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Visualizing Mathematics with 3D Printing Illustrated Edition

by Henry Segerman (Author)
4.1 4.1 out of 5 stars 20 ratings
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The first book to explain mathematics using 3D printed models.

Winner of the Technical Text of the Washington Publishers

Wouldn’t it be great to experience three-dimensional ideas in three dimensions? In this book―the first of its kind―mathematician and mathematical artist Henry Segerman takes readers on a fascinating tour of two-, three-, and four-dimensional mathematics, exploring Euclidean and non-Euclidean geometries, symmetry, knots, tilings, and soap films. Visualizing Mathematics with 3D Printing includes more than 100 color photographs of 3D printed models. Readers can take the book’s insights to a new level by visiting its sister website, 3dprintmath.com, which features virtual three-dimensional versions of the models for readers to explore. These models can also be ordered online or downloaded to print on a 3D printer.

Combining the strengths of book and website, this volume pulls higher geometry and topology out of the realm of the abstract and puts it into the hands of anyone fascinated by mathematical relationships of shape. With the book in one hand and a 3D printed model in the other, readers can find deeper meaning while holding a hyperbolic honeycomb, touching the twists of a torus knot, or caressing the curves of a Klein quartic.

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  1. ISBN-10
    142142035X
  2. ISBN-13
    978-1421420356
  3. Edition
    Illustrated
  4. Publisher
    Johns Hopkins University Press
  5. Publication date
    October 4, 2016
  6. Language
    English
  7. Dimensions
    7.25 x 0.75 x 10 inches
  8. Print length
    200 pages
  9. See all details
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Editorial Reviews

Review

My best advice is to go out and buy yourself a copy of the book.
―Chalkdust Magazine

The breadth of Segerman’s 3D printing explorations is impressive. Coupled with the clarity of his explanations of the mathematics behind those explorations, this book becomes an easy recommendation for any reader interested in learning some beautiful mathematical ideas.
―Journal of Mathematics and the Arts

No previous mathematical maturity is required. The work is a good addition to any academic library. Highly recommended
―Choice

I have great difficulty thinking about Visualizing Mathematics with 3D Printing as "just a book." The careful choice, quality and effectiveness of the 140+ images in the book is outstanding. What Segerman has developed is much bigger than a book he has developed a whole platform to complement the book and explore mathematical concepts. Visualizing Mathematics with 3D printing allows the reader to manipulate with a computer or 3D print the objects discussed, making it possible to physically interact with the concepts.
―Mathematical Association of America

. . . this book serves as a launching point for teachers who are interested in exploring more advanced geometries or topology themselves. It could also guide conversations between STEM and arts educators trying to build an integrated learning experience.
―National Council of Teachers of Mathematics

The focus is on a number of areas that absolutely lend themselves to 3D models, and in these areas the author has excelled . . . wonderful illustrations that inspire much deeper thinking and investigation taking the reader on a fascinating journey.
―Mike Lane, CMath FIMA, Dstl Platform Systems Division, Mathematics Today

[Visualizing Mathematics with 3D Printing] conveys a level of intuition that's difficult to find elsewhere, and it would be an extremely valuable additional resource for any student wanting to develop their geometric and topological understanding and intuition. The innovative way in which material is introduced could also be useful for teachers and lecturers when designing lessons . . . the elegance and beauty of the presentation makes it wholly accessible for accomplished mathematicians, aspiring mathematicians, and non-mathematicians alike.
―Dr. Joel Haddley, Department of Mathematical Sciences, The University of Liverpool, The Mathematical Gazette

This book truly reaches into the third dimension and makes complex geometrical models easier to understand. As a bonus, it's closely coupled with an interactive website and the 3D printed models you can access there. Equally valuable for those of us wrapping our heads around 3D printed mathematical objects and for students of symmetry, topology, knot theory, or regular polyhedra.
―Carlo H. Séquin, University of California, Berkeley

Henry Segerman has made a name for himself demystifying advanced mathematics with the help of 3D printed models. Here, he tackles some difficult concepts―from symmetry to curvature to the shadowy world of four-dimensional shapes―with clear, inviting explanations and beautiful 3D printed illustrations.
―Evelyn Lamb, University of Utah, author of Scientific American's Roots of Unity blog

Visual thinkers, rejoice! Three-dimensional shapes have never been so lovingly illustrated. Segerman’s gorgeous 3D printed models, and his equally beautiful explanations, make this book a treat for the right-brained among us.
―Steven Strogatz, Cornell University, author of The Joy of x: A Guided Tour of Math, from One to Infinity

When someone unfamiliar with mathematics walks into my office expecting an explanation of the fourth dimension or hyperbolic space, the first thing I do is pull out some of Henry Segerman's sculptures. His book reveals the mathematics of these forms, as well as his deep aesthetic sensibility.
―Vi Hart, mathemusician and virtual reality philosopher

Review

When someone unfamiliar with mathematics walks into my office expecting an explanation of the fourth dimension or hyperbolic space, the first thing I do is pull out some of Henry Segerman's sculptures. His book reveals the mathematics of these forms, as well as his deep aesthetic sensibility.

-- Vi Hart

Product details

  • Publisher ‏ : ‎ Johns Hopkins University Press; Illustrated edition (October 4, 2016)
  • Language ‏ : ‎ English
  • Hardcover ‏ : ‎ 200 pages
  • ISBN-10 ‏ : ‎ 142142035X
  • ISBN-13 ‏ : ‎ 978-1421420356
  • Item Weight ‏ : ‎ 1.55 pounds
  • Dimensions ‏ : ‎ 7.25 x 0.75 x 10 inches
  • Customer Reviews:
    4.1 4.1 out of 5 stars 20 ratings

Customer reviews

4.1 out of 5 stars
20 global ratings

Customers say

Customers find the book inspiring, instructive, and fun to read. They appreciate the nice math concepts written in clear language. Readers also mention the book is great for those who enjoy geometry and want to venture.

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Book inspirationMath content
6 customers mention "Book inspiration"6 positive0 negative

Customers find the book inspiring, instructive, and fun to read. They say it's a good read if you are into topology.

"...The math concepts are written in clear language, and fun to read even if you don't have a 3D printer...." Read more

"The book is inspiring, well written and wonderfully printed.It is accessible as it is more like an art book than a technical..." Read more

"...mathematics (which leads ultimately to some confusion), but a very interesting book...." Read more

"...Good read if you are into topology, less interesting otherwise." Read more

4 customers mention "Math content"4 positive0 negative

Customers find the math concepts in the book nice, clear, and fun to read. They say it's useful information on mathematics and 3D printing. Readers also mention the book is great for those who enjoy geometry.

"...The math concepts are written in clear language, and fun to read even if you don't have a 3D printer...." Read more

"...Great for those who enjoy geometry and want to venture further." Read more

"...The math is well-written, in about as much layman's language possible. Good read if you are into topology, less interesting otherwise." Read more

"...Also useful information on mathematics and 3D printing." Read more

Top reviews from the United States

Fatal-Noogie
5.0 out of 5 stars Flabergastingly beautiful
Reviewed in the United States on June 25, 2017
Verified Purchase
Whenever I have it in the company of a friend, I'll tell that friend to open to a random page and take a look. The reaction is always the same, "WOAH!" And then it takes them a minute or two before they're willing to put it down again. It's filled cover to cover with gorgeous mind-bending art.

The math concepts are written in clear language, and fun to read even if you don't have a 3D printer.
The book talks mostly about the theoretical math side, and not so much about the technical aspects of 3D printing,
so if you're a starting hobbyist you should choose another guide book.

Henry's 3D Printed "illustrations" have already given me a lot of inspiration in my own 3D printed art.
This book definitely deserves a spot among my top 10 favorite books ever.
4 people found this helpful
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Oliver
5.0 out of 5 stars inspiring book
Reviewed in the United States on October 6, 2016
Verified Purchase
The book is inspiring, well written and wonderfully printed.
It is accessible as it is more like an art book than a technical
or mathematical book.

The choice of objects which were printed is rather
conservative: polyhedra and polytopes, three dimensional
curved objects, knots and surfaces. Some topics were inspired
by early pioneers of 3D printing like George Hart. There
are also example sculptures from artists like
Vladimir Bulatov or Bathsheba Gossman.

An appendix contains some comments on pictures, sometimes with
hints on where the inspiration comes from. Unfortunately a
bibliography is missing.
The first chapter contains some information how the photographs
were obtained. In an appendix there is some information on
how the objects were generated. It is however not a technical
"how to" book. This is smart, as such a book would be short lived.
It is also not a mathematical book. I would place it into the
art and graphics section as sculptures are a form of graphics.

Having seen a draft of an early version of the book, I felt
already then, it would become a nice book. As it is challenging to bring
mathematics to a more general audience, I'm surprised how well
it turned out. I approve of the perfect title as I had
co-authored in 2013 an article with a similar title and it really
hits the spot of the book: it is all about the art of
visualization of mathematical structures with an exciting new
technology.
4 people found this helpful
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Angel Bermudez
5.0 out of 5 stars Great for those who enjoy geometry and want to venture ...
Reviewed in the United States on July 4, 2017
Verified Purchase
Skimpy on the mathematics (which leads ultimately to some confusion), but a very interesting book. It, and especially the companion website, piqued my interest in 3D printing and now I'm hooked. Great for those who enjoy geometry and want to venture further.
One person found this helpful
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Amazon Customer
3.0 out of 5 stars Lots of nice math, but I miss some 'how to' info - extending Appendix B
Reviewed in the United States on December 23, 2016
Verified Purchase
But then again, this is a math book not a '3d printing for dummies' . The math is well-written, in about as much layman's language possible. Good read if you are into topology, less interesting otherwise.
4 people found this helpful
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Warner Mach
5.0 out of 5 stars 3D Printing for 3D & Beyond
Reviewed in the United States on March 16, 2017
Verified Purchase
Very interesting book. Addresses the problem of visualizing 4D objects, to the extent that this is possible. Also useful information on mathematics and 3D printing.
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Terry Beaubois
5.0 out of 5 stars and Math) at it's best and most instructive
Reviewed in the United States on March 16, 2017
Verified Purchase
To see mathmatical formulae come to life in 3D increases the interest in both math and art.
This is STEAM (Science, Technology, Engineering, Art, and Math) at it's best and most instructive.
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Amazon Customer
3.0 out of 5 stars Three Stars
Reviewed in the United States on June 5, 2018
Verified Purchase
ehhhhh I wish it had more math and less philosophy
2 people found this helpful
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Travis Williams
5.0 out of 5 stars This is next level stuff right here.
Reviewed in the United States on May 25, 2021
Verified Purchase
Get this book! These prints are fire!
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Top reviews from other countries

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A.
2.0 out of 5 stars Overpriced
Reviewed in the Netherlands on December 23, 2023
Verified Purchase
Book is fine but not worth the money
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Amazon Kunde
5.0 out of 5 stars Großartigess Buch!
Reviewed in Germany on August 16, 2020
Verified Purchase
Wie immer kommt es darauf an was der Leser erwartet von einem Buch. Ich arbeite in Bereich 3D Druck und habe verschiedene mathematische Konzepte als 3D gedruckte Objekte erwartet um mich inspirieren zu lassen. In keinster Weise wurde ich enttäuscht. Aktuell bin ich noch am Anfang des Buchs. Hier werden zum Teil sehr schwierige Konzepte recht gut populärwissenschaftlich dargestellt, sodass man gut folgen kann. Natürlich blättert man mal durch und guckt sich alle Bilder an. Die breitgefächerten Objekte sind sehr beeindruckend, inspirierend und vorallem ästhetisch, auch wenn man sich nicht für die Mathematik dahinter ineteressiert. Der Autor stellt auf "Thingiverse" die meisten, der im Buch vorgestellten, 3D Daten zur Verfügung, was großartig ist. Somit wird das Buch interaktiv. Ein großes Aber habe ich trotzdem... 3D Druck ist nicht gleich 3D Druck. Der Begriff ist eigentlich ein Übergriff für eine ganze Reihe von Fertigungsverfahren die additiv (es wird immer Material hinzugefügt und nicht abgetragen) funktionieren. Am weitesten verbeitet und mittlerweile am günstigsten sind FDM Drucker (im Grunde sind diese Drucker automatisierte und hochpräzise Heißklebepistolen). Wer erwartet dieses Buch zu kaufen und zuhause diretkt loszudrucken wird leider etwas enttäuscht werden. Alle Objekte im Buck sind über Pulverbasierte Druckverfahren hergestellt worden. Das heißt, dass andere Geometrien auf Grund des anderen Druckprinzips möglich sind. Einige wenige Obejkte werden kein Problem mit FDM sein, andere hingegen lassen sich sicherlich mit den passenden Stüzen in FDM drucken. Wiederrum andere werden mehr oder minder unmöglich oder zu Aufwendig für FDM sein. Alternativ kann man sich natürlich die 3D Daten runterladen und bei einem Dienstleister wie Shapeways oder Materialise mit einem Pulver Verfahren Fertigen und zu senden lassen.

Nichtsdestotrotz ist das ein großartiges Buch. Man merkt was für ein Enthusiast der Autor ist. Das Buch und die Drucke sind seine Babys und das bringt er auch rüber. Es lässt das Nerd Herz definitiv höher schlagen. Auf Youtube findet man auch Vorträge vom Autor zu dem Thema, ebenfalls interessant. Auch wenn das Buch ein paar Euro mehr kostet als viele andere Bücher, ist es jeden Cent Wert weil es außergewöhnlich ist. Ich kann das Buch also nur wärmstens Empfehlen wenn man sich mit 3D Druck und/oder Mathematik beschäftigt.
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Durieux
1.0 out of 5 stars Mauvais état.
Reviewed in France on October 8, 2019
Verified Purchase
Le livre est arrivé en mauvais état. Il n'est pas neuf comme indiqué lors de l'achat. Déçu par l'état général. Le rapport qualité/prix est déplorable. Les bords sont bien usés, le livre a des traces de coup dessus. Et le livre n'est pas sous protection plastique, ce qui prouve qu'il n'est pas du tout neuf.
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Durieux
1.0 out of 5 stars Mauvais état.
Reviewed in France on October 8, 2019
Le livre est arrivé en mauvais état. Il n'est pas neuf comme indiqué lors de l'achat. Déçu par l'état général. Le rapport qualité/prix est déplorable. Les bords sont bien usés, le livre a des traces de coup dessus. Et le livre n'est pas sous protection plastique, ce qui prouve qu'il n'est pas du tout neuf.
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Marco D'Abramo
2.0 out of 5 stars Speranza disattesa
Reviewed in Italy on April 19, 2017
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Avevo bisogno di un manuale da consultare per approcciare la mia tesi in Calcolo numerico sulla matematica nel 3D Printing, ho acquistato questo convinto che potesse essere la soluzione ai miei problemi, ma sono rimasto molto deluso dai suoi contenuti.
E' un libro scritto da un matematico, ma non è un libro matematico. Mi spiego: avrei avuto bisogno di spunti e di formule, ho trovato solo definizione approssimate e tante tante immagini di modelli 3D di funzioni matematiche stampate dall'autore.

Insomma, non era quello di cui avevo bisogno, e a giudicare dai contenuti, è più la spesa che l'impresa.
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cholita
5.0 out of 5 stars Tolles Buch
Reviewed in Germany on July 22, 2017
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Hatte das Buch für einen Mathematiker zu Weihnachten gekauft - es kam sehr gut an. Die Fotos sind auch für Nicht-Mathematiker ein Hingucker.
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