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Affascinanti forme per oggetti topologici

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Matematica e cultura 2011

Part of the book series: Matematica e cultura ((MACU))

Riassunto

La topologia è lo studio delle forme deformabili; per disegnare un’immagine di un oggetto topologico è necessario scegliere una forma geometrica particolare. Una strategia è quella di minimizzare un’energia geometrica del tipo che si presenta anche in molte situazioni fisiche. I minimizzatori di energia o forme ottimali sono spesso anche esteticamente interessanti.

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Bibliografia

  1. F.J. Almgren, J.M. Sullivan (1992) Visualization of soap bubble geometries, Leonardo 24:3/4, 267–271 e Color Plate C, ristampato in [5]

    Article  Google Scholar 

  2. K.A. Brakke (1992) The Surface Evolver, Experimental Mathematics 1:2, 141–165

    MathSciNet  MATH  Google Scholar 

  3. J. Cantarella, J. Fu, R. Kusner, J.M. Sullivan, N. Wrinkle (2006) Criticality for the Gehring link problem, Geometry and Topology 10, 2055–2115, arXiv.org/math.DG/0402212

    Article  MathSciNet  MATH  Google Scholar 

  4. J. Cantarella, R.B. Kusner, J.M. Sullivan (2002) On the minimum ropelength of knots and links, Inventiones Math. 150:2, 257–286, arXiv:math.GT/0103224

    Article  MathSciNet  MATH  Google Scholar 

  5. M. Emmer (a cura di) (1993) The Visual mind: Art and mathematics, MIT Press, Cambridge (Mass.)

    MATH  Google Scholar 

  6. G. Francis, B. Morin (1979) Arnold Shapiro’s eversion of the sphere, Math. Intelligencer 2, 200–203

    Article  MathSciNet  Google Scholar 

  7. G. Francis, J.M. Sullivan, R.B. Kusner, K.A. Brakke, C. Hartman, G. Chappell, The minimax sphere eversion, in: H.-C. Hege, K. Polthier (a cura di) (1997) Visualization and Mathematics, Springer-Verlag, Heidelberg, 3–20

    Google Scholar 

  8. C. Gunn, J.M. Sullivan (2008) The Borromean rings: A new logo for the IMU, in: MathFilm Festival 2008, Springer-Verlag; comprende un video di 5 minuti

    Google Scholar 

  9. C. Gunn and J.M. Sullivan (2008) The Borromean rings: A video about the new IMU logo, Bridges Proceedings (Leeuwarden), 63–70

    Google Scholar 

  10. H. Karcher and U. Pinkall (1997) Die Boysche Fläche in Oberwolfach, Mitteilungen der DMV 97:1, 45–47

    Google Scholar 

  11. R. Kusner, J.M. Sullivan (1996) Comparing the Weaire-Phelan equal-volume foam to Kelvin’s foam, Forma 11:3, 233–242, ristampato in [21]

    MathSciNet  MATH  Google Scholar 

  12. F. Morgan (2001) Proof of the double bubble conjecture, Amer. Math. Monthly 108:3, 193–205

    Article  MathSciNet  MATH  Google Scholar 

  13. U. Pinkall, I. Sterling (1987) Willmore surfaces, Math. Intelligencer 9:2, 38–43

    Article  MathSciNet  MATH  Google Scholar 

  14. J.M. Sullivan, G. Francis, S. Levy, The Optiverse, in: H.-C. Hege, K. Polthier (a cura di) (1998) VideoMath Festival at ICM’98, Springer-Verlag; comprende un video di 7 minuti, torus.math.uiuc.edu/optiverse/

    Google Scholar 

  15. J.M. Sullivan, F. Morgan (a cura di) (1996) Open problems in soap bubble geometry, Int’l J. of Math. 7:6, 833–842

    Article  MathSciNet  MATH  Google Scholar 

  16. J.M. Sullivan (1991) Generating and rendering four-dimensional polytopes, The Mathematica Journal 1:3, 76–85

    Google Scholar 

  17. J.M. Sullivan, The geometry of bubbles and foams, in: N. Rivier, J.-F. Sadoc (a cura di) (1998) Foams and Emulsions, NATO Advanced Science Institute Series E: Applied Sciences, Kluwer, Dordrecht, vol. 354, 379–402

    Google Scholar 

  18. J.M. Sullivan (1999) “The Optiverse” and other sphere eversions, Bridges Proceedings (Winfield), 265–274, arXiv:math.GT/9905020

    Google Scholar 

  19. J.M. Sullivan (2010) Minimal flowers, Bridges Proceedings (Pécs), 395–398

    Google Scholar 

  20. W. Thompson (Lord Kelvin) (1887) On the division of space with minimum partitional area, Philos. Mag. 24, 503–514, pubblicato anche in Acta Math. 11, 121-134, ristampato in [21]

    Google Scholar 

  21. D. Weaire (a cura di) (1997) The Kelvin problem, Taylor & Francis, London

    Google Scholar 

  22. T.J. Willmore (1992) A survey on Willmore immersions, in: Geometry and Topology of Submanifolds, IV (Leuven, 1991), World Sci. Pub., 11–16

    MathSciNet  Google Scholar 

  23. D. Weaire, R. Phelan (1994) A counter-example to Kelvin’s conjecture on minimal surfaces, Phil. Mag. Lett. 69:2, 107–110, ristampato in [21]

    Article  Google Scholar 

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Sullivan, J.M. (2011). Affascinanti forme per oggetti topologici. In: Matematica e cultura 2011. Matematica e cultura. Springer, Milano. https://doi.org/10.1007/978-88-470-1854-9_12

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