From: Marcelo <marcelo.magallon@...>
Date: 2008-04-25T01:42:23+09:00
Subject: Re: [SUMMARY] Triangle Area (#160)

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