Skip to main content
Log in

Minimal Surfaces, Crystals, Shortest Networks, and Undergraduate Research

  • Article
  • Published:
The Mathematical Intelligencer Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Reference

  1. Manuel Alfaro, Mark Conger, Kenneth Hodges, Adam Levy, Rajiv Kochar, Lisa Kuklinski, Zia Mahmood, and Karen von Haam, Segments can meet in fours in energy- minimizing networks,J. Undergrad. Math. 22 (1990), 9–20.

    Google Scholar 

  2. Manuel Alfaro, Mark Conger, Kenneth Hodges, Adam Levy, Rajiv Kochar, Lisa Kuklinski, Zia Mahmood, and Karen von Haam, The structure of singularities in Φ-minimizing networks inR 2,Pacific J. Math. 149 (1991), 201–210.

    Article  MATH  MathSciNet  Google Scholar 

  3. Marshall W. Bern and Ronald L. Graham, The shortest-network problem,Scientific American 45 (January 1989), 84–89.

    Article  Google Scholar 

  4. E. J. Cockayne, On the Steiner problem,Can. Math. Bull. 10 (1967), 431–450.

    Article  MATH  MathSciNet  Google Scholar 

  5. Mark A. Conger, Energy-minimizing networks inR“, Honors thesis, Williams College, 1989, expanded 1989.

  6. R. Courant and H. Robbins,What is Mathematics?, Oxford: Oxford Univ. Press (1941).

    Google Scholar 

  7. Martin E. Glicksman and Narsingh B. Singh,Microstructural scaling laws for dentritically solidified aluminum alloys, Special Technical Pub. 890, Philadelphia: American Society for Testing and Materials (1986), 44–61.

    Google Scholar 

  8. M. Hanan, On Steiner’s problem with rectilinear distance,J. S1AM Appl. Math. 14 (1966), 255–265.

    MATH  MathSciNet  Google Scholar 

  9. Stefan Hildebrandt and Anthony Tromba,Mathematics and Optimal Form, New York: Scientific American Book, Inc. (1985).

    Google Scholar 

  10. Gary Lawlor and Frank Morgan, Paired calibrations applied to soapfilms, immiscible fluids, and surfaces or networks minimizing other norms, preprint (1991).

  11. Adam Levy, Energy-minimizing networks meet only in threes,J. Undergrad. Math. 22 (1990), 53–59.

    Google Scholar 

  12. Frank Morgan,Geometric Measure Theory: a Beginner’s Guide, Boston: Academic Press (1988).

    MATH  Google Scholar 

  13. Frank Morgan,Riemannian Geometry: a Beginner’s Guide, Boston: Jones and Bartlett (1992).

    Google Scholar 

  14. Frank Morgan, Soap bubbles and soap films, inMathematical Vistas: New and Recent Publications in Mathematics from the New York Academy of Sciences (Joseph Malkevitch and Donald McCarthy, eds.), New York: New York Academy of Sciences (1990), Vol. 607.

    Google Scholar 

  15. Frank Morgan,Compound soap bubbles, shortest networks,and minimal surfaces, video of AMS-MAA address, Winter Mathematics Meetings, San Francisco, 1991.

  16. C. M. Petty, Equilateral sets in Minkowski spaces,Proc. AMS 29 (1971), 369–374.

    Article  MATH  MathSciNet  Google Scholar 

  17. Bruce Schecter, Bubbles that bend the mind,Science 84 (March 1984) 89.

    Google Scholar 

  18. Jean E. Taylor, Crystalline variational problems,Bull. AMS 84 (1987), 568–588.

    Article  Google Scholar 

  19. Jean E. Taylor, The structure of singularities in soapbubble-like and soap-film-like minimal surfaces,Ann. Math. 103 (1976), 489–539.

    Article  MATH  Google Scholar 

  20. Steve Smale, Beautiful crystals calendar, 69 Highgale Road, Kensington, CA 94707.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Frank Morgan.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Morgan, F. Minimal Surfaces, Crystals, Shortest Networks, and Undergraduate Research. The Mathematical Intelligencer 14, 37–44 (1992). https://doi.org/10.1007/BF03025868

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03025868

Keywords

Navigation