Thomas Banchoff's Research-Oriented Articles

  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 E^n , Trans. Amer. Math. Soc. 161 (1971), 259-267. (abstract) ( AMS review #44#4760)

  9. [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), pp. 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), pp. 233-243. (abstract)

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

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  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, pp. 1-88. (abstract)

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

  30. Double Tangency Theorems for Pairs of Submanifolds, Geometry Symposium Utrecht (1980), Springer-Verlag Lecture Notes 894, pp. 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, BirkhŠuser (1983), 34-55. (abstract)

  37. La Quarta Dimensio i Salvador Dali, Breu Viatge al mon de la Mathematica, 1 (1984), pp. 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) pp. 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)