Prev: The best way of writing FOL with identity and membership.
Next: Call for participants
From: bill on 8 May 2010 19:12
On May 7, 2:54 am, Thomas Nordhaus <thomas.nordh...(a)googlemail.com>
wrote:
> Hi.
> I'm trying to solve the following (self-posed ;-) ) problem:
>
> "Let ABC and A'B'C' be given triangles of the Euclidean plane.
> Determine whether A'B'C' can be inscribed inside of ABC. That means,
> determine whether there is a triangle T' congruent to A'B'C' such that
> T' is a subset of ABC".

What do you mean by "T is a subset of ABC"?
>
> Right now, I only have a few necessary conditions and a few sufficient
> conditions. But they don't come close to "closing the gap". Here is
> list of conditions I found so far:
>
> Necessary:
>
> 1. max(a',b',c') <= max(a,b,c) (Condiion on the diameters of the
> triangle)
> 2. a'b'sin(gamma') <= absin(gamma) (Condition on the areas + similar
> conditions for different pairs of sides and enclosed angles).
>
> Sufficient:
>
> 1. Radius of circumscribed circle of A'B'C' <= Radius of inscribed
> circle of ABC.
>
> I'm not much further than this. It would be nice to know whether the
> following is true:
>
> (*) Suppose A'B'C' \subset ABC, then there is a congruent copy T of
> A'B'C' such that T \subset ABC and T shares one or more vertices with
> ABC.
>
> If (*) were true one could  reduce the problem considerably.
>
> Thanks for any kind of help.
>
> --
>
> Thomas Nordhaus

First  |  Prev  | 
Pages: 1 2
Prev: The best way of writing FOL with identity and membership.
Next: Call for participants