I was thinking that raindrop formation on windows would suggest some shape that is approximately circular.
If we have a half circle, the circle's radius should be R=: 100%1p1 and the half circle's area should be: (o.R^2)%2 1591.55 So if there's a better shape it must have a larger area. I expect that a shape with larger area would have a maximum distance from the wall which is shorter than R but I would have to think a bit about how to characterize where the resulting extra length belongs. That said... I've not worked with calculus of variations and the wikipedia article does not come with enough concrete examples for me to figure out what it is that I do not understand. FYI, -- Raul On Sat, Feb 23, 2013 at 10:24 PM, Eldon Eller <[email protected]> wrote: > Old and senile as I am, this looks to me like a problem in calculus of > variations.See, e.g., en. wikipedia.org/wiki/Calculus_of_variations. You are > not likely to get the solution by guessing that the shape is elliptical, or > catenary, or parabolic, etc. I am too old and lazy to try to solve it > myself. I would like to see someof you who are smarter and more energetic > than I give it a go. I feel reasonably certain that the problem has a closed > form solution and that writing that out in J would not be difficult. What > would be reallyimpressive would be a numerical method of doing calculus of > variations, in J, of course. > > > On 2/23/2013 4:28 PM, Ric Sherlock wrote: >> >> Kip, >> Alternative formulations for your adverb that require fewer calculations >> of >> u y. >> >> Max1 =: 1 : 0 >> >> ((= >./)@:u # ] ,. u) y >> >> ) >> >> >> Max2 =: 1 : 0 >> >> fnres=. u y >> >> where=. (= >./) fnres >> >> where # y ,. fnres >> >> ) >> >> I'd be interested in a tacit implementation of one of the adverbs Max >> above. I came up with the same as Pepe for a simple Max ( >./@: ) but >> can't see how to "factor out" the verb area from the adverbs in the >> following: >> Max3=: (({~ area ((i. >./)@:)) , area (>./@:)) >> >> On Sun, Feb 24, 2013 at 9:18 AM, km <[email protected]> wrote: >> >>> Borrowing ideas from Raul, I like >>> >>> Max =: 1 : 0 >>> max =. >./ u y >>> where =. max = u y >>> where # y ,. u y >>> ) >>> >>> which identifies the max and where it occurs: >>> >>> *: Max i:2 >>> _2 4 >>> 2 4 >>> (4 - *:) Max i:2 >>> 0 4 >>> >>> Sent from my iPad >>> >>> >>> On Feb 23, 2013, at 1:04 PM, Jose Mario Quintana < >>> [email protected]> wrote: >>> >>>> I did not see your second post! >>>> >>>> area=. ] * 50 - %&2 >>>> area(max=. (>./) @:) 0 to 100 >>>> 1250 >>>> max >>>>> >>>>> ./@: >>>> >>>> On Sat, Feb 23, 2013 at 1:46 PM, km <[email protected]> wrote: >>>> >>>>> Can we have an adverb Max so that f Max y finds the maximum of f on >>>>> the list y ? >>>>> >>>>> Sent from my iPad >>>>> >>>>> >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm >> >> >> ----- >> No virus found in this message. >> Checked by AVG - www.avg.com >> Version: 2013.0.2899 / Virus Database: 2641/6125 - Release Date: 02/23/13 >> >> > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
