Stewart's Theorem

Date: 5/18/96 at 18:7:7
From: Anonymous
Subject: Information on Stewart's Theorem
 
Hi,

I have to give a lesson/report on Stewart's Theorem, and am 
looking for information on history, uses (in "real life" or in 
math), examples, or anything else that might be useful. I know 
the theorem, its proof, and a minimal history of the proof. 
I've searched and so far have come up with very little. 
Thank you for any information you might be able to provide.

Michael Sonsino

Date: 5/23/96 at 13:56:8
From: Doctor Betsy
Subject: Re: Information on Stewart's theorem


Hi Michael, 

I found some information on Stewart's Theorem in the archives of the 
Math Forum's geometry.college newsgroup.  If you have access to the 
World Wide Web, the address for the information is at 

http://mathforum.org/kb/message.jspa?messageID=1074570   

Here is a little of what I found.

On Wed, 22 Mar 1995, REBECCA BROWN wrote:

  I'm looking for any information on Stewart's Theorem.  Any help on 
  this topic will be greatly appreciated.
 
Rebecca,

You might want to check out Posamentier's "Excursions in Advanced 
Euclidean Geometry" (an excellent resource for any geometry class!)
It has a short section on Stewart's Theorem along with several 
applications of it to triangles.

Stewart's Theorem: Let d be the length of a Cevian of a triangle that 
divides the opposite side of length c into segments of length m and n 
adjacent to the sides of length a and b respectively. Then 
na^2+mb^2 = c(d^2+mn). (See crudely drawn picture below.)

        /\
       /  \\
      /    \ \
     /      \  \
  a /      d \   \ b
   /          \    \
  /     m      \  n  \
 ----------------------
          c



Sandy Norman
University of Texas at San Antonio

Hope that helps.

-Doctor Betsy,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/