete, thorough, fun to read;
this will be a classic."
Tony Orton, who at the time was
a Fellow in the School of Education at the University of Leeds,
wrote a very nice review in the May 1999 issue (volume 28, number 3) of
Mathematics in School,
a periodical published by the
Mathematical Association
of Great Britain.
(Follow this link to the
homepage
for the periodical.)
Dr. Orton retired in 2001.
Excerpting from the review,
which appears on page 46:
"This is a wonderful book for enthusiastic dissectors."
"The content is so comprehensive that many new ideas and revelations
can be absolutely guaranteed to any reader.
Detailed study of the dissection types leads to mathematical analysis
which demands real application, and readers will be further tested by
the exercises (`puzzles') set throughout the book,
for which there are solutions at the back.
For those interested in the origins and development of dissections,
there is an excellent historical strand running throughout,
with pen-portraits of many of the most significant
contributors down the centuries.
The bibliography of over 200 entries bears testimony
to the amount of research which has gone into its production.
It is the kind of book you can dip into,
both for relaxation and for ideas for work with learners.
I liked it, and hope it will at least find a place in libraries
and in the home of addicts, and who knows,
it might enthuse others who have hitherto not realized the extent
of the possible applications of geometric dissections in mathematics."
Peter Cromwell,
in the Department of Pure Mathematics
at the University of Liverpool,
wrote a review in the July 1999 issue (volume 83, number 497) of the
Mathematical Gazette,
a periodical published by the
Mathematical Association
of Great Britain.
(Follow this link to the
homepage
for the periodical.)
Excerpting from the review,
which appears on pages 359-360:
"The author, an expert in the field,
has collected dissections from many sources and has traced the origins of many,
searching out old collections and magazines.
His research has led to a few reattributions,
and also short biographical sketches of the many contributors.
Some are well-known, others would possibly go unrecorded.
The subject is brought fully up-to-date with recent ideas,
many of which originate from the author himself.
This will be the definitive reference work on the subject for many years."
Jan van de Craats,
a professor at the Korteweg-de Vries Institute for Mathematics
at the University of Amsterdam,
wrote a very nice review in the November 1999 issue
(Fourth series, volume 17, number 3) of the
Nieuw Archief voor Wiskunde,
the journal of the Dutch Mathematical Society
`Het Wiskundig Genootschap'.
(Follow this link to the homepage
for the periodical.)
Excerpting from the review,
which appears on pages 513-514:
"Greg Frederickson probeert alles wat er op dit gebied bekend is,
te verzamelen.
Hij heeft zelf ook een flink aantal bijdragen geleverd in de
vorm van fraaie dissecties en nieuwe records.
Het boek dat hij erover heeft geschreven,
is een toonbeeld van stijl, grafische vormgeving en perfectie."
Translation (with the assistance of Anton Hanegraaf throughout):
"Greg Frederickson has tried to collect everything
that is known in this domain.
He has himself also made a good number of contributions
in the form of beautiful dissections and new records.
The book that he has written
is a model of style, graphic design, and perfection."
"Alle illustraties in het boek zijn schitterend:
elk probleem en elke methode is van perfecte tekeningen voorzien.
Van alle puzzels is geprobeerd de oorspronkelijke bedenker te achterhalen.
Alle belangrijke `dissectionisten' krijgen een korte biografie.
Van alle puzzels voor de lezer staat de oplossing achterin.
Het nawoord bevat interessante achtergrondinformatie,
er is een uitgebreide biografie, een gewone index en een index van dissecties.
Kortom, een prachtig boek!"
Approximate translation:
"All illustrations in this book are brilliant:
each problem and each method are supplied with perfect drawings.
For all puzzles it is attempted to trace the original inventor.
All important `dissectionists' receive a short biography.
With all puzzles for the reader there is a solution at the back of the book.
The afterword contains interesting background information,
there is an extensive [bibliography], a general index and an index of dissections.
In short, a magnificent book!"
Kieran Gillick,
then a student at Gresham's School in Holt, Norfolk, England,
wrote a very nice review in the January 2000 issue (volume 32, number 2) of the
Mathematical Spectrum,
a magazine for students and teachers in schools, colleges, and universities,
and published by the
Applied Probability Trust
of Great Britain.
(Follow this link to the homepage
for the periodical.)
Gillick graduated from Gresham's School in 1998,
from Cambridge University in 2001,
completed a Ph.D. in Biochemistry in 2006,
and completed a degree in medicine from St. George's, University of London in 2014
Excerpting from the review,
which appears on pages 46-47:
"His book contains a huge number of problems and their various solutions,
covering everything from squares and triangles, to stars,
Maltese crosses and tessellations, to how to cheat in solving puzzles.
The main focus of the text, however,
is not so much on the solutions as on how to arrive at them.
Frederickson tries throughout to give the reader
a feel for the various methods available,
and introduces thorough mathematical descriptions of many dissections."
"The text is written in a conversational style
that makes it easy to dip into at will.
Diagrams abound, as indeed they must in such a book,
and the text is also dotted with the histories of various puzzle-solvers,
past and present.
All in all, this is a very well written work,
which is bound to interest anyone with a taste for recreational mathematics."
Peter Schmitt,
an ausserordentliche professor in the Department of Mathematics
at the University of Vienna,
in Vienna, Austria,
wrote a nice review in the April 2000 issue (number 183) of the
Internationale Mathematische Nachrichten,
or International Mathematical News,
a newsletter published by the
Österreichische Mathematische Gesellschaft
(Austrian Mathematical Society).
(Follow this link to the
homepage
for the periodical,
and follow this link for the
pdf for number 183.)
Excerpting from the review,
which appears on page 49:
"Dissection problems usually are classified as `recreational' mathematics
and, of course, dealing with them is fun.
However, it is also a good training in problem solving,
and it is `serious' mathematics, as well,
albeit of a subject for which (so far?) no systematic theory exists."
"First of all, this delightful monograph (for "anyone who has had
a course in high school geometry and thought
that regular hexagons were rather pretty")
includes an extensive collection of ingenious examples
of dissection problems and methods (of plane figures and solids),
as they have been discovered by puzzle authors,
by amateurs, and by mathematicians,
but it also brings some systematic order to a diverse subject,
tells about its history, and provides an extensive bibliography."
Eike Hertel,
a professor at the Mathematical Institute
in Friedrich-Schiller-Universität,
Jena, Germany,
wrote a nice review that appeared in
Mathematical Reviews,
a publication of the American Mathematical Society.
(Follow this link to the Mathematical Reviews on the web.)
Excerpting from review 2000m:52002,
on page 8748 of the December 2000 issue:
"The beautifully illustrated book is easy to read---
only a basic knowledge of high school geometry is needed.
The title of the fourth chapter (It's hip to be a square)
is the title of a song from the children's television show
Sesame Street!
The book is directed at mathematical puzzle enthusiasts:
In twenty-four chapters they can find a wealth of puzzle
problems (with solutions) from the author himself
and many others, e.g., H. Dudeney, S. Loyd, H. Lindgren,
M. Gardner.
A serious mathematician can also find interesting suggestions
and much historical and biographical information."
Johannes Boehm,
a retired professor at the Mathematical Institute
in the Friedrich-Schiller Universität,
Jena, Germany,
wrote a review that appeared in
Zentralblatt für Mathematik und Ihre Grenzgebiete,
a publication of the Deutsche Akademie der Wissenschaften zu Berlin
and the Heidelberger Akademie der Wissenschaften.
(Follow this link to the homepage
for the periodical.)
Excerpting from the review, which is indexed as 939.52008
and appears in volume 939:
"In this book the author presents in more than twenty chapters
interesting and also amazing examples of dissections,
above all in the plane,
in three chapters also for special three-dimensional solids."
"Many ingenious ways of solutions are shown
and several conjectures are proposed.
Various properties of dissections are studied,
for instance, translational, hinged or symmetrical dissections."
"Many historical remarks complete the text;
especially biographical information is given on the people
who worked on these problems. . . .
This is a good catalogue for all who are looking for special dissections
and want to get instructions on how to dissect."
Charles Ashbacher,
the book review editor,
wrote a very nice review that appeared in
volume 30, number 3 (1999-2000) of the
Journal of Recreational Mathematics.
He was president and CEO of Charles Ashbacher Technologies from 1997 to the present.
He was an instructor at Mount Mercy College, 2000-2008,
and an adjunct instructor at Upper Iowa University from 2009 to the present.
He was co-editor of the Journal of Recreational Mathematics 2000-2010.
Excerpting from the review,
which appears on pages 214-215:
"Art and hobbies aside, this is a fun book to explore.
Since the subject matter is
the slicing and splicing of geometric figures, most of the
results are presented as diagrams, making the solutions easy to understand.
One thought constantly leapt to mind when I was examining some of the diagrams,
"How did they think of doing that?"
Obvious only after the fact, many dissections are hardly
something that would easily leap to mind.
Additional puzzles are interspersed throughout the text
and solutions to all are included at the end of the book.
The public loves puzzles, as the popularity of some game shows and regular
puzzle columns in newspapers and magazines demonstrates.
In this book, you will find some of the most challenging
of dissection type puzzles, sure to keep
you interested from the opening slice to the final splice."
Doris Schattschneider,
was a professor of mathematics at Moravian College,
in Bethlehem, Pennsylvania,
wrote a very nice review that appeared in
the March 2001 (volume 43, number 1) issue of
SIAM Review,
a publication of the Society for Industrial and Applied Mathematics.
Professor Schattschneider retired in 2002.
She won the MAA Carl B. Allendorfer Award in 1979
and the MAA Award for Distinguished Teaching in 1993.
She was made a Fellow of the AMS in 2012.
Excerpting from the review,
which appears on pages 220-223:
"One of the most popular topics in books on recreational mathematics
is dissection puzzles.
Greg Frederickson's Dissections: Plane and Fancy
is a feast of such puzzles, beautifully and wittily presented,
along with lots of interesting ancillary information.
The book can be enjoyed at many levels,
from that of the browser or beginner who will primarily be a spectator,
to that of the afficianado who wants to match wits with masters of the game."
"Although many dissections can be serendipitous,
happened upon after much trial and error,
the masters have always looked for (and found) general techniques
that could be applied to produce large classes of dissections.
These required both ingenuity and mathematical understanding
of the underpinnings.
Frederickson's aim is not merely to report on dissections,
but to illuminate the reader as to how dissections
can be found and why they work.
Indeed, he is not content with reporting a dissection unless
he can show how it could result from an application of one of
the standard techniques."
"Chapter titles are witty ("It's Hip to Be a Square," "Strips Teased"),
and several chapters continue in character, with Frederickson obviously
enjoying puns, double-entendres, or mimicking a well-known voice.
. . .
And there are many mysteries uncovered by Frederickson,
which he relates with some relish."
"The book is very nicely designed, with clear and accurate diagrams
for each dissection."
"Frederickson's delightfully rich book is long overdue
and will surely be a classic in the field."
Wolf Barth,
a professor who held a chair at the Mathematical Institute
in Friedrich-Alexander-Universität,
Erlangen-Nürnberg, Germany,
wrote a review that appeared in
the July 2001 (Band 103, Heft 2) issue of
Jahresbericht der Deutschen Mathematiker-Vereinigung,
a publication of the German mathematical society DMV.
(Professor Barth retired in 2011 and passed away in 2016.)
Excerpting from the review,
which appears in zweitem Abteilung, pages 48-49:
"So ist das Buch eine systematische Zusammenstellung geometrischer Puzzles.
Es dürfte von unschätzbarem Wert für jeden sein,
der sich für diese Art von Puzzle interessiert.
Ich kann nicht von mir sagen, daß ich dazu gehöre.
Aber auch auf mich übt das Buch einen starken Reiz aus.
Wahrscheinlich wegen seiner Einzigartigkeit (soweit ich weiß)
und der Konsequenz und der Systematik,
mit der hier Zerlegungen aufgefuehrt werden.
Es gibt Einblick in eine mir bisher fremde Welt
von (meist) Amateur-Mathematikern.
So hat das Buch weniger mit Mathematik,
mehr mit Kultur zu tun."
Approximate translation:
"So the book is a systematic compilation of geometrical puzzles.
It can be of inestimable value for anyone who is interested
in this type of puzzle.
I cannot say that I belong to this group.
But the book also exercised a strong attraction on me.
Probably because of its singular nature (as far as I know)
and the consequence and systematic nature with which the dissections
are specified.
It gives a view into the for-me-previously foreign world of
(most) amateur mathematicians.
So the book has less to do with mathematics
and more with culture."
Helen Joyce,
as editor of Plus Magazine,
an internet magazine published by the
Millennium Mathematics Project,
wrote a lovely review for the May 2003 (number 25) issue.
Excerpting from the
review:
Helen Joyce had earned a Ph.D. at Cambridge University.
She became editor of Significance in 2004,
the Education Correspondent of the Economist in 2005,
and the Brazil Bureau Chief in 2009.
" ... the ingenuity of the
dissections shown here may still be a revelation to
you, as they were to this reviewer."
"Greg N. Frederickson explains the mathematical techniques - many
involving tessellations, or tilings - used to create some extraordinary
dissections. The techniques are all elementary, though some are very
cunning. Triangles, squares, crosses, and other polyhedra and
many-pointed stars are ingeniously disassembled and reassembled until the
reader's mind whirls."
"The illustrations are beautiful and plentiful, and I would imagine that this
book would make an excellent source for craftsmen, makers of children's
toys and puzzle setters."
"Handy readers may be tempted by this delightful book to follow in their
footsteps, and even the less practically minded will find their feeling for
plane geometry enhanced."
In "Education Notes",
Ed Barbeau,
an emeritus professor in the Department of Mathematics
at the University of Toronto,
wrote what is essentially a review for
CMS Notes / Notes de la SMC,
vol. 35, no. 6 (October 2003).
Excerpting from his article, which appears on pages 9-10:
"... one can also push mathematics because of its sheer capacity
to bring enjoyment.
Some mathematics is self-contained and relies on no outside
experience or background; it quickly leads to investigations
that become the testing ground for the mental discipline
and ingenuity of the user.
There are many topics that an amateur can readily take up
and even find some new results; geometry is a particularly
rich area for these. So the second book I want to take up is
Dissections: Plane & Fancy"
"Anyone who wants to take dissections seriously could use it
as a training manual, but it also lends itself to dipping.
It is fun to just look at the pictures..."
"... it provides a venue where amateurs can get in quickly
and make some real progress.
Accordingly, it would well be worth the while of any teacher
seeking a respite from the regular syllabus to acquaint her students
with the topic and to make sure that the school or college library
has a copy for any student who might actually get hooked."
Adhemar Bultheel,
a professor in the Department of Computer Science at the
Katholieke Universiteit Leuven,
wrote a nice review that appeared in the
September 15, 2003 (no. 44) issue of the
BMS-NCM News.
The newsletter is published five times a year by the
Belgian Mathematical Society.
The review covers my first two books and appears on pages 10-11,
as well as online.
Professor Bultheel was president of the Belgian Mathematical Society 2002-2005
and retired as Professor Emeritus in 2009.
An excerpt from the review:
"These books give many new perspectives for all those who love math puzzles.
They will adore the second book as much as they loved the first,
and they will devour it with great enthusiasm.
The style is lively and pleasant to read.
Practically no mathematical prerequisites are needed,
so that everybody can be intrigued by this fascinating play
of fancy pieces swinging and twisting around."
Jan M. Broeders wrote
a nice review in the February 2004 issue (number 200) of
Optische Fenomenen (Optical Phenomena),
the newsletter of the
Nederlandse Stichting voor Waarneming & Holografie
(Dutch Foundation for Perception and Holography).
(Follow this link to the homepage
for the periodical.)
Jan Broeders has been the compiler and publisher of Optische Fenomenen since 1987.
Excerpting from the review, which is entitled "Symmetrie in vlakverdelingen" (Symmetry in dissections) and appears on page 4:
See the online review.
"Het puzzelboek "Dissections: Plane & Fancy"
van onderzoeker en puzzelaar Greg N. Frederickson
geeft een schat aan uitdagende, bekende en nieuwe
puzzelvoorbeelden en oplossingen van leuke
geometrische vlakverdelingen en wiskundige kunst
met uitgesneden stukjes en vele voorbeelden van
gerealiseerde figuren met deze stukjes."
Rough translation:
"The puzzle book Dissections: Plane & Fancy,
by researcher and puzzler Greg N. Frederickson,
gives a treasure of challenging, well-known, and novel puzzle examples,
solutions of lovely geometrical dissections,
mathematical art with cut-out pieces,
and many examples of figures realised with these pieces."
"Het boek beschrijft op een uitgebreide wijze
de vele mogelijkheden om op een ingenieuze wijze
de aangegeven problemen op te lossen en daarbij
de meest fantastische constructies te creëren.
"
Rough translation:
"The book describes the many possibilities of solving the given problems
in a comprehensive and ingenious manner,
thereby creating the most fantastic constructions.
"
A. Robert Pargeter,
a retired teacher of mathematics at Blundell's School
in Tiverton, Devon, England,
wrote a very nice
review in the July 2004 issue (volume 88, number 512) of the
Mathematical Gazette,
a periodical published by the
Mathematical Association
of Great Britain.
(Follow this link to the
homepage
for the periodical.)
Excerpting from the review,
which appears on pages 371-373:
"it would not be unfair to regard this as a recipe-book
--- but what fascinating recipes!
The author's style is friendly, gently humorous, and eminently readable.
The text is very lavishly illustrated,
and as is only to be expected from the publisher
the printing and layout are impeccable."
"The topic of this book is very restricted,
but within its limits the wealth of material is amazing:
if you are already into it, you will be in clover,
while if you are new to it, you will become hooked!
An earlier review (quoted on the back cover of the present book)
of the hardback edition says `His book will be a classic'.
I fully agree!"
"Thoroughly recommended."
Leo Bocek, in the Department of Mathematics Education, Charles University, Prague,
wrote a nice review in the December 2004 issue (number 54) of the
EMS Newsletter,
published by the
European Mathematical Society.
(Follow this link to the homepage
for the newsletter.)
Leo Bocek received a Ph.D. in mathematics, specializing in geometry, in 1967.
He became Associate Professor of Mathematics Education in 1987
Excerpting from the review, which appears on page 42:
"Every puzzle fan will like this interesting and amusing book."
Robert J. Clarke, in Stourbridge, West Midlands, England,
wrote a very nice review in the January 2005 issue (volume 37, number 2) of the
Mathematical Spectrum,
a magazine for students and teachers in schools, colleges, and universities,
and published by the
Applied Probability Trust
of Great Britain.
(Follow this link to the homepage
for the periodical.)
Excerpting from the review, which appears on page 89:
"the numerous diagrams are very clearly presented.
Some of these are very easy to understand,
but many of them may need close attention.
The notation and various trigonometric statements will
intrigue some readers and others may be encouraged to try
their hand at model making.
Judging from the attractive front cover,
some of these models could be used as
very elegant Christmas decorations."
"This is an interesting book,
which should be a good source of project work.
It is a valuable addition for any library in school, college or home."
Robert Bilinski, then at the Collège Montmorency
in Laval, Québec, Canada,
wrote a very nice review in the December 2005 issue (volume 45, number 4) of the
Bulletin de l'Association Mathématique du Québec,
published by the
Association Mathématique du Québec.
(Follow this link to the homepage
for the periodical.)
More recently (as of 2019), Robert Bilinski is listed in LinkenIn as the owner of Biomaths consultants.
Excerpting from the review
(of both Dissections: Plane & Fancy
and Hinged Dissections), which appears on pages 63-65:
"Je vais aussi être franc, je n'ai pas fini de lire les deux livres avant de faire la chronique.
Mais, il est clair qu'ils ont été bien écrits,
de manière consciencieuse et minutieuse,
avec passion et surtout avec rigueur.
De plus, je ne pense pas me tromper en parlant de la fascination
et de l'émerveillement que ce livre a suscités chez moi et les autres (non-mathématiciens) à qui j'ai montré les livres.
De tout manière, je n'ai aucune honte à le dire,
parce que ce livre est à mon chevet depuis quelques mois de
manière « active ».
Au moins une fois par semaine,
j'ouvre au hasard un des deux livres et je découvre quelque chose de nouveau, de beau et de fascinant.
Ces livres sont pleins de constructions abracadabrantes."
Approximate translation (any additional assistance would be greatly appreciated!):
"I will also be honest, I did not finish reading the two books
before writing this column.
But it is clear that they have been well written,
in a conscientious and meticulous manner,
with passion and especially with rigor.
Moreover, I do not think I am mistaken while speaking about the fascination
and amazement that this book caused in me and others
(nonmathematicians) to whom I have shown the books.
In any case, I am not ashamed to state this
because this book has been by my bedside for a few months in an `active' way.
At least once a week, I randomly open one of the two books
and discover something new, beautiful and fascinating.
These books are full of extravagant constructions."
"Voilà une lecture de longue haleine ou un livre à
mettre sur la table de son salon pour faire la conversation à
la manière d'un livre d'art. Bonne lecture!"
Approximate translation (with the assistance of Luc Mongeau):
"Here is a seminal book, to keep on the
coffee table to stimulate conversations,
like an art book. Good Reading!"
Élisabeth Busser wrote a very nice review in the co-authored (with Michel Criton)
"notes de lecture" section entitled
"Découpages: la trilogie de Greg Frederickson,"
of the French mathematics magazine tangente: l'aventura mathématique,
Hors série no. 64 (Septembre 2017), p. 19.
She and Criton identified my three books, Dissections: Plane and Fancy,
Hinged Dissections: Swinging and Twisting, and Piano-Hinged Dissections: Time to Fold!
as a trilogy!
The subsection on Dissections: Plane and Fancy was entitled
"Une référence incontournable et inépuisable"
which translates to "An unavoidable and inexhaustible reference".
Excerpting from her review:
"Ce livre très riche, premier d'une trilogie en anglaise consacrée au même thème, explore les dissections, autrement die les découpages et recompositions de figures géométriques. Tout l'art est de n'utiliser qu'un minimum de morceaux, ce qui conduit souvent à d'ingénieuses constructions...
On trove ici toutes le astuces de l'histoire des mathématiques, toute l'ingéniosité des créateurs de puzzles géométriques d'aujourd'hui, avec grande variété de dessins, une foule d'anecdotes et une biographie succincte de tous les acteurs de ce théâtre de formes."
Approximate translation (any additional assistance would be greatly appreciated!)
"This very rich book, the first in a trilogy in English devoted to the same theme, explores dissections, which are the cut-outs and recompositions of geometric figures. All art is to use only a minimum of pieces, which often leads to ingenious constructions...
Here we find all the tricks of the history of mathematics, all the ingenuity of today's geometric puzzle creators, with a great variety of drawings, a host of anecdotes and a succinct biography of all the actors in this theater of shapes.
Last updated March 3, 2020.