Marcelo
4/24/2008 4:42:00 PM
On Thu, Apr 24, 2008 at 8:46 AM, Matthew Moss <matthew.moss@gmail.com> wrote:
> Alex reminded me that it is similar to taking half of the magnitude
> of the cross-product of two vectors that form the triangle. (A bit of
> a mouthful, I know...). In fact, they are exactly the same thing:
> that's what the determinant of the matrix calculates.
The norm of the cross product of two vectors corresponds to the area of
the parallelogram spanned by those vectors. Since a parallelogram can
be split into two identical triangles, the area of the triangle whose
sides are described by the vectors corresponds to half the area of the
parallelogram.
(And I probably got the language wrong, I'm a bit rusty)
> Next, we have Heron's (or Hero's) Formula, credited to Heron of
> Alexandria circa 60 A.D., though it may be even older. This is new
> technique to me, and I was delighted by its simplicity.
The story behind how Heron arrived at this result is very interesting.
I think there's a book called "the joy of mathematics" which contains a
very nice account of it.
Thanks for the quiz!
Marcelo