Walter Whiteley's Home Page

Walter Whiteley's Home Page

Coordinator, Graduate Diploma in Mathematics Education

Directtor, Mathematics for Education Program

Office Ross S 518; Extension 22598.

In 2013-14, I am teaching Math 3050. This course has a moodle site

You may find the materials at relevant. Theses are materials we collected for a working group at the June 2007 meeting of the Canadian Mathematics Education Study Group
You may also find some of the materials at relevant.
Here are links to two of my recent talks on Mathematics Education.
A public lecture at the Royal Canadian Institute on Mathematics with Eye and Hand. This is on-line as a
flash document or as a webcast
A lecture at the First Canadian Computer Algebra and Dynamic Geometry Systems in Mathematics Education (CCADGME)
Math with Eye and Hand: GSP, Manipulatives, and Post-Secondary Math

Pedagogical Projects

Work for the York University Faculty Association

Areas of Current Research

Discrete Applied Geometry

I currently hold an NSERC grant for research in discrete applied geometry. This covers a range of problems related to geometric constraints: rigidity of frameworks, CAD programming, scene analysis, ... .

This May, Bernd Schulze completed his Ph.D. Thesis on Combinatorial and Geometric Rigidity with Symmetry Constraints. It is available for download

Recent work, available only in preprint form, includes:

Protein Flexibility

I am also a senior researcher on a team four year National Institute of Health grant through Arizona State University and Michigan State University on New algorithms for protein flexibility. My collaborators there are Professor Michael Thorpe and Professor Leslie Kuhn . Some of the materials from the work are now available for downloading or for use from the web, at

Recently, we organized a workshop at BIRS (Banff) on this topic. From the workshop, there is a Web Comptes Rendus site with a number of papers which are freely available for downloading by the public. The site also includes some 'problems' (and solutions) from the discussions around the workshop.

I am working with a Masters Student in Computer Science, two Ph.D students in mathematics, and several undergraduate students in mathematics and computer science on problems in bioinformatics, molecular flexibility and rigidity, etc..

We are now informally gathering researchers at York who are interested in bioinformatics, including protein structure and classification. If you share this interest, get in touch with me. There is a graduate course in bioinformatics COSC 5290 which is taught in the Computer Science Graduate Program. More information is available from the web pages of Mariana Kant, the course director.

Localization in a multi-agent network

For several years I have been collaborating with a group centered in computer science at Yale. Two of the senior researchers are Professor Stephen Morse and Professor Yang (Richard) Yang . Working in particular with a recent Ph.D. student (now a post-doc at Columbia) Tolga Eren, we have a number of conference papers published, and some journal articles being submitted.

Pseudo Triangulations and Rigidity of planar graphs.

Following from a workshop on rigidity in Barbados a few years ago, there have been a number of joint papers connecting planar graphs which are generically rigid in the plane, with pseudo-triangulations. Some of these papers can be found at the sites of some members of this collaboration: Professor Ileana Streinu and Professor Gunter Rote . One of these papers can be downloaded from arXiv:math.CO/0307347, and a second one can be downloaded from arXiv:math.MG/0309156.

A specific project, with Ileana Streinu, applied the analysis of convexifying simple polygons in the plane to one-vertex origami: when can a folded paper with one vertex (a folded cone) be flattened, or made into a convex cone, without any new folds?

Research Background

I was a student of Gian-Carlo Rota, at MIT. My thesis was on logic and invariant theory - really the background of analytic geometry and its connections to matroid theory. If people are interested in more information about this remarkable individual, there is further information available at Rota.Org

Recent Preprints

  1. with Franco Saliola, Contraining Plane Configurations in CAD: circles lines and angles; preprint, accepted for publication. Avialable in PDF format from Franco Saliola's site
  2. with Laura Chavez and Lily Moshe, Basis and Circuits for 2-rigidity by Tree Coverings, 2002
  3. Constraining Plane Configurations in CAD: geometry of lengths and directions; March 1996.
  4. with H. Crapo, 3-stresses in 3-space and projected 4-polytopes: reciprocals liftings and parallel configurations, preprint (1993).
  5. with J. Owen (D-Cubed Ltd, Cambridge England), Constraining Plane Geometric Configurations in CAD: directions and distances, 1994.

Recent Publications

  1. To see like a mathematician, to be presented at the Visual Representation and Interpretation conference in Liverpool England in September 2002. download
  2. Dynamic Geometry and the Practice of Geometry, for distribution at ICME9 Tokyo, July 2000.
    download a PDF file of this paper.
  3. The Decline and Rise of Geometry, to appear in the Proceedings of the 1999 CMESG Conference
    download a PDF file of this paper.
  4. with Brigitte Servatius, Constraining Plane Configurations in CAD: combinatorics of lengths and directions; SIAM J. Discrete Math. 12 (1999), 136-153.
  5. Modeling Molecular Structures, in P. Duxbury and M. Thorpe (eds.), Rigidity Theory and Applications, Birkhauser Boston.
  6. An analogy in geometric homology: rigidity and cofactors on geometric graphs; Accepted for the Proceedings of the RotaFest, 1997.
  7. Matroids from Discrete Geometry, in Matroid Theory, J. Bonin, J. Oxley and B. Servatius (eds.), AMS Contemporary Mathematics, (1997), 171-313.
  8. Rigidity and Scene Analysis; in the Handbook of Discrete and Computational Geometry, J. Goodman and J. O'Rourke (ed.), CRC Press, 1997, 893-916.
  9. with Robert Connelly, Second-order rigidity and pre-stress stability for tensegrity frameworks; SIAM J. on Discrete Methods 9 (1996), 453-491.
  10. Representing geometric objects, Learning and Geometry: Computational Approaches, D. Kueker and C. Smith (eds.), Birkhauser 1996, 143-178.
  11. Analytic vs synthetic geometry for computers, Learning and Geometry: Computational Approaches, D. Kueker and C. Smith (eds.), Birkhauser 1996, 121-141.
  12. with Tiong-Seng Tay and Neil White, Skeletal rigidity of simplicial complexes: I; European J. of Combinatorics 16 (1995), 381-403.
  13. with Tiong-Seng Tay and Neil White, Skeletal rigidity of simplicial complexes: II; European J. of Combinatorics 16 (1995), 503-523.
  14. with H. Crapo, Spaces of stresses, projections, and parallel drawings for spherical polyhedra, Beitraege zur Algebra und Geometrie / Contributions to Algebra and Geometry 35 (1994), 259-281.
  15. How to design or describe a polyhedron, J. of Intelligent and Robotic Systems 11 (1994), 135-160.
  16. with Peter Alfeld and Larry Schumaker, The generic dimension of the space of C1 splines of degree d>8 on tetrahedral decompositions, SIAM J. Numerical Analysis (1993), 889-920.
  17. with H. Crapo, Plane stresses and projected polyhedra I: the basic pattern, Structural Topology 20 (1993), 55-68.

Walter Whiteley
email address:
Department of Mathematics and Statistics.
York University

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