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ABSTRACT
Recent research indicates machine computation and mathematical theory have proceeded hand in hand and have proved to be of great benefit to one another.
REFERENCES
Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.
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1
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Anderson, D. Studies in the microstructure of microemulsions. Ph,D. thesis, Dept. of Chemical Engineering, Univ. of Minnesota, Minneapolis, Minn. June 1986.
|
| |
2
|
Anderson, D., and Thomas, E.L. Microdomain morphology of star copolymers in the strong-segregation limit. Dept. of Polymer Science, Univ. of Massachusetts, Amherst.
|
| |
3
|
Callahan, M., Hoffman, D., and Meeks, W., III. Embedded minimal surfaces with an infinite number of ends. Geometry, C, omputation and Graphics Preprint Series, Department of Mathematics, Univer- - sity of Massachusetts, Amherst, Mass., Sept. 1987.
|
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4
|
Callahan, M., Hoffman, D., and Meeks, W., III. Embedded minimal surfaces with four ends. Geometry, Computation and Graphics Preprint Series, Department of Mathematics, University of Massachusetts, Amherst, Mass., in preparation.
|
| |
5
|
Costa, C. Example of a complete minimal immersion :.n R3 of genus one and three embedded ends. Bull. Soc. Bras. Mat. 15 (1984), 47-54.
|
| |
6
|
Crypton. Shapes that eluded discovery. Sci. Dig. 94, 4 (Apr. 1986), 50-55.
|
| |
7
|
Hoffman, D. The computer-aided discovery of new embedded minimal surfaces. Math. Intell. 9, 3 (July 1987), 8-21.
|
| |
8
|
Hoffman, D. The construction of families of embedded minimal surfaces. In Variational Methods for Free Surface Interfaces, P. Concus and R. Finn, Ed. Springer-Verlag, New York, 1987, pp. 25-36.
|
| |
9
|
Hoffman, D., and Meeks, W., III. Complete embedded minimal surfaces of finite total curvature. Bull. A. M. S. 12, 1 (Jan. 1985), 134-136.
|
| |
10
|
Hoffman, D., and Meeks, W., III. A complete embedded minimal surface with genus one, three ends and finite total curvature. J. Differ. Geom. 21 (Mar. 1985), 109-t27.
|
| |
11
|
11. Hoffman, D., and Meeks, W., III. The global theory of embedded minimal surfaces. Geometry, Computation and Graphics Preprint Series, Department of Mathematics, University of Massachusetts, Amherst, Mass., Nov. 1987.
|
| |
12
|
Hoffman, D., and Meeks, W., III. One-parameter families of embedded minimal surfaces. Geometry, Computation and Graphics Preprint Series, Department of Mathematics, University of Massachusetts, Amherst, Mass., April 1988.
|
| |
13
|
Hoffman, D., and Meeks, W., III. Properties of properly embedded minimal surfaces of finite total curvature. Bull. A. M. S. 17, 2. To be published.
|
| |
14
|
Hopf, H. Differential Geometry in the Large. Lecture Notes in Mathematics, vol. 1000. Springer-Verlag, New York, 1984.
|
| |
15
|
Karcher, H. Families of triply-periodic surfaces of constant mean curvature. Preprint, SFB, Univ. of Bonn, Bonn, Germany. April 1987.
|
| |
16
|
Osserman, R. A Survey of Minimal Surfaces. 2nd ed. Dover Publications, New York, 1986.
|
| |
17
|
Rotman, D. A new look in block copolymers. Ind. Chem. News 7, 11 (Nov. 1986), 4-5.
|
| |
18
|
Schoen, A. Infinite periodic minimaI surfaces without self-intersections. Tech. Note D-5541, NASA, Cambridge, Mass., May 1970.
|
| |
19
|
Scriven, L.E. Bicontinuous structures. Nature 263, 5573 (Sept. 1976), 123.
|
| |
20
|
Stewart, I. One hundred per cent proof. Nature 324, (Dec. 1986), 4O6-4O7.
|
| |
21
|
Thomas, E.L., Alward, D.B., Kinning, D.J., Martin, D.C., Jr., Handlin, D.L., and Fetters, L.J. Ordered bicontinuous double-diamond structure of star block copolymers: A new equilibrium microdomain morphology. Macromolecules 19, (1986), 2197-2202.
|
| |
22
|
Wente, H. Counterexampte to a conjecture of H. Hopf. Pac. }. 121 (1986), 193-243.
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CITED BY 3
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Carlo H. Séquin , Houman Meshkin , Laura Downs, Interactive generation of Scherk-Collins sculptures, Proceedings of the 1997 symposium on Interactive 3D graphics, p.163-ff., April 27-30, 1997, Providence, Rhode Island, United States
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Randy Hudson , Charlie Gunn , George K. Francis , Daniel J. Sandin , Thomas A. DeFanti, Mathenautics: using VR to visit 3-D manifolds, Proceedings of the 1995 symposium on Interactive 3D graphics, p.167-170, April 09-12, 1995, Monterey, California, United States
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