3dprintmath

Visualizing mathematics with 3D printing. Mathematics often swings between abstract and concrete notions. For instance it happens frequently to speak about topological spaces, functions, isometries by drawing shapes, arrows and thinking about moving them as if they were... real, and then going back in a spiral which leads to a better understanding of such concepts. This beautiful book describes how the technology of 3D printing can help this process by making models of mathematical concepts. par The seven chapters of the book focus on various examples with a particular attention to geometry. Chapter $1$ deals with symmetry and how to visualize the discrete subgroups of the symmetry group of a sphere. Chapters $2$ and $3$ are about polygons, polyhedra and their four-dimensional relatives, investigating how it is possible to see such objects by studying (and printing) their three-dimensional shadow. Chapter $4$ is about tilings and curvature; the first concept can be roughly described as fitting together polygons with certain properties and can be related in a very interesting way with the second, which is an abstract notion in differential geometry. 3D print can be used to create interesting games about tiling the three dimensional euclidean space, and also to make beautiful model of tilings of three-dimensional hyperbolic space. Chapter $5$ and $6$ focus on knots and surfaces from the point of view of topology, with lots of examples to study several topics, from isotopy to the euler characteristic. Chapter $7$ includes a collection of various objects for instance fractals and gears, which stand out for both their mathematical interest and their intriguing realization through 3D printing. par The author devotes particular attention to the general audience: in the last years the technology of 3D printing has become cheaper: it is even possible to build a 3D printer directly at home. The interested readers can find all the models described in the book through the website url{http://3dprintmath.com}. The possibility to download, visualize and print the models really makes this book a working tool and a source of inspiration. par In conclusion, this is the perfect book where to find insights about how to use this technology for explaining and thinking about Mathematics in a new way, whether you are a teacher, or just a curious person who wants to begin a journey from abstraction to reality.