Re: [math-fun] Window puzzle, sort of
Bill T. wrote: << It used to be a standard and well-known geometry fact that given a point and a circle, all lines through the point intersect the circle at two distances that have the same geometric mean = the length of a tangent. This is easy to prove using similar triangles, given the fact that all arcs of circles subtend the same angle as seen from any point on the circle outside the arc. Apply this to the bottom of the wall.
Phrased in this manner, this has to be the Book proof. --Dan P.S. What's this about a Paris fashion show in which at least one designer based their clothing on geometric theories of some American mathematician? More -- but way too little -- at < http://www.nytimes.com/2010/03/06/fashion/06iht-rrick.html >. ________________________________________________________________________________________ "Outside of a dog, a book is man's best friend. Inside of a dog, it's too dark to read." --Groucho Marx
Sorry. My post about the window was held up for a day, long after several people had made my reply obsolete. It was held up because I sent it from a different email address. On Mar 12, 2010, at 7:08 PM, Dan Asimov wrote: .... Phrased in this manner, this has to be the Book proof.
P.S. What's this about a Paris fashion show in which at least one designer based their clothing on geometric theories of some American mathematician? More -- but way too little -- at < http://www.nytimes.com/2010/03/06/fashion/06iht-rrick.html >.
My involvement with Dai Fujiwara of Issey Miyake and Paris Fashion Week was, to say the least, a surreal (but exhilarating) experience. For those who are curious, here's a link to a relatively complete version of the AP story that gives a little more information, and a couple of YouTubes. Google will deliver plenty more from around the world if you're even more curious. All in all, I was pleased that most of the press coverage (a) took in stride that mathematics could be relevant to design and fashion, and (b) cast this in a generally positive light. http://www.newstimes.com/living/article/Fashion-and-advanced-mathematics-mee... YouTube - Issey Miyake Fashion Show: Women's Ready to Wear Autumn/Winter 2010/11 YouTube - Interview with Dai Fujiwara and Professor William Thurston at the Issey Miyake Fashion Show in Paris
participants (2)
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Bill Thurston -
Dan Asimov