Doubts in Extremal principle

Discussion in 'General Math' started by kishore, Nov 29, 2006.

  1. kishore

    kishore Guest

    HI ,
    I am a new member to this group .I am reading 'Problem solving
    strategies' by arthur engel.I could not get how one proceeds with the
    application of 'Extremal principle'(chapter 3).Can anybody direct me to
    a website where i can get information about this Or else can anybody
    clarify how to solve problems using 'extremal principle
    kishore, Nov 29, 2006
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  2. It's hard to answer without knowing that specific book, because
    "extremal principle" seems to be that author's personal terminology
    [*]. Somebody at
    might know the book. Mathlinks is quite a good forum, with a lot of
    interest in contest problems (which Engel seems to be using). And it
    has a high-school section.

    [*] It seems to be a name for some general scheme of solving or proving
    things. Since the book is for keen high-school students, I'm sure he is
    not referring to the calculus of variations, where the term "extremal
    principle" is also heard.

    Larry Hammick, Nov 29, 2006
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  3. kishore

    hagman Guest

    I obtained my training for IMO many years ago from Engel personally.
    But it's a long time ago. I think the term as used in that book refers
    to the idea in problem solving to investigate extremal aspects of
    anobject in question even if the original question doesn't ask for it.

    Assume You have n points in the plane. The triangle made from any 3 of
    these has an area of at most 1. Show that there exists a triangle of
    area at most 4 that contains all given points.
    It is not obvious from the problem statement, but finding A,B,C among
    the given points such that area(ABC) is maximal is extremely helpful in
    constructing the desired triangle XYZ (hint: area(XYZ)=4*area(ABC)).

    But since this method is mainly addressed to problem solving strategies
    in contests, You may find additional material in sites dealing with
    mathi contests.
    hagman, Nov 29, 2006
  4. kishore

    kishore Guest

    I searched the net for any material .I could not find any that
    explains and trains to use the extremal principle.Do you know any site
    kishore, Nov 30, 2006
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