tag:blogger.com,1999:blog-6213919025256134910.post6526210613348103963..comments2023-05-15T08:32:02.241-07:00Comments on The Math Contest: 2002: 1 and 41Curmudgeonhttp://www.blogger.com/profile/04323026187622872114noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-6213919025256134910.post-85931404090967385882011-04-23T11:30:23.395-07:002011-04-23T11:30:23.395-07:00Yeah--I'm just getting back to doing these now...Yeah--I'm just getting back to doing these now, and I did it the same way as Jonathan's friend. That's part of another nice proof of the Pythagorean theorem.Lsquaredhttp://www.blogger.com/profile/00858524638866166691noreply@blogger.comtag:blogger.com,1999:blog-6213919025256134910.post-76350996396999074222011-03-31T18:48:17.177-07:002011-03-31T18:48:17.177-07:00Handed it to my friend, who carved 4 3-4-5 triangl...Handed it to my friend, who carved 4 3-4-5 triangles out of the 5x5 square, leaving a 1x1 central square (pause, while you try it), and thus had the altitudes of each of the stranger triangles.jd2718http://jd2718.wordpress.com/noreply@blogger.comtag:blogger.com,1999:blog-6213919025256134910.post-4697188210694237702011-03-30T18:34:29.695-07:002011-03-30T18:34:29.695-07:00Smooth.Smooth.Curmudgeonhttp://www.blogger.com/profile/04323026187622872114noreply@blogger.comtag:blogger.com,1999:blog-6213919025256134910.post-48445211284047947302011-03-30T17:48:30.751-07:002011-03-30T17:48:30.751-07:00On 41 I have a solution, but I followed a very dif...On 41 I have a solution, but I followed a very different path:<br><br>Enclose the entire figure in a rectangle (it helps to ignore the remote sides of the outer triangles.<br><br>Focus on the 5x5 square - it can be surrounded by 4 3-4-5 rt triangles (much like in the famous proof). Now complete the big rectangle by drawing horizontals and perpendiculars. All exterior segments should be labeled (3 or 4)<br><br>The big rectangle is 110, and quickly subtract out the 4 unneeded triangles. <br><br>Jonathanjd2718http://jd2718.wordpress.com/noreply@blogger.com