3D Printing
and Maths

A stand based on the work of Henry Segerman
and displayed at the Brazilian edition of the
exhibition 3D: Printing the Future

About the exhibition

3D printing technology, which is provoking an explosion of creativity and innovation reflected in advances in science, arts, industry, medicine, engineering and many other fields, is the theme of the exhibition 3D: Printing the Future ( 3D: Imprimindo o Futuro, in portuguese), held at the Museum of Astronomy and Related Sciences (MAST, Rio de Janeiro) inaugurated on May 31.

As a result of a partnership between MAST and the British Science Museum, the exhibition is comprised of more than 100 original models and several printed models from research developed by leading Brazilian institutions.

Among them, nine models compose a stand curated by Visgraf Lab (that belongs to the Institute of Pure and Applied Mathematics, IMPA) with the purpose of showing how geometric concepts like curvature, 4-dimensional spaces and hyperbolic geometry can be understood through 3D models.

The stand is called “Visualizando a Matemática através da impressão 3D” and reflects the research of Henry Segerman in his book Visualizing Mathematics with 3D Printing.

The stand is divided in three groups of 3D printing models: Tilling and curvatures, Four-dimensional space and Hyperbolic plane.

GROUP 1: TILLING AND CURVATURES

Four 3D models of surfaces with positive, zero and negative curvatures

See the 3D models

...

Circular
paraboloid

See more

...

Parabolic
cylinder

See more

...

Hyperbolic
paraboloid

See more

...

Pseudosphere

See more

GROUP 2: 4-DIMENSIONAL SPACE

Four 3D models that represent projections of three dimensional objects

See the 3D models

...

Hypercube

See more

...

"Beach ball
5-cell"

See more

...

Half of the
24-cell

See more

...

Triangle tilling
of the sphere

See more

GROUP 3: HYPERBOLIC PLANE

Putting a point light source at the equator of the hemisphere model casts the upper half plane model as a shadow

See the 3D model

...

Hemisphere model
of the hyperbolic plane

See more

Illuminating hyperbolic
geometry

Watch the video

THE EXHIBITION

Exhibition opening images

...

EXHIBITION
"3D:IMPRIMINDO O FUTURO"

Gallery 1

...

"Visualizando a Matemática
através da impressão 3D"

Gallery 2