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Research articles by Thomas F. Banchoff


  1. Tightly embedded 2-dimensional polyhedral manifolds, Amer. J. Math., 87 (1965) 462-472. (abstract) (AMS review #31#2729)

  2. Critical points and curvature for embedded polyhedra, J. Differential Geometry, 1 (1967) 257–268. (abstract) (AMS review #85b:53061)

  3. Total central curvature of curves, Duke Math. J., 37 (1970) 281–289. (abstract) (AMS review #41#4447)

  4. Periodic points of Anosov diffeomorphisms (with Michael I. Rosen), Proceedings of Symposia in Pure Mathematics, Global Analysis, Vol. XIV (1970) 17–21. (abstract) (AMS review #43#2738)

  5. The spherical two piece property and tight surfaces in spheres, J. Differential Geometry, 4 (1970) 193–205. (abstract) (AMS review #42#3720)

  6. Critical points and curvature for embedded polyhedral surfaces, Amer. Math. Monthly, 77 (1970) 475–485. (AMS review #41#4444)

  7. Non-rigidity theorems for tight polyhedral tori, Archiv der Mathematik, 21 (1970) 416–423. (abstract) (AMS review #42#8426)

  8. The two-piece property and tight n-manifolds-with-boundary in En, Trans. Amer. Math. Soc. 161 (1971) 259–267. (abstract) (AMS review #44#4760)

  9. On a generalization of the isoperimetric inequality (with William Pohl), J. Differential Geometry, 6 (1971) 175–192. (AMS review #46#4449)

  10. High codimensional 0-tight mappings on spheres, Proc. Amer. Math. Soc., 29 (1971) 133–137. (abstract) (AMS review #43#5541)

  11. Polyhedral Catastrophe I: Maps of the Line to the Line, Dynamical Systems, Academic Press (1973) 7–22. (AMS review #49#6268)

  12. Foliations of Knot Complements in the Bicylinder Boundary, Separata do Boletim da Sociedade Brasileira de Matematica Vol. 5, No. 1 (1974) 31–43. (abstract)

  13. Global Geometry of Polygons I: The Theorem of Fabricius-Bjerre, Proc. A.M.S. 45 (1974) 237–241. (abstract) (AMS review #51#6826)

  14. Tight Polyhedral Klein Bottles, Projective Planes, and Mobius Bands, Math. Ann. 207 (1974) 233–243. (abstract)

  15. Triple Points and Surgery for Immersed Surfaces, Proc. A.M.S. 46 (1974) 407–413. (abstract)

  16. Triple Points and Singularities of Projections for Immersed Surfaces, Proc. A.M.S. 46 (1974) 402–407. (abstract)

  17. 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. (abstract) (AMS review #51#14090)

  18. 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. (abstract) (AMS review #52#4312)

  19. Height functions with three critical points (with Floris Takens), Illinois J. Mathematics, 76 (1975) 325–335. (abstract) (AMS review #51#14079)

  20. Minimal submanifolds of the Bicylinder Boundary, Boletim da Sociedade Brasileira de Matematica, 7 (1976) 37–57. (AMS review #58#12844)

  21. Self-Linking Numbers of Space Polygons, Indiana University Mathematics Journal 25 (1976) 1171–1188. (abstract) (AMS review #55#4227)

  22. Immersions and Mod 2 Quadratic Forms (with Lou Kauffman), American Mathematical Monthly 84 (1977) 168–185. (Awarded Lester Ford Award for exposition, Summer 1978). (abstract) (AMS review #55#4210)

  23. 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. (AMS review #56#6678)

  24. Combinatorial Formula for Normal Stiefel-Whitney Classes (with Clint McCrory), Proceedings of the A.M.S. 76 (1979) 171–177. (abstract)

  25. Selected Papers in Geometry (Edited by Ann Stehney, Tilla Milnor, Joseph D'Atri and Thomas Banchoff), Mathematical Association of America (1979). (AMS review #82c:01041)

  26. Sur les points paraboliques des surfaces: erratum et complements (with Rene Thom), C. R. Acad. Sc. Paris, 291 (27 Octobre 1980) 503–505.

  27. Every Sphere Eversion has a Quadruple Point (with Nelson Max), Am. J. Math., Supplementary Issue (1981) 191–209. (abstract) (AMS review #83g:57020)

  28. Cusps of Gauss Mappings (with T. Gaffney and C. McCrory), Pitman Advanced Publishing Program, 55 (1982), London, 1–88. (abstract)

  29. Frenet Frames and Theorem of Jacobi and Milnor for Space Polygons, Jugoslavenska Akademija Znanosti I Umjetnosti, iz Rada 396 (1982) 101–108. (abstract)

  30. Double Tangency Theorems for Pairs of Submanifolds, Geometry Symposium Utrecht (1980), Springer-Verlag Lecture Notes 894, 26–48. (AMS review #83h:53005)

  31. Geometrical Class and Degree for Surfaces in Three-Space (N. Kuiper), J. Diff. Geom. 16 (1981) 559–576. (abstract) (AMS review #83j:53056)

  32. Circular and Countercircular Images of Plane Curves (with E. Beckenbach), General Inequalities 3 (1983), ISNM64, Birkhäuser-Verlag, 321–337. (abstract) (AMS review #86h:53003)

  33. The Nine-Vertex Complex Projective Plane (with W. Kühnel), Mathematical Intelligencer 5 (1983) 11–22. (abstract) (AMS review #85d:51016)

  34. Linear Algebra Through Geometry (with J. Wermer), Springer-Verlag (1983). (AMS review #84f:15001)

  35. DIAL: A Diagrammatic Animation Language (with S. Feiner and D. Salesin), IEEE Computer Graphics and Applications, 2, No. 7 (1982) 43–54.

  36. Critical points and curvature for embedded polyhedra II, Differential Geometry, Proc. Special Year, Maryland, Progress in Math 32, Birkhäuser (1983) 34–55. (abstract)

  37. La Quarta Dimensio i Salvador Dalí, Breu Viatge al mon de la Mathematica, 1 (1984) 19–24.

  38. Normal Curvatures and Euler Classes for Polyhedral Surfaces in 4-Space, Proc. A.M.S.,92 (1984) 593–596. (abstract) (AMS review #86c:57019)

  39. Counting Tritangent Planes of Space Curves (with T. Gaffney and C. McCrory), Topology 34 (1985) 15–24. (abstract) (AMS review #86m:58028a)

  40. Visualizing Two-Dimensional Phenomena in Four-Dimensional Space, Statistical Image Processing, Marcel Dekker (1986) 187–202. (abstract) (AMS review #89a:58001)

  41. 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. (abstract) (AMS review #88a:58069)

  42. Global Theorems for Symmetry Sets of Smooth Curves and Polygons in the Plane (with Peter Giblin) Proc. Royal Soc. Edinburgh 106A (1987) 221–231. (AMS review #88j:53003)

  43. Torus Decompositions of Regular Polytopes in 4-Space, Shaping Space (1988), Birkhäuser-Verlag, 221–230. (AMS review #937 089)

  44. Geometry of the Hopf Mapping and Pinkall's Tori of Given Conformal Type, Computers in Geometry, Marcel Dekker, New York (1990) 57–62. (abstract) (AMS review #90c:53035)

  45. Linear Algebra Through Geometry (with J. Wermer), revised and expanded second edition, Springer-Verlag (1991).

  46. 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.

  47. Equilibrium Triangulations of the Complex Projective Plane (with Wolfgang Kühnel), Geometriae Dedicata. 44(1992) 313–333. (abstract) (AMS review #94a:52035)

  48. Symmetry Sets of Piecewise Circular Curves (with Peter Giblin), Proc. Royal Soc. Edinburgh 123A (1993) 1–15. (abstract) (AMS review #95a:58007)

  49. Tangential and Normal Euler Numbers, Complex Points, and Singularities of Projections for Oriented Surfaces in Four-Space (with Frank Farris), Pacific Journal of Mathematics Vol. 161 No. 1. (1993) 1–24. (abstract)

  50. On the Geometry of Piecewise Circular Curves (with Peter Giblin), American Mathematical Monthly 101 No. 5 (1994) 403–416. (abstract) (AMS review #95k:51030a)

  51. Circumscribing Conics around Convex Quadrilaterals (with Philip J. Davis) (abstract)

  52. An interactive gallery on the internet: "Surfaces beyond the third dimension" (with Davide Cervone), International Journal of Shape Modeling 5 (1999) 7–22; (PDF, 1M)
    (see also the URL http://www.math.brown.edu/~banchoff/art/PAC-9603/)

  53. Osculating Tubes and Self-Linking Numbers of Curves on the Three-Sphere Proceedings of the Alfred Gray Memorial Conference, Bilbao, Spain 2000, Contemporary Math., Amer. Math .Soc., 288 (2001) 10–19.

  54. Midpoint Polygons Revisited on the Internet (with Stephen Canon, et. al.), accepted for publication in the NCTM electronic journal OnMath, under revision.

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