[math-fun] Dolphins have and use audible individual names
Let P = (-1,0) and Q = (1,0) in the plane. Let L be the locus of all points X such that the angle PXQ is 120 degrees. Include in L the points P and Q as well. QUESTION: Does L have a well-defined tangent line at P and Q ??? (And if so, is it C^oo or C^w (real analytic) at P and Q as well?) --Dan
I think, as you have phrased it, that the answer is "no"; the locus is two circular arcs whose tangents meet at 60 degree angles; it looks like a pointy American football. On Tue, Jul 23, 2013 at 1:02 PM, Dan Asimov <dasimov@earthlink.net> wrote:
Let P = (-1,0) and Q = (1,0) in the plane.
Let L be the locus of all points X such that the angle PXQ is 120 degrees.
Include in L the points P and Q as well.
QUESTION: Does L have a well-defined tangent line at P and Q ??? (And if so, is it C^oo or C^w (real analytic) at P and Q as well?)
--Dan
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Thanks, Allan. I see that now. --Dan On 2013-07-23, at 10:10 AM, Allan Wechsler wrote:
I think, as you have phrased it, that the answer is "no"; the locus is two circular arcs whose tangents meet at 60 degree angles; it looks like a pointy American football.
On Tue, Jul 23, 2013 at 1:02 PM, Dan Asimov <dasimov@earthlink.net> wrote:
Let P = (-1,0) and Q = (1,0) in the plane.
Let L be the locus of all points X such that the angle PXQ is 120 degrees.
Include in L the points P and Q as well.
QUESTION: Does L have a well-defined tangent line at P and Q ??? (And if so, is it C^oo or C^w (real analytic) at P and Q as well?)
--Dan
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_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
http://languagelog.ldc.upenn.edu/nll/?p=5453 On Tue, 23 Jul 2013, Warren D Smith wrote:
http://www.guardian.co.uk/environment/2013/jul/22/bottlenose-dolphins-names-...
-- Tom Duff. Stop writing passwords down on scraps of paper!
participants (4)
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Allan Wechsler -
Dan Asimov -
Tom Duff -
Warren D Smith