Abstract
The theme New Directions in Applied and Computational Mathematics gives all of us who think of ourselves as “pure mathematicians” the chance to reexamine the changes that have taken place in our understanding of that term as a result of the new directions which have appeared in our lifetimes. I have always thought of myself as a geometer, as soon as I realized that it was possible to think of different subspecies of mathematician, and I can make the case today that there will be major differences in the way we do geometry and the way we present our insights to our students and colleagues because of the dramatic developments in visualization capabilities in the form of interactive computer graphics. One effect of these developments is that I find myself revising my concept of the differences between pure and applied mathematics. A virture of a symposium such as this, honoring a wide-ranging mathematician like Gail Young, is that we speakers are encouraged to be introspective about these changes in our careers, and of course that encourages in turn a certain anecdotal style.
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References
T. Banchoff, “Tightly embedded 2-dimensional polyhedral manifolds,” Amer. J. Math., 87 (1965), 462–472.
T. Banchoff, “The sperical two piece property and tight surfaces in spheres,” J. Differential Geometry, 4 (1970), 193–205.
T. Banchoff, “The two-piece property and tight n-manifolds-with-boundary in E3” Trans. Amer. Math. Soc., 161 (1971), 259–267.
T. Banchoff, “Non-rigidity theorems for tight polyhedral tori,” Archiv der Mathematik, 21 (1970), 416–423.
T. Banchoff and C. Strauss, “Real time computer graphics techniques,” Proceedings of Symposia in Applied Mathematics, Vol. 20 ( The Influence of Computing on Mathematical Research and Education) American Math. Soc., 1974, 105–111.
T. Banchoff, “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.
T. Banchoff, T. Gaffney and C. McCrory, Cusps of Gauss Mappings, Pitman Advanced Publishing Program 55, London, 1982, 1–88.
T. Banchoff and W. Kiihnel, “The nine-vertex complex projective plane,” Mathematical Intelligencer, 5 (1983), 11–22.
T. Banchoff, S. Feiner and D. Salesin, “DIAL: a diagrammatic animation language,” IEEE Computer Graphics and Applications, 2 (7) (1982), 43–54.
T. Banchoff, “Differential geometry and computer graphics,” Perspectives in Mathematics, Anniversary of Oberwolfach 1984, Birkhauser Verlag, Basel, 43– 60.
T. Banchoff, “Visualizing two-dimensional phenomena in four-dimensional spaces,” in Statistical Image Processing, Marcel Dekker, to appear.
T. Banchoff, H. Kogak, F. Bisshopp and D. Laidlaw, “Topology and mechanics with computer graphics: linear Hamiltonian systems in four dimensions,” Advances in Applied Mathematics, to appear.
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© 1986 Springer-Verlag New York Inc.
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Banchoff, T.F. (1986). Computer Graphics Applications in Geometry: “Because the Light is Better Over Here”. In: Ewing, R.E., Gross, K.I., Martin, C.F. (eds) The Merging of Disciplines: New Directions in Pure, Applied, and Computational Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4984-9_1
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DOI: https://doi.org/10.1007/978-1-4612-4984-9_1
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