Yet another mysterious mailing-list holdback. -- Rich --- Date: Thu, 11 Mar 2010 15:08:13 -0700 Subject: RE: [math-fun] Window puzzle, sort of From: "Payton, Paul" <paul.payton@lmco.com> To: "'math-fun'" <math-fun@mailman.xmission.com> I did this by taking the derivative of two near-identical copies of the atan function, setting the two algebraic quantities equal, and thoroughly enjoying how things cancel and winding up with a clean sqrt of something rather simple. I'm not sure how didactic that is, but it is remarkably straightforward. Only about four lines of symbols... -----Original Message----- From: math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Allan Wechsler Sent: Thursday, March 11, 2010 2:02 PM To: Dan Asimov; math-fun Subject: Re: [math-fun] Window puzzle, sort of I did this with a geometric construction, but even though the algebra was easy, I wouldn't have been able to predict the answer in the form that Dan obviously intends. And I agree with him; it sort of calls out for something that qualifies as an explanation, rather than a mere proof. On Thu, Mar 11, 2010 at 4:05 PM, Dan Asimov <dasimov@earthlink.net> wrote: [Hide Quoted Text] This is the window puzzle: Given a window -- on the front of a building -- whose lowest point is height A and whose highest point is height B, how far from the building should a ground-level observer be so that the angle subtended by the window is maximum? <<clipped repeat of older messages -- rcs>>