I fixed the errors at http://math.stackexchange.com/questions/1819928/triangle-dissection-no-share... and found a new solution. http://i.imgur.com/F00ldIl.gif That has 19 internal triangles. Has anyone found new solutions with 7 to 18 triangles? Ed Pegg Jr On Thu, Jun 9, 2016 at 7:56 PM, David Wilson <davidwwilson@comcast.net> wrote:
Or rather, the convex quadrilateral dissection.
-----Original Message----- From: math-fun [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of David Wilson Sent: Thursday, June 09, 2016 6:24 PM To: 'math-fun' Subject: Re: [math-fun] Dissection problem
I'd really be interested in the quadrilateral dissection, since that, I believe, would imply a dissection of any polygon.
-----Original Message----- From: math-fun [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Tom Rokicki Sent: Thursday, June 09, 2016 5:46 PM To: math-fun Subject: Re: [math-fun] Dissection problem
I've managed to solve both.
On Thu, Jun 9, 2016 at 2:42 PM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
I stand well bamboozled! WFL
On 6/9/16, Tom Rokicki <rokicki@gmail.com> wrote:
The second solution looks wrong; it appears there are two small triangles with a shared edge.
What do you mean by "no subtriangles are allowed"?
On Thu, Jun 9, 2016 at 9:57 AM, Ed Pegg Jr <ed@mathpuzzle.com> wrote:
A 16-19-21 triangle can be divided into 5-7-8, 9-15-21, 6-14-16, and 7-13-19, with the 7 edges not touching.
I posted four solutions at
http://math.stackexchange.com/questions/1819928/triangle-dissection- no -shared-edges
On Thu, Jun 9, 2016 at 11:03 AM, Zak Seidov <
math-fun@mailman.xmission.com
> wrote:
> Have a look at my last post in FB: > > >
https://www.facebook.com/zak.seidov/allactivity?privacy_source=activ it y_log&log_filter=cluster_11
> > > Zak > > > >Четверг, 9 июня 2016, 18:45 +03:00 от Tom Rokicki < rokicki@gmail.com>: > > > >And that's why it is a puzzle. > > > >On Thu, Jun 9, 2016 at 8:13 AM, Allan Wechsler < > >acwacw@gmail.com > > wrote: > > > >> It can't be edge-to-edge *anywhere. *I am not seeing how to > >> do this at > all. > >> > >> > >> On Thu, Jun 9, 2016 at 10:58 AM, Veit Elser < > >> ve10@cornell.edu > >> > wrote: > >> > >> > > >> > > On Jun 9, 2016, at 10:34 AM, Fred Lunnon < fred.lunnon@gmail.com > > >> wrote: > >> > > > >> > > Any interior edge is common to two small triangles, > >> > > so all interior sides must be equal in pairs? WFL > >> > > >> > True, the dissection/tiling cannot be edge-to-edge. But > >> > consider a > >> > triangle, and mark one point on each of its edges, always > >> > within the > >> first > >> > half in a clockwise sense. Joining vertices to marked > >> > points on > opposite > >> > edges will form an internal triangle — that is one of the triangles of > >> the > >> > dissection. I’ll leave it to you to find the other three. > >> > > >> > -Veit > >> > _______________________________________________ > >> > math-fun mailing list > >> > math-fun@mailman.xmission.com > >> > https://mailman.xmission.com/cgi-bin/mailman/listinfo/math > >> > -f > >> > un > >> > > >> _______________________________________________ > >> math-fun mailing list > >> math-fun@mailman.xmission.com > >> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-f > >> un > >> > > > > > > > >-- > >-- http://cube20.org/ -- [ < http://golly.sf.net/ >Golly > >link > suppressed; > >ask me why] -- > >_______________________________________________ > >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
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