Re: visualizing a maximum in the intersection between two surfaces

• To: mathgroup at smc.vnet.net
• Subject: [mg131089] Re: visualizing a maximum in the intersection between two surfaces
• From: Dusko Cakara <dusko.cakara at gmail.com>
• Date: Tue, 11 Jun 2013 02:28:31 -0400 (EDT)
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```Dear Bob,
What you posted as the alternative method is exactly what I was looking for
(I particularly like you manipulation with Exclusions), but the first one
is absolutely sleek! Thanks a lot!
Best regards
Dusko

------------------------------------------------------
Dr. Dusko Cakara
Dpt. of Biotechnology
University of Rijeka
Radmile Matejcic 2, 51000 Rijeka, Croatia
Email: dusko.cakara at uniri.hr
Tel: +385/51/584555
Fax: +385/51/584599
Mobile: +385/91/9570399
-------------------------------------------------------

On Sun, Jun 9, 2013 at 4:42 PM, Bob Hanlon <hanlonr357 at gmail.com> wrote:

> An alternate method
>
>
> Show[
>  ContourPlot3D[Tooltip[x + y == 1],
>   {x, 0, 1}, {y, 0, 1}, {z, 0, 1/2},
>   ContourStyle -> Opacity[.7],
>   MeshStyle -> Gray],
>  Plot3D[Tooltip[x*y], {x, 0, 1}, {y, 0, 1},
>   PlotStyle -> Opacity[.7],
>   Exclusions -> {x == 1/2, y == 1/2, x + y == 1},
>   ExclusionsStyle ->
>    Directive[Opacity[1], Black, Thick],
>   MeshStyle -> Gray,
>   PlotPoints -> 100]]
>
>
>
> Bob Hanlon
>
>
>
>
> On Sat, Jun 8, 2013 at 2:34 AM, <dusko.cakara at gmail.com> wrote:
>
>> Hello,
>> I want to visualize that for x+y=1, maximum x*y occurs when y=0.5 and
>> x=0.5.
>>
>> Graphically, this can be visualized as the maximum of the projection
>> curve of the x+y=1 line in the x-y plane, at the x*y surface. Equivalently,
>> we can look for the maximum in the intersection curve between the surface
>> x*y and the surface peripendicular to the x-y plane with the base x+y=1.
>>
>> Can I plot this in a simple manner?
>>