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2 results

  • Diophantine Steiner triples

  • Bojan Hvala
  • Journal:
    The Mathematical Gazette / Volume 95 / Issue 532 / March 2011
    Published online by Cambridge University Press:
    23 January 2015, pp. 31-39
    Print publication:
    March 2011

  • Computer programs for dynamic geometry provide a very effective tool for motivating students. It is my experience that a certain effort in preparing an adequate applet and spending some time on a careful presentation can result in a great change of the atmosphere in the classroom. On the other hand, these programs also open new perspectives in geometry exploration and can provoke new interesting research questions related to the already known topics. The possibility of experimenting and the chance of visual examination of the results add new dimensions to research and can also be appealing to non-mathematical audiences.

  • On additive maps of prime rings

  • Matej Brešar, Bojan Hvala
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 51 / Issue 3 / June 1995
    Published online by Cambridge University Press:
    17 April 2009, pp. 377-381
    Print publication:
    June 1995
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  • Let R be a prime ring of characteristic not 2, C be the extended centroid of R, and f: R → R be an additive map. Suppose that [f(x), x2] = 0 for all x ∈ R. Then there exist λ ∈ C and an additive map ζ: R → C such that f(x) = λx + ζ(x) for all x ∈ R. In particular, if f(x)2 = x2 for all x ∈ R, then ζ = 0 and either λ = 1 or λ= -1.