# Doubts in Extremal principle

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

1. ### kishoreGuest

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
clarify how to solve problems using 'extremal principle
thanks
kishore

kishore, Nov 29, 2006

2. ### Larry HammickGuest

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

Larry Hammick, Nov 29, 2006

3. ### hagmanGuest

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.

Example:
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. ### kishoreGuest

hi,
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
?
thanks

kishore, Nov 30, 2006