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benice
Joined: 25 Jan 2011 Posts: 3

Posted: Fri Feb 04, 2011 4:53 am Post subject: [Funny Math Art] Guess what's inside? (answers included) 


The surface in above image is a portion of the graph of
some mathematical equation.
Let's do some brainstorming:
Can you guess what's inside the surface?
Answers:
A funny 3D image:
A funny curve:
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Last edited by benice on Tue Jul 12, 2011 10:48 pm; edited 2 times in total 

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nextstep Site Admin
Joined: 06 Jan 2007 Posts: 538

Posted: Fri Feb 04, 2011 9:22 am Post subject: 


Hi,
It looks like the ''millefeuille" or ''Napolitain'' cake made by a child
Is it the same isosurface at different levels? _________________ Cheers,
Abderrahman 

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abdelhamid belaid
Joined: 13 Aug 2009 Posts: 170

Posted: Fri Feb 04, 2011 7:46 pm Post subject: 


hello all ,
I think the issue is the same with these isosurfaces :
sin(4*pi*( sqrt((cos(x) + cos(y) )^2+z^2) 0.3 )) = 0
sin( 2*pi*( cos(x)+cos(y)+cos(z) )) =0 :
the idea is the use of another dimension " k " so that F(x,y,z) = k/n , that means n*pi*F(x,y,z) = pi*k
so sin( n*pi*F(x,y,z) ) = 0 ( k : whole number ) .
In our first exemple F(x,y,z) = sqrt((cos(x) + cos(y) )^2+z^2) 0.3 :
Now , each form with 4 dimensions F(x,y,z, k) =0 ( k € Z ) is a three dimensional form G(x,y,z) =0 ? _________________ My YouTube channel 

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benice
Joined: 25 Jan 2011 Posts: 3

Posted: Sun Feb 06, 2011 10:10 am Post subject: Thanks for your reply. 


Hi nextstep,
Yes, it's a 3D contour plot at different levels.
Hi abdelhamid belaid,
Your gallery is very great.
Thanks for share your nice graphics.
Hint:
Consider the intersection of a horizontal plane with the surface.
The intersection consists of a family of funny curves.
(An example curve is shown below. It has nothing to do with the answer.)
Cut off the upper surface above the horizontal plane
to get a funny 3D image.
(This curve is obtained from another surface.) 

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nextstep Site Admin
Joined: 06 Jan 2007 Posts: 538

Posted: Tue Feb 08, 2011 10:44 am Post subject: 


Hi,
Ok, so it's a 3D contour plot...My bet then is that it's a 3D contour " movie " but I can't imagine the caracters nor the scenario of this film from the given image _________________ Cheers,
Abderrahman 

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nextstep Site Admin
Joined: 06 Jan 2007 Posts: 538

Posted: Fri Feb 11, 2011 10:07 pm Post subject: 


Hi,
I was thinking about something similar but with a 3d contour changing with the different slices of the isosurface. For example, a 3D contour like this changing to something like that . It should be feasible with an implicitly defined surface or even with a set of parametric surfaces.
Very funny math and keep it up _________________ Cheers,
Abderrahman 

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benice
Joined: 25 Jan 2011 Posts: 3

Posted: Tue Feb 15, 2011 3:01 am Post subject: Funny animations 


Hi nextstep,
Funny animations can be done by changing a parameter of the function.
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