Re: [math-fun] Random slice of a cube
Keith Lynch wrote: ----- ... I would ask, not what the average number of sides is, but the proportion of each number of sides ... ----- And then for each number of sides, its proportion is averaged over all planes (obtained by the 3-points-on-circumsphere method)? Or if not, what? —Dan
Slicing a cube is reasonably easy to visualize, but some of the patterns revealed with a Menger Sponge is sliced are really quite startling. Here's one of many videos presenting this: https://www.youtube.com/watch?v=8pj8_zjelDo On Mon, Oct 9, 2017 at 9:23 AM, Dan Asimov <dasimov@earthlink.net> wrote:
Keith Lynch wrote: ----- ... I would ask, not what the average number of sides is, but the proportion of each number of sides ... -----
And then for each number of sides, its proportion is averaged over all planes (obtained by the 3-points-on-circumsphere method)?
Or if not, what?
—Dan
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- -- http://cube20.org/ -- http://golly.sf.net/ --
Sorry; wrong link; try this one instead: https://www.youtube.com/watch?v=fWsmq9E4YC0 On Mon, Oct 9, 2017 at 9:34 AM, Tomas Rokicki <rokicki@gmail.com> wrote:
Slicing a cube is reasonably easy to visualize, but some of the patterns revealed with a Menger Sponge is sliced are really quite startling.
Here's one of many videos presenting this:
https://www.youtube.com/watch?v=8pj8_zjelDo
On Mon, Oct 9, 2017 at 9:23 AM, Dan Asimov <dasimov@earthlink.net> wrote:
Keith Lynch wrote: ----- ... I would ask, not what the average number of sides is, but the proportion of each number of sides ... -----
And then for each number of sides, its proportion is averaged over all planes (obtained by the 3-points-on-circumsphere method)?
Or if not, what?
—Dan
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- -- http://cube20.org/ -- http://golly.sf.net/ --
-- -- http://cube20.org/ -- http://golly.sf.net/ --
Just to rephrase the problem: Given a "randomly chosen" plane that cuts three or more edges of the unit cube, what is the probability that the plane cuts exactly k of the edges, for k = 3, 4, 5, 6? Jim Propp On Mon, Oct 9, 2017 at 12:35 PM, Tomas Rokicki <rokicki@gmail.com> wrote:
Sorry; wrong link; try this one instead:
https://www.youtube.com/watch?v=fWsmq9E4YC0
On Mon, Oct 9, 2017 at 9:34 AM, Tomas Rokicki <rokicki@gmail.com> wrote:
Slicing a cube is reasonably easy to visualize, but some of the patterns revealed with a Menger Sponge is sliced are really quite startling.
Here's one of many videos presenting this:
https://www.youtube.com/watch?v=8pj8_zjelDo
On Mon, Oct 9, 2017 at 9:23 AM, Dan Asimov <dasimov@earthlink.net> wrote:
Keith Lynch wrote: ----- ... I would ask, not what the average number of sides is, but the proportion of each number of sides ... -----
And then for each number of sides, its proportion is averaged over all planes (obtained by the 3-points-on-circumsphere method)?
Or if not, what?
—Dan
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- -- http://cube20.org/ -- http://golly.sf.net/ --
-- -- http://cube20.org/ -- http://golly.sf.net/ -- _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (3)
-
Dan Asimov -
James Propp -
Tomas Rokicki