List of Publications of Thomas F. Banchoff

Tightly embedded 2-dimensional polyhedral manifolds, Amer. J. Math., 87 (1965), 462-472. (abstract)
Critical points and curvature for embedded polyhedra, J. Differential Geometry, 1 (1967), 257-268.
Total central curvature of curves, Duke Math. J., 37 (1970), 281-289.
Periodic points of Anosov diffeomorphisms (with Michael I. Rosen), Proceedings of Symposia in Pure Mathematics, Global Analysis, Vol. XIV (1970), 17-21.
The spherical two piece property and tight surfaces in spheres, J. Differential Geometry, 4 (1970), 193-205.
Critical points and curvature for embedded polyhedral surfaces, Amer. Math. Monthly, 77 (1970), 475-485.
Non-rigidity theorems for tight polyhedral tori, Archiv der Mathematik, 21 (1970), 416-423.
The two-piece property and tight n-manifolds-with-boundary in E^n , Trans. Amer. Math. Soc. 161 (1971), 259-267.
[9] On a generalization of the isoperimetric inequality (with William Pohl), J. Differential Geometry, 6 (1971), 175-192.
High codimensional 0-tight mappings on spheres, Proc. Amer. Math. Soc., 29 (1971), 133-137.
Applications of elementary calculus, Eight lectures in an NSF Sponsored Conference for College Teachers of Mathematics, Summer 1971, published in the Proceedings of the Conference.
Polyhedral Catastrophe I: Maps of the Line to the Line, Dynamical Systems, Academic Press (1973), 7-22.
Global Geometry of Polygons I: The Theorem of Fabricius-Bjerre, Proc. A.M.S. 45 (1974), 237-241.
Real Time Computer Graphics Techniques in Geometry (with Charles Strauss), Proceedings of Symposia in Applied Mathematics Vol. 20, The Influence of Computing on Mathematical Research and Education, Amer. Math. Soc. (1974), 105- 111.
Triple Points and Surgery for Immersed Surfaces, Proc. A.M.S. 46 (1974), 407-413.
Stiefel-Whitney Homology Classes and Singularities of Projections for Polyhedral Manifolds, Amer. Math. Soc. Proc. Sympos. Pure Math., Vol. XXVII, Stanford University 1973, Part I (1975), 333-347.
The Behavior of the Total Twist and Self-Linking Number of a Closed Space Curve under Inversions (with James E. White), Mathematica Scandinavica 36 (1975), 254- 262.
Height functions with three critical points (with Floris Takens), Illinois J. Mathematics, 76 (1975), 325-335.
Minimal submanifolds of the Bicylinder Boundary ,Boletim da Sociedade Brasileira de Matematica, 7 (1976), 37-57.
Self-Linking Numbers of Space Polygons, Indiana University Mathematics Journal 25 (1976), 1171-1188.
Immersions and Mod 2 Quadratic Forms (with Lou Kauffman), American Mathematical Monthly 84 (1977), 168-185. (Awarded Lester Ford Award for exposition, Summer 1978).
Whitney Duality and Singularities of Projections (with Clint McCrory), Proceedings of Escuela Latino-americana de Mathematica, Rio de Janeiro, Springer-Verlag Lecture Notes in Mathematics 5997 (1977), 68-81.
Computer Animation and the Geometry of Surfaces in 3- and 4-Space, Proceedings of the International Congress of Mathematicians, Helsinki (1978), (Invited 45 minute address), 1005-1013.
Real-Time Computer Graphics Analysis of Figures in Four-Space (with Charles Strauss),American Association of the Advancement of Science Selected Symposium 24 (1978), Westview Press, Colo., pp. 159-168.
Combinatorial Formula for Normal Whitney Classes (with Clint McCrory), Proceedings of the A.M.S. 76 (1979), 171-177.
Selected Papers in Geometry (Edited by Ann Stehney, Tilla Milnor, Joseph D'Atri and Thomas Banchoff), Mathematical Association of America (1979).
Sur les points paraboliques des surfaces: erratum et complements (with Rene Thom), C. R. Acad. Sc. Paris, 291 (27 Octobre 1980), 503-505.
Every Sphere Eversion has a Quadruple Point (with Nelson Max), Am. J. Math., Supplementary Issue (1981), 191-209.
Cusps of Gauss Mappings (with T. Gaffney and C. McCrory), Pitman Advanced Publishing Program, 55 (1982), London, pp. 1-88.
Double Tangency Theorems for Pairs of Submanifolds, Geometry Symposium Utrecht (1980), Springer-Verlag Lecture Notes 894, pp. 26-48.
Geometrical Class and Degree for Surfaces in Three-Space (N. Kuiper), J. Diff. Geom. 16 (1981), 559-576.
Circular and Countercircular Images of Plane Curves (with E. Beckenbach), General Inequalities 3 (1983), ISNM64, Birkhäuser-Verlag, 321-337.
The Nine-Vertex Complex Projective Plane (with W. Kühnel), Mathematical Intelligencer 5 (1983), 11-22.
Linear Algebra Through Geometry (with J. Wermer), Springer-Verlag (1983).
DIAL: A Diagrammatic Animation Language (with S. Feiner and D. Salesin), IEEE Computer Graphics and Applications, 2, No. 7 (1982), 43-54.
Computer Graphics in Geometric Research, Recent Trends in Mathematics, Teubner- Texte 50 (1983), 316-327.
Critical points and curvature for embedded polyhedra II, Differential Geometry, Proc. Special Year, Maryland, Progress in Math 32, BirkhŠuser (1983), 34-55.
Normal Curvatures and Euler Classes for Polyhedral Surfaces in 4-Space, Proc. A.M.S.,92 (1984), 593-596.
Differential Geometry and Computer Graphics, Perspective in Mathematics, Anniversary of Oberwolfach (1984) BirkhŠuser-Verlag, Basel, pp. 43-60.
Counting Tritangent Planes of Space Curves (with T. Gaffney and C. McCrory), Topology 34 (1985), 15-24.
Visualizing Two-Dimensional Phenomena in Four-Dimensional Space, Statistical Image Processing, Marcel Dekker (1986), 187-202.
Topology and Mechanics with Computer Graphics: Linear Hamiltonian Systems in Four Dimensions (with H. Koçla;ak, F. Bisshopp and D. Laidlaw), Advances in Applied Mathematics (1986), 282-308.
Computer Graphics and Differential Geometry: Because the Light is Better over Here. The Merging of Disciplines: New Directions in Pure, Applied, and Combinatorial Mathematics, Springer-Verlag(1986) 1-11.
Global Theorems for Symmetry Sets of Smooth Curves and Polygons in the Plane (with Peter Giblin) Proc. Royal Soc. Edinburgh 106A (1987) 221-231.
Torus Decompositions of Regular Polytopes in 4-Space. Shaping Space (1988), Birkhäuser-Verlag, 221-230.
From Flatland to Hypergraphics: Interacting with Higher Dimensions Interdisciplinary Science Reviews,15, No. 4 (1990) 364-372.
Beyond the Third Dimension, (1990) New York: W. H.Freeman & Co., Scientific American Library, 1-210.
Student Generated Interactive Software for Calculus of Surfaces in a Workstation Laboratory, (with student associates) UME Trends 1, No. 3, (1990) 7-8.
Geometry of the Hopf Mapping and Pinkall's Tori of Given Conformal Type Computers in Geometry, Marcel Dekker, New York (1990) 57-62.
Computer Graphics Tools for Rendering Algebraic Surfaces and the Geometry of Order Geometric Analysis and Computer Graphics, Springer-Verlag, New York (1991) 31-37.
Computer Laboratory Magnification of Idiosyncrasies MAA Notes 20 (1991) 1-8.
Investigating Volumes: The Air France Cup Geometry's Future, COMAP (1991) 87- 93.
Dimensions On the Shoulders of Giants, National Academy of Sciences Press (1991) 11-59.
Flatland: A New Introduction Princeton Science Series, Princeton University Press (1991) xv-xxxi.
Linear Algebra Through Geometry (with J. Wermer), revised and expanded second edition, Springer-Verlag (1991).
Illustrating Beyond the Third Dimension, (with Davide Cervone) Leonardo, special issue on mathematics and computer graphics, 25 3/4 (1992) 273-280.
Euler Numbers, Complex Points and Singularities of Projections for Oriented Surfaces in Four-Space (with F. Farris) Pacific Journal of Mathematics 161 no. 1 (1993) 1, 24..
Equilibrium Triangulations of the Complex Projective Plane (with Wolfgang Kühnel), Geometriae Dedicata.44(1992)313-333.
With Coxeter at the International Congress on Mathematics Education VII, Focus12 No. 5 (1992) 4, 16.
Symmetry Sets of Piecewise Circular Curves (with Peter Giblin), Proc. Royal Soc. Edinburgh 123A (1993) 1-15.
Interactive Computer Graphics, Higher Dimensional Geometry, and Electronic Publication: From Flatland to Hypertext, The Serials Librarian24 No. 3-4 (1994) 9-15. simultaneously in New Scholarship, New Serials: POroceedings of the North American Serials Group The Haworth Press (1994) 9-15.
ODE on a Grecian Urn, American Mathematical Monthly100 No. 9 (1993) cover.
On the Geometry of Piecewise Circular Curves (with Peter Giblin), American Mathematical Monthly 101 No. 5 (1994) 403-416.