Dr. Christoph Pöppe wrote my book's first review, which appeared in
Spektrum der Wissenschaft on May 2, 2018.
From 1989 until recently he was an editor for Spektrum der Wissenschaft. He
received a doctorate in mathematics from the University in Heidelberg in 1982
and then spent several years in research, including at Forschungszentrum Jülich and the University of Minnesota. In 2004 he was awarded the German Mathematical Association's (Deutsche Mathematiker-Vereinigung) "Media Prize for Services to the Representation of Mathematics in the Public" ("Medienpreis für Verdienste um die Darstellung der Mathematik in der Öffentlichkeit").
Some excerpts from the review:
"Ein grosses Meister der Geometrie hat das nachgelassene Werk eines anderen Meisters entdeckt und liebevoll aufgearbeitet"
Rough translation: A great master of geometry has discovered the posthumous work of another master and lovingly restored it.
"Noch schöner sind Zerlegungen in Teile, die man durch Verschiebungen - ohne Drehung - in die eine wie die andere Form bringt ("translational dissections"); oder solche, bei denen man die Teile an den Ecken zu einer gelenkigen Kette verbindet, die so herum zusammengefaltet sich zu der einen Figure und andersherum zu der anderen fügt ("hingeable dissections")."
Rough translation: Even more beautiful are decompositions into parts, which one brings only by displacement - without rotation - in the one and the other form ("translational dissections"); or those in which the parts at the corners are joined into a hinged chain that folds up to form one figure and vice versa ("hingeable dissections").
"Dass Freese (1886-1957) der Welt eine Fülle neuer Zerlegungen schenken würde, hätte zu seinen aktiven Zeiten sicherlich niemand vermutet. Ja, er war technischer Zeichner, und zwar einer der besten. ... Aber der Sinn stand ihm vorrangig nach Aberteuern. Mehrfach reiste er um die Welt, während er sich zwischendurch immer wieder einmal zum Zeichnen verdingte. Erst auf seine alten Tage wendete er sich der geometrischen Zerlegerei zu. Kurz vor seinem Tod vollendete er 200 ganzseitige Zeichnungen, die von grosser Fantasie, sorgfältiger systematischer Arbeit und ungeheurer Geduld zeugen."
Rough translation: Certainly no one would have suspected that Freese (1886-1957) would give the world a wealth of new dissections. Yes, he was a technical draftsman, and one of the best. ... But his overriding spirit was for adventure. Several times he traveled around the world, while he worked in between times again and again to draw. It was not until his final years that he turned to geometric dismemberment. Shortly before his death, he completed 200 full-page drawings, which testify to great imagination, meticulous systematic work and immense patience.
"In diesem Buch reproduziert Frederickson die 200 Zeichnungen und versieht sie mit umfangreichen Kommentaren nebst einer angedeuteten Systematik für das Gebiet, das sich sozusagen von Natur aus gegen eine Systematisierung sperrt. Damit gewinnt der Leser über Freeses Werk hinaus einen hervorragenden Überblick über die Flächenzerlegung - und lernt interessante and unkonventionelle Anwendungen der euklidischen Geometrie kennen."
Rough translation: In this book Frederickson reproduces the 200 drawings and provides them with extensive commentary along with hinted systematics for the area, which, as it were, naturally blocks itself against systemization. This gives the reader an excellent overview of the area decompositions beyond Freese's work - and gets to know interesting and unconventional applications of Euclidean geometry..
Adhemar Bultheel, a faculty member at KU Leuven, in Belgium,
wrote a review appearing on May 9, 2018, for the European Mathematical Society. (See
"Ernest Irving Freese's Geometric Transformations".)
.
Some excerpts from the review:
"The main purpose of this book is to publish 200 plates illustrating geometric dissections that were produced by E.I. Freese, a Los Angeles architect, shortly before his death in 1957. Due to circumstances, the plates got lost and was only recovered by G. Frederickson in 2003. This book contains a short history of geometric dissections, and a biography of Freese, followed by the reproduction of the plates subdivided into chapters and introduced and commented by Frederickson."
"Frederickson has kept the order of the numbering of the plates, subdivided them into chapters and provided an introductory text and explaining notes, references, and new results per chapter ... and this text is followed by the relevant plates."
"The plates are beautifully reproduced after being digitally processed to remove stains."
"Everyone interested in geometric dissections, and this kind of puzzles, either mathematically or recreationally will embrace this publication. But also the readers interested in the history and certainly those who became curious about this mystery man and his manuscript ... will be fully satisfied with this respectful reproduction eventually made available for a general public."
Herve Lehning wrote a short description of the book, entitled "Ernest Freese et le manuscrit disparu: L'aventurier des decoupages disparus",
("Ernest Freese and the missing manuscript: The adventurer of the missing decoupages"),
which appeared on page 63 of Decoupages et pavages: Entre art et geometrie,
in the series Bibliotheque Tangente Hors-serie no. 64, editions POLE, ISBN: 9782848842172, in September 2018.
Herve Lehning was a special mathematics teacher at Lycee Janson-de-Sailly in Paris, France.
From 2012 to 2015, he was editor-in-chief of Tangente.
During his career he authored or co-authored, in French, many mathematics books.
An excerpt from the review:
"Dans Geometric Dissections (paru en 1964), le premier ouvrage uniquement dedie aux decoupages geometriques, Harry Lindgren decrit un grand nombre de decoupes en citant ses sources. Comme createur de neuf d'entre elles, il cite un mysterieux Irving L. Freese, n'ayant pourtant rien publiee sur la question. Sur cet homme, alors inconnu, il precise seulement qu'il etait architecte a Los Angeles et est mort en 1957. L'erreur sur le prenom n'empeche pas de retrouver la trace d'Ernest Freese (1886-1957), de son auto-biographie (parue
disparu. La suite est digne d'un roman d'aventure.
Le fameux manuscrit, redige en 1957, sera finalement retrouve par Greg Frederickson, qui le publiera chez World Scientific sous le titre Ernest Irving Freese's Geometric Transformations en 2018."
Rough translation: "In Geometric Dissections (published in 1964), the first work solely dedicated to geometric dissections, Harry Lindgren describes a large number of dissections, citing his sources. He identifies, as the creator of nine of them, a mysterious Irving L. Freese, who had not yet published anything on the question. About this man, then unknown, he only specifies that he was an architect in Los Angeles and died in 1957. The error in the name does not prevent the tracing of Ernest Freese (1886-1957), nor his auto-biography (published in 1930 by Pencil Points) and of a mysterious manuscript that has disappeared. The rest is worthy of an adventure novel.
The famous manuscript, written in 1957, would finally be found by Greg Frederickson, who would publish it at World Scientific under the title Ernest Irving Freese's Geometric Transformations in 2018."
Salim Salem, a professor and head of the department of mathematics at the Universite Saint-Joseph, in Beirut, Lebanon, wrote an enthusiastic review appearing on January 21, 2019, for MAA Reviews. (See
"Ernest Irving Freese's Geometric Transformations".)
The USJ is a very good university, where all material is taught in French, but Prof. Salem did write his review in English.
Some excerpts from the review:
"Ernest Irving Freese's Geometric Transformations does not just uncover a mathematical gem.
It is also a piece of art and a mind-puzzling set of ingenious dissections done by a master of architectural drawings and amateur mathematician. Greg Frederickson is the expert ``gemologist'' who knows how to polish and reshape his gem so it shows all its hidden beauty and allows the startled reader to enjoy discovering it. In this book Frederickson publishes Freese's manuscript and inserts explanations to help the reader to understands these geometric dissections."
"Frederickson asks whether Freese's constructions are done with the smallest number of pieces and leaves it to the reader's imagination to improve on this work."
"This book contains a lot of geometry, but Freese's manuscript is not concerned with the theory of dissection or with proving theorems about it. It is a practical book that shows the beauty of dissections and how we can get from a polygon to another by cutting it into pieces and recollect them in some special way."
"The book is written in a very elegant style, and nicely presented. Readers do not have to follow its structure; they can start anywhere and go to any chapter. Freese's manuscript was photographed and wasn't altered in any way; this preserved its beauty. Freese's drawing is ingenious and it shows how meticulous he was."
"For those people who are interested in geometry or in geometric dissections and for those who admire puzzles and recreational mathematics this book is a must."
Rick Mabry, a professor of mathematics at Louisiana State University Shreveport until he retired and moved to Germany in 2015, wrote an enthusiastic review (appearing in February 2019 on MathSciNet), for Mathematical Reviews. (See MR3752625)
(See "Ernest Irving Freese's Geometric Transformations"
Here are some excerpts from the review:
"The subtitle of this book sets the tone: The Man, the Manuscript, the Magnificent Dissections!"
"The main topic of the book is the third of these, geometric dissections. `The Man' is the architect Ernest Iriving Freese (1886-1957), who completed `the Manuscript' in the last year of his life. The `Magnificent Dissections' are (mainly) the roughly 360 constructions by Freese, printed on 200 plates, in what Freese and Frederickson seem to agree was `the first book on Geometric Transformations (Dissective Geometry) ever produced.' "
"The manuscript was known to but a few and was effectively lost shortly after Freese's death. It was finally hunted down in the year 2002 by Frederickson, who had increasingly mentioned its existence in his last three books: [G. N. Frederickson, Dissections: Plane & Fancy, Cambridge University Press, Cambridge, 1997. MR1735254]; [G. N. Frederickson, Hinged dissections: Swinging & twisting, Cambridge University Press, New York, 2002. MR1921477]; [G. N. Frederickson, Piano-hinged Dissections: Time to Fold!, A K Peters, Ltd., Wellesley, MA, 2006. MR2271292]. In particular, some 25 pages are devoted to Freese's manuscript in the 2006 text, including 7 reproductions of the manuscript plates.
"Now Freese's entire manuscript is embedded in this fourth book by Frederickson."
"Freese's dissections are carefully dissected by Frederickson---explained and evaluated for their proper magnitude of magnificence. Many, but not all of Freese's dissections were `improved' later by others (in particular, by Frederickson, Harry Lindgren, and Gavin Theobald), and these are pointed out. To that end, the book includes about 190 dissections in addition to the ones by Freese. According to Frederickson, more than 120 of these 190 can be considered new, at least by virtue of some feature (such as hingeability, etc.) not having been noted elsewhere."
"Also pointed out are the many cases in which Freese appears to be the first to dissect a pair of figures, such as his transformation of a regular hexagon to an equilateral triangle and also to a square. And the text is amply sprinkled with highly accessible (albeit difficult) open problems, even if not stated as such, some being implicit challenges."
"It is natural, therefore, that for most people who endeavor in this realm (as in the author's previous three texts on the subject), the usual basis for scoring the game is that magnificence is a decreasing function of the number of pieces. Dissections with other properties also get much attention, especially those that are hingeable or translational. The polygons that are of most interest are single regular polygons or small collections thereof, but are often regular star polygons or certain other simple figures. Symmetry and elegance can therefore also play a role in the judging of magnificence."
"Now that is cool!" --- "It's so sublime, we might view it as art!" --- "I wager that you'll be smitten by this ..."
"Just as in the author's first three books, the present one is delivered in the first person. It is written in a light, conversational, humorous style, infused with enthusiastic asides such as those above. And indeed, each of Frederickson's books can be enjoyed on a non-technical, perhaps even a non-mathematical level, without a great deal of background and at all levels of sophistication. This fourth book, perhaps even more than the others, is easy to browse or read for sheer aesthetic pleasure. Not to mention, there is this interesting character, Mr. Freese, at the center of it, who Frederickson very much wants us to meet. Thus, along with the `magnificent' mathematical treasures, the reader will find a biography of a human being---`The Man'---lovingly told by one author of another. For Frederickson, the telling of the story is an unabashedly personal undertaking and he makes great and welcome effort to make this obvious to the reader."
"Freese was primarily employed as an architect before (or as) he became an avid dissector. Freese inhabited an independent and adventurous mind, so much so that for several of his younger years, he inhabited no permanent residence---he traveled at times, by choice, as a `hobo' (even if it was not the choice of his employers). The author paints a vivid picture of Freese, through correspondence and articles of the time, and reveals him as a clever gadfly who delighted in taking the backroads in life. Embedded in the historical account of the person are, not surprisingly, some slices of life and trappings of the past that are interesting irrespective of their mathematical connections. Readers might find themselves curious and sidetracked by a variety of incidental topics mentioned, but not necessarily emphasized by the author:
Many a shaft at random sent Finds mark the archer little meant.
Which is to say, Frederickson writes an interesting story."
"The only thing missing in the indices of the text are the very handy references of the various types of dissections that are present in Frederickson's other texts. Where should one look to see a pentagram transformed into a square ({5/2} to {4})? The answer is the author's website, where such an index is found among the author's many other webpages devoted to the book. These, too, are well worth the reader's time, as they include not only minor errata, but also updates to the state of various dissections, other reviews of the book, and much more.
`What a thrill, to bring this legendary manuscript back from the brink of oblivion!'
`And how fascinating to examine this time capsule from the 1950s!'
`What a feast for the eyes!'
`Who was Ernest Irving Freese, and how had he come to craft his mesmerizing manuscript? Born in 1886 in Minneapolis, ...' "
Jan Broeders, who writes the blog
Optische Fenomenen,
wrote an enthusiastic review that appeared in November 2019.
Here are some excerpts from the review:
"Het uiterst praktisch gerichte wiskundeboek "Ernest Irving Freese's Geometric Transformations", met de ondertitel "de mens, zijn manuscript, zijn fascinerende dissecties!", is direct bruikbaar in het hedendaagse wiskunde-onderwijs en is voor alle wiskundigen en alle liefhebbers van het werken en spelen met wiskunst uiterst inspirerend om zelf aan de slag te gaan."
Rough translation:
"The extremely practical mathematics book
Ernest Irving Freese's Geometric Transformations,
with the subtitle The Man, the Manuscript, the Magnificent Dissections!
is directly usable in contemporary mathematics education and is, for all lovers of
working and playing with maths, extremely inspiring for getting yourself started."
"Het book laat lezers, studenten en docenten aan de hand van
een geillustreede introductie kennismaken met de
wiskundigen vindingen en de creatis van Ernest Irving Freese,
die hij bedacht voor enthousiaste personen met interesse
voor wiskunstige puzzels en die hij beschreef in een
eigen manuscript compleet met zijn ontwerpen.
Auteur Greg Norman Frederickson neemt de lezer mee
in de persoonlijke en avontuurlijke wereld Freese en zijn
merkwaardige maar zeker boeiende dissecties."
Rough translation:
"The book treats readers, students and teachers to an illustrated introduction
into the mathematical inventions and creations of Ernest Irving Freese, which he devised
for enthusiastic people interested in mathematical puzzles and which he described in
his own manuscript.
Author Greg Norman Frederickson transports the reader into the personal and adventurous world
of Freese and his remarkable but certainly fascinating dissections."
"De auteur laat ook eigen ontwerpen zien die hij onder andere maakte op
basis van modellen van Freese."
Rough translation:
"The author also shows his own designs that he made, among other things,
based on models from Freese."
"Ze formen een uitgaging om te ontdekken.
Ernest Irving Freese was een architect die tot zijn overlijden in 1957 in Los Angeles
woonde en werkte.
Kort voordat hij stief, voltooide hij zijn 200 pagina's tellend manuscript over
geometrische dissectie, de eerste behandling van het onderwerp in een publicate over
dat onderwerp. Hij gaf zijn unieke en handgeschreven concept de titel `Geometrische
Transformaties' mee. Zijn handschrift is helder en aantrekkelijke."
Rough translation:
"They are a challenge to discover. Ernest Irving Freese was an architect who lived and worked in Los Angeles until his death in 1957. Shortly before he died, he completed his 200-page geometric dissection manuscript, the first treatment of the subject in a publication on that subject. He gave his unique and handwritten concept the title `Geometric Transformations'. His handwriting is clear and attractive."
Beginning of the second part of the review:
"Freese ontwierp elegante tekeningen van dissecties die zowel origineel als slim zijn. Hij liet een blauwdruk vervaardigen van zijn levenswerk, maar er was geen interesse bij de uitgeverswereld om er een boek van te maken. Na zijn overlijden lag het manuscript vergeten in zijn voormalige huis tot dat Greg Frederickson via allerlei toevallige contacten het concept in 2003 in handen kreeg en met wat geluk en geduld heeft weten te redden!"
Rough translation:
"Freese designed elegant drawings of dissections that are both original and smart. He had made blueprints of his life's work, but there was no interest in the publishing world to turn it into a book. After his death, the manuscript lay forgotten in his former house until Greg Frederickson got hold of the concept in 2003 through all sorts of chance contacts and managed to save with some luck and patience!"
"Het boek van Greg N. Frederickson geeft een beeld van de geschiedenis van geometrische dissecties en een biografie van architect Ernest Irving Freese (1886-1957), gevolgd door een keurig hersteld en bewerkt exemplaar van Freese's manuscript, dat afwisselend van commentaar en aanvullingen is voorzien door Frederickson. Met dit boek laat hij liefhebbers van wiskundepuzzels door middel van zijn boeiende beschrijvingen kennismaken met de bijzondere ontwerpen van de mooie vlakverdelingen en de dissecties."
Rough translation:
"The book by Greg N. Frederickson gives a picture of the history of geometric dissections and a biography by architect Ernest Irving Freese (1886-1957), followed by a nicely restored and edited copy of Freese's manuscript, which is alternately provided with comments and additions by Frederickson. With this book he introduces enthusiasts of math puzzles, through his fascinating descriptions, to the special designs of the beautiful surface divisions and dissections."
"Het boek van Frederickson bevat ook opmerkelijke ontwerpen die het werk van Freese aanvullen. Het boek bevat twintig hoofdstukken met benamingen afgestemd op introducties op de veelheid aan dissecties en vlakverdelingen, algemene beschrijvingen en besprekingen over de opzet, inhoud en gedetailleerdheid van het manuscript van Freese’s en de diversiteit aan vele eenvoudige en gecompliceerde wiskundige figuren, zoals de gelijkbenige driehoek, vierkanten, rechthoeken, vijfhoeken, zeshoeken en meerdere uitdagende varianten. In de inleiding bespreekt Frederickson de opzet van zijn boek, geeft een toelichting over het gebruik ervan en spreekt zijn bewondering over Freese uit."
Rough translation:
"Frederickson's book also contains remarkable designs that complement Freese's work. The book contains twenty chapters with chapter names tailored to introductions of the multitude of dissections and surface divisions, general descriptions and discussions about the design, content and detail of the Freese's manuscript and the diversity of many simple and complicated mathematical figures, such as the equilateral triangle, squares, rectangles, pentagons, hexagons and several challenging variations. In the introduction, Frederickson discusses the design of his book, explains how it is used and expresses his admiration for Freese."
"Voordat hij aan de behandeling van het manuscript begint is er nog een essay over de historische bijdragen van het rijke werk van andere wiskundigen, als Geoffrey Thomas Bennett, Henry Ernest Dudeney, William Wallace, John Jackson, Harry Lindgren en Farkas Bolyai. Het geheel is geillustreerd met enkele fotos uit het familiealbum en sluit af met de compacte biografie over Freese als architect en over de verbazing waarom hij zo laat begon aan het maken van het boek."
Rough translation:
"Before the start of the manuscript, there is another chapter about the historical contributions and rich history of other mathematicians, such as Geoffrey Thomas Bennett, Henry Ernest Dudeney, William Wallace, John Jackson, Harry Lindgren and Farkas Bolyai. The whole is illustrated with a few photos like from a family album and concludes with a compact biography of Freese as an architect and his audacity to create his book so late in his life."
"Hidden in Plane Sight: The Extraordinary Vision of Ernest Irving Freese",
by Greg N. Frederickson, in the Journal of Applied Mechanics,
November 2019, vol. 86, no. 111005, pages 111005-1 to 111005-5.
Abstract: We assess selected geometric dissections associated with, or inspired by, Ernest Irving Freese's
1957 manuscript and identify noteworthy features that lay beneath their surface.
These include a dissection of a regular dodecagon to a regular hexagon,
a hingeable dissection of a Greek Cross to an equilateral triangle,
a hingeable dissection of an equilateral triangle to a regular hexagon,
a hingeable dissection of ten regular pentagons to a decagonal ring,
a translational dissection of two regular decagons to one,
a translational dissection of a dodecagram and a co-dodecagram to a regular dodecagon,
a translational dissection of ten regular pentagons to two 5-pointed pseudo-stars and a regular decagon,
a translational dissection of two regular heptagons to four 7-pointed pseudo-stars and a regular 14-gon,
a translational dissection of three regular octagons to a larger octagon,
a hingeable dissection of regular pentagons for (sin pi/5)^2 +(cos pi/5)^2 = 1,
a translational dissection of squares of areas 1, 3, 5, 7, 9, and 11 to a large square,
and a translational dissection of square for 8^2 + 9^2 + 12^2 = 17^2.
Unsubstantiated claims by Freese are also evaluated.
Anne Kraft, who writes the blog
Math Puzzler,
wrote Book Review, an enthusiastic review
that appeared in March 6, 2021.
Here are some excerpts from the review:
"This book had been on my wish list for some time....
And it just exceeded my expectations of a comprehensive volume on dissections full of figures to model and 'puzzle'.
Not only is this a treasure trove of new content for 'experienced' fans of geometric dissections,
but it would also make an engaging introduction to those just discovering the world of recreational mathematics.
Along the way, one is taken on the journey of Freese's history and that of his lost manuscript - which
the author Greg Frederickson fortunately discovered."
"The manuscript serves as the backbone of this work; each of Freese's original handwritten pages is restored and included,
interspersed with explanations, additions and digitally drawn figures. The book is organized by starting shape: N-gons, crosses, etc.
The majority of the material is the kind of two- and three-way dissections that I've been interested in for a while,
such as Gavin Theobald's comprehensive dissection page. But a majority of the puzzles are unique, providing a wealth
of new material to experiment with."
"And yet an exception has turned out to be one of my favorites so far:
Plate 151 details a set of shapes based on the square-inscribed-in-circle that also make up the Pillows I puzzle by Matthias Weber.
I've found that puzzle so amazing that it's made it to my collection of handmade physical models for working in real space."
"I plan to make a few detailed posts covering specific dissections in this book that I've explored in depth -- stay tuned!"
Last updated March 29, 2021.