Comments about Dissections: Plane & Fancy


Martin Gardner

Martin wrote a very nice quote for the dust jacket:
"Cutting a geometrical figure into the smallest number of pieces that will rearrange to make a different figure is one of the most elegant and surprising branches of recreational mathematics. No one knows more about this, or is more skilled at breaking old records, than Greg Frederickson. His book will be a classic."

Ian Stewart, in his column in Scientific American

Ian based his Mathematical Recreations column in the October 1997 issue of Scientific American (pages 140-141, 143, 145, "Two-Way Jigsaw Puzzles") on the book. Two excerpts:
"Puzzles of this kind are known as dissections. A wonderfully entertaining book on this time-honored theme is soon to be published; it is Dissections: Plane and Fancy, by Greg N. Frederickson (Cambridge University Press)."
"The real fun comes in finding neat examples of shapes that are equivalent by dissection. You can make some progress by inspired trial and error, but only if you have a vivid spatial imagination. One of the virtues of Dissections is that it explains many of the general principles involved in finding them."
Scientific American is published in a number of foreign language editions, and Ian's column is translated for many of them. I have tracked down the translation of the dissections column in:

Ian Stewart, in his book Math Hysteria

Ian amplified his comments when he included the column as a chapter of his book Math Hysteria: Fun and Games with Mathematics (Oxford University Press, 2004):
"Puzzles of this kind are known as `dissections'. A wonderfully entertaining book on this time-honoured mathematical recreation is Greg N. Frederickson's Dissections: Plane and Fancy. Every puzzle enthusiast and amateur mathematician should own a copy."
"The real fun, of course, comes in finding neat or surprising examples of shapes that are equivalent by dissection. You can make some progress by inspired trial and error, but only if you have a vivid spatial imagination. One of the great virtues of Dissections: Plane and Fancy is that, as well as exhibiting a vast number of dissections, it explains many of the general principles involved in finding them."
Two cautionary notes:
1. The cuts in the pentagram (pentacle) in Figure 23(a) are misdrawn. There are two pieces more than there should be in that figure.
2. The caption to Figure 31(a) should read "Five octagons to one." The text directly above the figure should also say "five" rather than "four."

Jan de Geus, in his column in Natuur & Techniek

Jan de Geus writes a puzzle column "Prijsvraag" ("Prize Contest"), for Natuur & Techniek, the monthly science and technology magazine in the Netherlands. In the July 1998 issue (volume 66, number 7) he posed the puzzle "Meetkundig hakwerk" ("Geometric carving"), asking for a dissection of Greek crosses for 32 + 42 = 52. The column appeared on page 56, from which is excerpted:
"Onlangs verscheen het prachtig uitgevoerde boek Dissections: Plane & Fancy van Greg N. Frederickson ... In dit boek van 310 bladzijden vinden we allerlei methoden, zowel in het platte vlak als ruimtelijk."
Translation: "Recently the magnificent book Dissections: Plane & Fancy by Greg N. Frederickson appeared ... In this book of 310 pages we find all manner of methods, in the plane as well as in space."
The solution appeared in the September issue (volume 66, number 9), page 56.

Elisabeth Busser and Gilles Cohen, in their column in La Recherche

Elisabeth Busser and Gilles Cohen write a column on mathematical recreations, entitled "Chercher Jouer Trouver" ("Seek Play Find"), for La Recherche, the monthly science magazine in France. In the November 1998 issue (number 314) of La Recherche, they included a section, "Record pour une dissection de carré" ("Record for a dissection of a square"). Besides presenting one dissection from my book, they leave as a puzzle for the readers my dissection of squares for 82 + 152 = 172, which is referred to in the subtitle. The column appeared on page 102, from which is excerpted:
"On peut trouver ce découpage et bien d'autres dans un ouvrage que Greg Frederickson a publié l'an dernier chez Cambridge University Press : Dissections : Plane & Fancy. Dans ce livre passionnant, vous rencontrerez toutes sortes de curiosités géométriques étonnantes, dont un nouveau « record » de l'auteur."
Approximate translation: "One could find this dissection and many others in a work by Greg Frederickson published last year at Cambridge University Press: Dissections: Plane & Fancy. In this passionate book, you will meet all manner of astonishing geometric curiosities, along with a new record by the author."

Jean-Paul Delahaye, in his column in Pour La Science

Jean-Paul Delahaye writes a column entitled "Logique et calcul" ("Logic and calculation"), for Pour La Science,the French edition of Scientific American. In the March 1999 issue (number 257) of Pour La Science, he has written about my book and related material in "Les découpages artistiques" ("Artistic decoupage"), pages 100-105. An excerpt:
"Depuis 1972, de nombreux ajouts ayant fait progresser l'art populaire des dissections, une nouvelle synthèse s'imposait. Le livre de Greg Frederickson paru récemment sous le titre Dissection : Plane and Fancy est le recueil attendu. Sa réalisation est d'une remarquable qualité, tant sur le plan des informations que l'auteur est allé recherche patiemment dans toutes sorts de publications, pour la plupart inaccessibles, que pour les belles illustrations qui nous font découvrir à chaque page des constructions astucieuses et élégantes."
Approximate translation: "Since 1972, many additions have been made to progress the popular art, and for some dissections a new synthesis has been imposed. The book of Greg Frederickson that has appeared recently under the title Dissection : Plane and Fancy is the awaited compilation. Its realization is of remarkable quality, as much for the plan of the information that the author patiently researched in all manner of publications, even the most inaccessible, as for the beautiful illustrations that allow us to discover on every page astute and elegant constructions."

Jean-Paul Delahaye, in his book Les inattendus mathématiques: Art, casse-tête, paradoxes, superstitions

Chapter 6 (pages 68-79) of Jean-Paul Delahaye's book (Belin, Pour La Science, 2004) appears to be an exact transcription of his March 1999 column. However, he also discusses some of my book later, in chapter 8:
«Greg Frederickson, le spécialiste mondial actuel des découpages géométriques a découvert que l'affirmation de Lindgren est fausse: il a en effet proposé un découpage général pour la classe de Platon qui utilise à nouveau la technique de l'escalier mais d'une manière assez subtile.»
Approximate translation: "Greg Frederickson, the current world specialist of geometric dissections has discovered that the assertion of Lindgren is false: he has indeed proposed a general dissection for the class of Plato which has recently used the technique of the staircase but in a rather subtle way."
«D'autres découpages souvent très astucieux et s'appliquant parfois à des classes infinies d'identités, comme précédemment, ont été découverts par Greg Frederickson. Vous les trouverez décrites dans son merveilleux livre Dissections Plane and Fancy (Cambridge University Press, 1997).»
Approximate translation: "Other dissections, often very astute and sometimes applying infinite classes of identities, like previously, have been discovered by Greg Frederickson. You will find them described in his marvellous book Dissections Plane and Fancy (Cambridge University Press, 1997)."

Rodolfo Kurchan, in Puzzle Fun

Rodolfo Kurchan publishes the Argentine newsletter Puzzle Fun. Follow this link for the online version. In the August 1999 issue (number 21), he has written about dissections involving the X pentomino and has posed a number of problems about it and other pentominoes. See pages 10 and 11. He reproduces three dissections from the book and writes:
"the excellent book by Greg N. Frederickson"

Scott Kim, in his February 2004 column in Discover Magazine

Scott Kim featured hinged dissections as one of two topics in his "Bogglers" column, "Going to Pieces", in the February 2004 issue (vol. 5, no. 2) of Discover Magazine, on page 83. The magazine was published until 2005 by Buena Vista Magazines, a subsidiary of Disney Publishing Worldwide. Scott also mentioned regular dissections:
"Tangrams are just one of a large class known as dissection puzzles. Purdue computer science professor Greg Frederickson, author of Dissections: Plane and Fancy (Cambridge University Press, 1997), is a connoisseur of these geometric marvels."

Friedemann Sittig, in Welt am Sonntag

Friedemann Sittig, a journalist for the Sunday German publication Welt am Sonntag, wrote a 2-page article, "Puzzles mit mehr als einer Lösung" ("Puzzles with more than one solution"), which appeared on February 19, 2006. This article appears to be a condensation of the German translation of Ian Stewart's column, which had appeared in Spektrum der Wissenschaft, with the exception of using two figures that Ian had inserted into his original article when he replublished it in Math Hysteria.
Even so, I appreciate Herr Sittig's vote of confidence in the material extracted from my book, that he would publish it in a popular venue like Welt am Sonntag. Vielen Dank!

David Bailey - in his webpages "David Bailey's World of Escher-like Tessellations"

"An absolute delight! Highlight after highlight, too many to list here, although I am merely an "interested bystander" in the field. 24 chapters and an excellent bibliography. Speculations as to who "A. E. Hill" was, pp. 157-158, 290-291. Has many interesting brief biographies of the main people in the field, past and present, including Dudeney, p. 81. For me at least, and I suspect most other people, this is the more important of his books."

Sean M. Stewart - in "A cabinet of curiosities", American Journal of Physics vol. 89, no. 10 (2021); https://doi.org/10.1119/10.0002885

Stewart (9 Tanang Street, Bomaderry NSW2541, Australia) references DPF, pp. 30-31, which contains the figures and description of Henry Perigal's dissection, and also my capsule biography of Perigal. As Stewart notes, "Perigal is perhaps most remembered today for his elegant dissection proof he gave for Pythagoras' theorem.... As your archetypal Victorian scientific amateur his hobbies and interests could be described as being broadly geometric. Living to a great age, by his latter years his home had turned into his own private cabinet of curiosities. As one fortunate visitor recalled: 'What a scene it was, that labyrinth of strange relics of science, the marvels of bow-pen lacework, the instruments covered up to keep the dust off, the Philosopher's simple couch in the corner all in view of these quaint things, and the Philosopher himself indefatigably squaring the circle or trisecting an angle, or proving that the world is all wrong about the moon.' ... It was exquisite. It must have been a magical place to visit that now has all been lost."

Last updated December 30, 2020.