Stewart's TheoremDate: 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/ |
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