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Before carrying out these transformations, make sure the glasses are not filled too full

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  • Mathematical Table-turning Revisited
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References

  1. de Mira Fernandes, A. Funzioni continue sopra una superficie sferica.Portugaliae Math 4 (1943), 69–72.

    MATH  MathSciNet  Google Scholar 

  2. Dyson, F. J. Continuous functions defined on spheres.Ann. of Math. 54 (1951), 534–536.

    Article  MATH  MathSciNet  Google Scholar 

  3. Emch, A. Some properties of closed convex curves in a plane,Amer. J. Math. XXXV (1913), 407–412.

    Article  MathSciNet  Google Scholar 

  4. Fenn, Roger. The table theorem.Bull. London Math. Soc. 2 (1970), 73–76.

    Article  MATH  MathSciNet  Google Scholar 

  5. Fenn, Roger. Some applications of the width and breadth of a closed curve to the two-dimensional sphere.J. London Math. Soc. (2)10 (1975), 219–222.

    Article  MATH  MathSciNet  Google Scholar 

  6. Floyd, E. E. Real-valued mappings of spheres.Proc. Amer. Math. Soc. 6(1955), 957–959.

    Article  MATH  MathSciNet  Google Scholar 

  7. Gardner, Martin. Mathematical Games column inScientific American (May 1973), 104.

  8. Gardner, Martin. Mathematical Games column inScientific American (June 1973), 109–110.

  9. Gardner, Martin.Knotted Doughnuts and Other Mathematical En- tertainments. W.H. Freeman and Company, New York, 1986.

    Google Scholar 

  10. Hadwiger, H. Ein Satz über stetige Funktionen auf der Kugelfläche.Arch. Math. 11 (1960), 65–68.

    Article  MATH  MathSciNet  Google Scholar 

  11. Hunziker, Markus. The Wobbly Table Problem.In Summation Vol. 7 (April 2005), 5–7 (Newsletter of the Department of Mathematics, Baylor University).

    Google Scholar 

  12. Joshi, Kapil D. A non-symmetric generalization of the Borsuk-Ulam theorem.Fund. Math. 80 (1973), 13–33.

    MATH  MathSciNet  Google Scholar 

  13. Kraft, Hanspeter. The wobbly garden table.J. Biol. Phys. Chem. 1 (2001), 95–96.

    Article  Google Scholar 

  14. Kronheimer, E. H. and Kronheimer, P. B. The tripos problem.J. London Math. Soc. 24 (1981), 182–192.

    Article  MATH  MathSciNet  Google Scholar 

  15. Livesay, George R. On a theorem of F. J. Dyson.Ann. of Math. 59 (1954), 227–229.

    Article  MathSciNet  Google Scholar 

  16. Martin, Andre. On the stability of four feet tables. http://=20 arxiv.org/abs/math-ph/0510065

  17. Meyerson, Mark D. Balancing acts. The Proceedings of the 1981 Topology Conference (Blacksburg, Va., 1981),Topology Proc. 6 (1981), 59–75.

    MathSciNet  Google Scholar 

  18. Meyerson, Mark D. Convexity and the table theorem.Pacific J. Math. 97 (1981), 167–169.

    Article  MATH  MathSciNet  Google Scholar 

  19. Meyerson, Mark D. Remarks on Fenn’s “the table theorem” and Zaks’ “the chair theorem”.Pacific J. Math. 110 (1984), 167–169.

    Article  MATH  MathSciNet  Google Scholar 

  20. Polster, Burkard; Ross, Marty and QED (the cat). Table Turning Mathsnack inVinculum 42(2), June 2005. (Vinculum is the quarterly magazine for secondary school teachers published by the Mathematical Association of Victoria, Australia. Also available at www.mav.vic.edu.au/curres/mathsnacks/mathsnacks.html).

  21. Royden, H. L,Peal Analysis. Prentice-Hall, 1988.

  22. Vinculum, Editorial Board. Mathematical inquiry—from a snack to a meal.Vinculum,42(3), September 2005, 11–12 (also available at www.mav.vic.edu.au/curres/mathsnacks/mathsnacks.html).

    Google Scholar 

  23. Polster, Burkard; Ross, Marty and QED (the cat). Turning the Tables: feasting from a mathsnack.Vinculum 42(4), 4 November 2005, 6–9 (also available at www.rnav.vic.edu.au/curres/math-snacks/mathsnacks.html).

    Google Scholar 

  24. Yamabe, Hidehiko and Yujobô;, Zuiman. On the continuous function defined on a sphere.Osaka Math. J. 2 (1950), 19–22.

    MATH  MathSciNet  Google Scholar 

  25. Yang, Chung-Tao. On theorems of Borsuk-Ulam, Kakutani-Yam-abe-Yujobô and Dyson. I.Ann. of Math. 60 (1954), 262–282.

    Article  MATH  MathSciNet  Google Scholar 

  26. Yang, Chung-Tao. On theorems of Borsuk-Ulam, Kakutani-Yam-abe-Yujobo and Dyson. II.Ann. of Math. 62 (1955), 271–283.

    Article  MATH  MathSciNet  Google Scholar 

  27. Yang, Chung-Tao. Continuous functions from spheres to euclid-ean spaces.Ann. of Math. 62 (1955), 284–292.

    Article  MATH  MathSciNet  Google Scholar 

  28. Yang, Chung-Tao. On maps from spheres to euclidean spaces.Amer. J. Math. 79 (1957), 725–732.

    Article  MATH  MathSciNet  Google Scholar 

  29. Zaks, Joseph. The chair theorem. Proceedings of the Second Louisiana Conference on Combinatorics, Graph Theory and Computing (Louisiana State Univ., Baton Rouge, La., 1971), pp. 557–562. Lousiana State Univ., Baton Rouge, 1971.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand

    Bill Baritompa

  2. Institut für Analysis und Algebra, Technische Universität, 38106, Braunschweig, Germany

    Rainer Löwen

  3. School of Mathematical Sciences, Monash University, 3800, Victoria, Australia

    Burkard polster

  4. P.O. Box 83, 3078, Fairfield, Victoria, Australia

    Marty Ross

Authors
  1. Bill Baritompa
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  2. Rainer Löwen
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  3. Burkard polster
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  4. Marty Ross
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Correspondence to Bill Baritompa.

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Baritompa, B., Löwen, R., polster, B. et al. Before carrying out these transformations, make sure the glasses are not filled too full. The Mathematical Intelligencer 29, 49–58 (2007). https://doi.org/10.1007/BF02986206

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