The Geometry Center was a

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

research and education center at the

University of Minnesota The University of Minnesota Twin Cities (historically known as University of Minnesota) is a public university, public Land-grant university, land-grant research university in the Minneapolis–Saint Paul, Twin Cities of Minneapolis and Saint ...

. It was established by the

National Science Foundation The U.S. National Science Foundation (NSF) is an Independent agencies of the United States government#Examples of independent agencies, independent agency of the Federal government of the United States, United States federal government that su ...

in the late 1980s and closed in 1998. The focus of the center's work was the use of

computer graphics Computer graphics deals with generating images and art with the aid of computers. Computer graphics is a core technology in digital photography, film, video games, digital art, cell phone and computer displays, and many specialized applications. ...

and visualization for research and education in

pure mathematics Pure mathematics is the study of mathematical concepts independently of any application outside mathematics. These concepts may originate in real-world concerns, and the results obtained may later turn out to be useful for practical applications ...

and

geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

. The center's founding director was Al Marden. Richard McGehee directed the center during its final years. The center's governing board was chaired by David P. Dobkin.

Geomview

Much of the work done at the center was for the development of Geomview, a three-dimensional interactive geometry program. This focused on mathematical visualization with options to allow

hyperbolic space In mathematics, hyperbolic space of dimension ''n'' is the unique simply connected, ''n''-dimensional Riemannian manifold of constant sectional curvature equal to −1. It is homogeneous, and satisfies the stronger property of being a symme ...

to be visualised. It was originally written for

Silicon Graphics Silicon Graphics, Inc. (stylized as SiliconGraphics before 1999, later rebranded SGI, historically known as Silicon Graphics Computer Systems or SGCS) was an American high-performance computing manufacturer, producing computer hardware and soft ...

workstations, and has been ported to run on

Linux Linux ( ) is a family of open source Unix-like operating systems based on the Linux kernel, an kernel (operating system), operating system kernel first released on September 17, 1991, by Linus Torvalds. Linux is typically package manager, pac ...

systems; it is available for installation in most Linux distributions through the package management system. ''Geomview'' can run under

Windows Windows is a Product lining, product line of Proprietary software, proprietary graphical user interface, graphical operating systems developed and marketed by Microsoft. It is grouped into families and subfamilies that cater to particular sec ...

using

Cygwin Cygwin ( ) is a free and open-source Unix-like environment and command-line interface (CLI) for Microsoft Windows. The project also provides a software repository containing open-source packages. Cygwin allows source code for Unix-like operati ...

and under

Mac OS X macOS, previously OS X and originally Mac OS X, is a Unix, Unix-based operating system developed and marketed by Apple Inc., Apple since 2001. It is the current operating system for Apple's Mac (computer), Mac computers. With ...

. Geomview is built on the Object Oriented Graphics Library (OOGL). The displayed scene and the attributes of the objects in it may be manipulated by the graphical command language (GCL) of Geomview. Geomview may be set as a default 3-D viewer for

Mathematica Wolfram (previously known as Mathematica and Wolfram Mathematica) is a software system with built-in libraries for several areas of technical computing that allows machine learning, statistics, symbolic computation, data manipulation, network ...

Videos

''Geomview'' was used in the construction of mathematical movies including: *''

Not Knot ''Not Knot'' is a 16-minute film on the mathematics of knot theory and low-dimensional topology, centered on and titled after the concept of a knot complement. It was produced in 1991 by mathematicians at the Geometry Center at the University of ...

'', exploring hyperbolic space rendering of

knot A knot is an intentional complication in Rope, cordage which may be practical or decorative, or both. Practical knots are classified by function, including List of hitch knots, hitches, List of bend knots, bends, List of loop knots, loop knots, ...

complements. *''Outside In'', a movie about

sphere eversion In differential topology, sphere eversion is a theoretical process of turning a sphere inside out in a three-dimensional space (the word ''wikt:eversion#English, eversion'' means "turning inside out"). It is possible to smoothly and continuou ...

. *''The Shape of Space'', exploring possible three-dimensional spaces.

Other software

Other notable software developed at the Center included: *''

Surface Evolver Surface Evolver is an interactive program for the study of surfaces shaped by surface tension and other energies, and subject to various constraints. A surface is implemented as a simplicial complex. The user defines an initial surface in a datafi ...

'', to explore

minimal surface In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature (see definitions below). The term "minimal surface" is used because these surfaces originally arose as surfaces that ...

s. *''

SnapPea SnapPea is free software designed to help mathematicians, in particular low-dimensional topologists, study hyperbolic 3-manifolds. The primary developer is Jeffrey Weeks, who created the first version as part of his doctoral thesis, supervise ...

'', a

hyperbolic 3-manifold In mathematics, more precisely in topology and differential geometry, a hyperbolic 3-manifold is a manifold of dimension 3 equipped with a hyperbolic metric, that is a Riemannian metric which has all its sectional curvatures equal to −1. It ...

analyzer.

Website

Richard McGehee, the center's director, has stated that the website was one of the first one hundred websites ever published.*

References

{{DEFAULTSORT:Geometry Center, The Mathematics education in the United States National Science Foundation mathematical sciences institutes Research institutes in Minnesota University of Minnesota Visualization (graphics) Geometry education