[math-fun] Saddle-shaped minimal surface bounding a non-planar hexagon
Do any of you know of any pictures (hand-drawn or computer-generated) of the saddle-shaped surface you get when you make a non-planar hexagonal frame consisting of all the edges of a cube that avoid two antipodal vertices an dip it in a soap film solution? This is not to be confused with the surface you get when you dip a non-planar octagonal frame consisting of the edges in a Hamiltonian cycle on the cube. I spent about five minutes searching images.google.com and didn't find what I'm looking for, and would appreciate help from any of you who may know about where such things can be found! Thanks, Jim Propp
If you apply Schwarz reflections it extends into the triply periodic “D-surface”: http://facstaff.susqu.edu/brakke/evolver/examples/periodic/dcell/dcube.8.gif -Veit
On Jan 4, 2016, at 2:04 PM, James Propp <jamespropp@gmail.com> wrote:
Do any of you know of any pictures (hand-drawn or computer-generated) of the saddle-shaped surface you get when you make a non-planar hexagonal frame consisting of all the edges of a cube that avoid two antipodal vertices an dip it in a soap film solution?
This is not to be confused with the surface you get when you dip a non-planar octagonal frame consisting of the edges in a Hamiltonian cycle on the cube.
I spent about five minutes searching images.google.com and didn't find what I'm looking for, and would appreciate help from any of you who may know about where such things can be found!
Thanks,
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Is there a way to create this surface in Mathematica? Jim On Mon, Jan 4, 2016 at 2:21 PM, Veit Elser <ve10@cornell.edu> wrote:
If you apply Schwarz reflections it extends into the triply periodic “D-surface”:
http://facstaff.susqu.edu/brakke/evolver/examples/periodic/dcell/dcube.8.gif
-Veit
On Jan 4, 2016, at 2:04 PM, James Propp <jamespropp@gmail.com> wrote:
Do any of you know of any pictures (hand-drawn or computer-generated) of the saddle-shaped surface you get when you make a non-planar hexagonal frame consisting of all the edges of a cube that avoid two antipodal vertices an dip it in a soap film solution?
This is not to be confused with the surface you get when you dip a non-planar octagonal frame consisting of the edges in a Hamiltonian cycle on the cube.
I spent about five minutes searching images.google.com and didn't find what I'm looking for, and would appreciate help from any of you who may know about where such things can be found!
Thanks,
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
On Jan 4, 2016, at 12:02 PM, James Propp <jamespropp@gmail.com> wrote:
Is there a way to create this surface in Mathematica?
I happened on this discussion in StackExchange, which may be useful: http://mathematica.stackexchange.com/questions/72203/can-mathematica-solve-p... <http://mathematica.stackexchange.com/questions/72203/can-mathematica-solve-plateaus-problem-finding-a-minimal-surface-with-specifie> —Dan
On Mon, Jan 4, 2016 at 2:21 PM, Veit Elser <ve10@cornell.edu> wrote:
If you apply Schwarz reflections it extends into the triply periodic “D-surface”:
http://facstaff.susqu.edu/brakke/evolver/examples/periodic/dcell/dcube.8.gif
-Veit
On Jan 4, 2016, at 2:04 PM, James Propp <jamespropp@gmail.com> wrote:
Do any of you know of any pictures (hand-drawn or computer-generated) of the saddle-shaped surface you get when you make a non-planar hexagonal frame consisting of all the edges of a cube that avoid two antipodal vertices an dip it in a soap film solution?
This is not to be confused with the surface you get when you dip a non-planar octagonal frame consisting of the edges in a Hamiltonian cycle on the cube.
I spent about five minutes searching images.google.com and didn't find what I'm looking for, and would appreciate help from any of you who may know about where such things can be found!
Thanks,
On Jan 4, 2016, at 3:02 PM, James Propp <jamespropp@gmail.com> wrote:
Is there a way to create this surface in Mathematica?
https://en.wikipedia.org/wiki/Schwarz_minimal_surface gives a good trigonometric approximation that can be rendered with ContourPlot3D. If you need the exact Weierstrass analytic expression, I suggest searching “D-surface” & Weierstrass. -Veit
Jim
On Mon, Jan 4, 2016 at 2:21 PM, Veit Elser <ve10@cornell.edu> wrote:
If you apply Schwarz reflections it extends into the triply periodic “D-surface”:
http://facstaff.susqu.edu/brakke/evolver/examples/periodic/dcell/dcube.8.gif
-Veit
On Jan 4, 2016, at 2:04 PM, James Propp <jamespropp@gmail.com> wrote:
Do any of you know of any pictures (hand-drawn or computer-generated) of the saddle-shaped surface you get when you make a non-planar hexagonal frame consisting of all the edges of a cube that avoid two antipodal vertices an dip it in a soap film solution?
This is not to be confused with the surface you get when you dip a non-planar octagonal frame consisting of the edges in a Hamiltonian cycle on the cube.
I spent about five minutes searching images.google.com and didn't find what I'm looking for, and would appreciate help from any of you who may know about where such things can be found!
Thanks,
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
This one's close; the corners have been rounded: http://www.daviddarling.info/images3/minimum-area_surface.jpg This one's not quite a cube, but is still hexagonal: https://www.pinterest.com/pin/224687468880647570/ On Mon, Jan 4, 2016 at 11:04 AM, James Propp <jamespropp@gmail.com> wrote:
Do any of you know of any pictures (hand-drawn or computer-generated) of the saddle-shaped surface you get when you make a non-planar hexagonal frame consisting of all the edges of a cube that avoid two antipodal vertices an dip it in a soap film solution?
This is not to be confused with the surface you get when you dip a non-planar octagonal frame consisting of the edges in a Hamiltonian cycle on the cube.
I spent about five minutes searching images.google.com and didn't find what I'm looking for, and would appreciate help from any of you who may know about where such things can be found!
Thanks,
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
I think such a surface would likely resemble a monkey saddle, since it seems to have the same symmetry. It's not clear to me that there is a unique minimal surface, or perhaps two congruent ones neither of which include the centroid. But there is software developed by Ken Brakke called the Surface Evolver that is designed to calculate (and draw, with an external drawing program) minimal surfaces with a given boundary, and related optimization problems: http://facstaff.susqu.edu/brakke/evolver/evolver.html <http://facstaff.susqu.edu/brakke/evolver/evolver.html>. —Dan
On Jan 4, 2016, at 11:04 AM, James Propp <jamespropp@gmail.com> wrote:
Do any of you know of any pictures (hand-drawn or computer-generated) of the saddle-shaped surface you get when you make a non-planar hexagonal frame consisting of all the edges of a cube that avoid two antipodal vertices an dip it in a soap film solution?
This is not to be confused with the surface you get when you dip a non-planar octagonal frame consisting of the edges in a Hamiltonian cycle on the cube.
I spent about five minutes searching images.google.com and didn't find what I'm looking for, and would appreciate help from any of you who may know about where such things can be found!
Thanks,
Funny — I e-mailed the message below 21 minutes before another word (that mentions the Stack Exchange discussion). The other one arrived 1 minute after sending it; this one took 32 minutes to arrive. What could explain such a big discrepancy? As far as I know the identical e-addresses were involved in both messages. —Dan
On Jan 4, 2016, at 11:46 AM, Dan Asimov <asimov@msri.org> wrote:
I think such a surface would likely resemble a monkey saddle, since it seems to have the same symmetry.
It's not clear to me that there is a unique minimal surface, or perhaps two congruent ones neither of which include the centroid.
But there is software developed by Ken Brakke called the Surface Evolver that is designed to calculate (and draw, with an external drawing program) minimal surfaces with a given boundary, and related optimization problems:
I've observed that my math-fun submissions sometimes post within a few minutes, sometimes after several hours. -- Gene From: Dan Asimov <asimov@msri.org> To: math-fun <math-fun@mailman.xmission.com> Sent: Monday, January 4, 2016 1:10 PM Subject: [math-fun] E-mail question Funny — I e-mailed the message below 21 minutes before another word (that mentions the Stack Exchange discussion). The other one arrived 1 minute after sending it; this one took 32 minutes to arrive. What could explain such a big discrepancy? As far as I know the identical e-addresses were involved in both messages. —Dan
NSA scratching their heads over the security implications of equestrian primates? WFL On 1/4/16, Eugene Salamin via math-fun <math-fun@mailman.xmission.com> wrote:
I've observed that my math-fun submissions sometimes post within a few minutes, sometimes after several hours.
-- Gene
From: Dan Asimov <asimov@msri.org> To: math-fun <math-fun@mailman.xmission.com> Sent: Monday, January 4, 2016 1:10 PM Subject: [math-fun] E-mail question
Funny — I e-mailed the message below 21 minutes before another word (that mentions the Stack Exchange discussion).
The other one arrived 1 minute after sending it; this one took 32 minutes to arrive.
What could explain such a big discrepancy? As far as I know the identical e-addresses were involved in both messages.
—Dan
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Find one instance of each species; view _all_ headers (not the usual subset presented by default... most email clients will let you do that); and compare delivery paths and times. On 01/04/2016 04:10 PM, Dan Asimov wrote:
Funny — I e-mailed the message below 21 minutes before another word (that mentions the Stack Exchange discussion).
The other one arrived 1 minute after sending it; this one took 32 minutes to arrive.
What could explain such a big discrepancy? As far as I know the identical e-addresses were involved in both messages.
—Dan
The man-in-the-middle was out to lunch. He’s back now.
On Jan 4, 2016, at 7:47 PM, John Aspinall <j@jkmfamily.org> wrote:
Find one instance of each species; view _all_ headers (not the usual subset presented by default... most email clients will let you do that); and compare delivery paths and times.
On 01/04/2016 04:10 PM, Dan Asimov wrote:
Funny — I e-mailed the message below 21 minutes before another word (that mentions the Stack Exchange discussion).
The other one arrived 1 minute after sending it; this one took 32 minutes to arrive.
What could explain such a big discrepancy? As far as I know the identical e-addresses were involved in both messages.
—Dan
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Took a while to reheat the steam kettle, so Mr. Twein could open those envelopes... http://www.military-history.us/2012/12/stasi-museum-leipzig-germany/ Envelope opening machine: http://www.military-history.us/wp-content/uploads/2012/12/IMG_1243-300x225.j... Envelope closing machine: http://www.military-history.us/wp-content/uploads/2012/12/IMG_1242-300x225.j... Envelope backlight to try to read through w/o opening: http://www.military-history.us/wp-content/uploads/2012/12/IMG_1244-300x225.j... At 05:09 PM 1/4/2016, Tom Knight wrote:
The man-in-the-middle was out to lunch.
He's back now.
participants (9)
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Dan Asimov -
Eugene Salamin -
Fred Lunnon -
Henry Baker -
James Propp -
John Aspinall -
Mike Stay -
Tom Knight -
Veit Elser