A Practical Use for the OrthocenterDate: 03/07/2001 at 17:35:48 From: Dustin Hodel Subject: Orthocentre My geometry teacher proposed a question, or challenge really, to find a practical use for the orthocentre. I've looked all over for an answer, with no luck. Please help. Date: 03/09/2001 at 07:35:44 From: Doctor Floor Subject: Re: Orthocentre Hi, Dustin, Thanks for writing. It seems very difficult to find a "practical" use for the orthocenter. But perhaps the following story will help you. Jonathan is competing in a bicycle cross-country race. The track will be a triangular one (with acute angles). Jonathan's mom wants to see her son ride the bike on each straight part of the track, and she wants to walk the minimum distance possible. So she connects each "vertex" of the course with its orthocenter, and sees where each line meets the opposite part of the track. This way she finds the three points where she can see her son ride the bicycle, while having to walk the minimum total distance. The property used here is this: The triangle formed by the feet of the altitudes of ABC is the triangle inscribed in ABC with the smallest perimeter. I hope this helps! Best regards, - Doctor Floor, The Math Forum http://mathforum.org/dr.math/ |
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