Experimental Geometry Group

Contact Information

Department of Mathematics and Statistics,
The University of Melbourne,
Parkville, VIC 3052, Australia.

Contact Person: Robert Sinclair.
E-mail: R.Sinclair@ms.unimelb.edu.au

WWW: http://www.egg.ms.unimelb.edu.au/

Experimental Geometry is a discipline concerned with the development and refinement of experimental methods and tools which assist in the understanding or illustration of geometry. It is an interdisciplinary enterprise, typically involving the application of modern computational tools and programming paradigms to geometry and vice-versa, but actually not restricted to computing (where would minimal surfaces be without soap bubbles?).

This discipline is useful in

Student Employability: The computational skills required to perform
geometric experimentation are of use in applied mathematics, engineering,
robotics, scientific computing, computer graphics, interactive visualization,
virtual reality and more.
Pure Mathematical Research: Serious geometric experimentation can
provide theoreticians with reliable conjectures and hints, and can act as
an aid in building up the intuitive understanding of a new area of geometry.
Mathematics education: Computational visualization tools can help
students understand difficult geometric concepts.
Computational science: The foundations of natural science can often be
expressed most naturally in terms of geometry. Computational science
benefits from computational geometry.
Computer science: Experimental geometry provides computer science with
nontrivial applications for cutting-edge computational tools.

The Geometry and Topology Group already has quite some expertise in the area of experimental geometry, particularly in computational hyperbolic geometry and global differential geometry.

Aims of the Group

To provide a forum for the discussion of techniques and tools relevant to
geometric experimentation, allowing an exchange of experience and thus
preventing unnecessary duplication of efforts.
To provide courses in computational geometry for staff and students.
To make the work in experimental geometry of this Department visible to
other Departments of Melbourne University and beyond.
To provide a natural interface to other such groups at Melbourne University
and beyond, and thus facilitate the forming of interdisciplinary collaborations
in this area.

Seminars

Downloadable Software

Oliver Goodman's personal home page.
- Snap is a computer program for studying arithmetic
  invariants of hyperbolic 3-manifolds.
Regina is a topological calculator which allows 3-manifolds
to be created, manipulated and their properties of interest
determined.
Software for computing cut loci from points on 2-surfaces:
- Loki computes the cut locus on torus-like surfaces,
  given an explicit, closed-form parametrization or metric.
- Thaw computes the cut locus on surfaces of the form
  (x/a)^(2n)+(y/b)^(2n)+(z/c)^(2n)=1.

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