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RE: Perpendicular Lines
Posted:
Jan 2, 2013 11:09 PM
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This could be extended to the idea of envelopes of lines --- here is a lovely site with examples: http://mathforum.org/mathimages/index.php/Envelope. Note the modeling examples of envelopes with sound ways, falling ladders, exploding fireworks. Quite exciting I think.
Lynne Ipina
Mathematics Dept.
University of Wyoming
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From: owner-mathedcc@mathforum.org [owner-mathedcc@mathforum.org] on behalf of Guy Brandenburg [gfbrandenburg@yahoo.com]
Sent: Wednesday, January 02, 2013 8:00 PM
To: Fred Siegeltuch; mathedcc@mathforum.org
Subject: Re: Perpendicular Lines
I would use the fact that with a circle, tangent lines are perpendicular to radii. Find lines tangent to a circle at such-and-such a point on the circle in the plane...
Guy Brandenburg, Washington, DC
http://gfbrandenburg.wordpress.com/
http://home.earthlink.net/~gfbranden/GFB_Home_Page.html
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________________________________
From: Fred Siegeltuch <notesforfred@yahoo.com>
To: "mathedcc@mathforum.org" <mathedcc@mathforum.org>
Sent: Wednesday, January 2, 2013 5:47 PM
Subject: Perpendicular Lines
Hi all,
I've seen tons of examples of math modeling where parallel lines arise and have a natural interpretation but I could use help in finding ones where the product of the slopes equals -1 is useful in modeling other than in doing bare geometry problems algebraically. I'd appreciate an example where this fact was used in such a way that covering this material didn't seem tangential (please forgive the pun) to a modeling perspective for algebra. I could try to embellish a problem that tries to find the tangent line to a circle or circular cylinder with a specific given radius but as of now I'm trying to do better. Ideally this should be no higher than the intermediate algebra level.
Thanks,
Fred Siegeltuch
City Colleges of Chicago
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