[math-fun] 24 sides 25 holes
I've just heard on a Russian YouTube stream (streamed live yesterday) that a polyhedron with 24 sides and 25 holes has been found, instead of the previously known 4095-sided polyhedron with 4096 holes. No picture was shown, unfortunately. Who posed the problem and when? Is a picture of the new solution available? Thanks, Leo
IIRC the "holyhedron" problem (assuming that's the same thing as you're referring to) was broached here on math-fun back in the late 90's, possibly by John Conway, and discussed here for a while (eg the "stella octangula" was ruled out). Then I think Conway and Jade Vinson found the first solution, and perhaps even offered a prize for a simpler one. I too would love to see a picture of a simple solution!
On Mar 19, 2020, at 9:44 PM, Leo Broukhis <leob@mailcom.com> wrote:
I've just heard on a Russian YouTube stream (streamed live yesterday) that a polyhedron with 24 sides and 25 holes has been found, instead of the previously known 4095-sided polyhedron with 4096 holes.
No picture was shown, unfortunately.
Who posed the problem and when? Is a picture of the new solution available?
Thanks, Leo _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Here is more information: https://mathworld.wolfram.com/Holyhedron.html On Fri, Mar 20, 2020 at 12:05 PM Marc LeBrun <mlb@well.com> wrote:
IIRC the "holyhedron" problem (assuming that's the same thing as you're referring to) was broached here on math-fun back in the late 90's, possibly by John Conway, and discussed here for a while (eg the "stella octangula" was ruled out). Then I think Conway and Jade Vinson found the first solution, and perhaps even offered a prize for a simpler one. I too would love to see a picture of a simple solution!
On Mar 19, 2020, at 9:44 PM, Leo Broukhis <leob@mailcom.com> wrote:
I've just heard on a Russian YouTube stream (streamed live yesterday) that a polyhedron with 24 sides and 25 holes has been found, instead of the previously known 4095-sided polyhedron with 4096 holes.
No picture was shown, unfortunately.
Who posed the problem and when? Is a picture of the new solution available?
Thanks, Leo _______________________________________________ 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
Hello Math-Fun, I'm investigating, together with Carole Dubois, a fascinating (for us) sequence: Say the fraction a/b has quotient q and the fraction b/a has quotient r. We want that the set of digits used by a U b has no common element with the set of digits used by q U r. Example 1: 2/3 = 0,6666... (q) 3/2 = 1,5 (r) The sets {2;3} and {0;1;5;6} are disjoint. Example 2: 41/148 = 0,2770270270270... (q) 148/41 = 3,609756097560975... (r) The sets {1;4;8} and {0;2;3;5;6;7;9} are disjoint. We have turned this idea into a draft: https://oeis.org/draft/A333437 Are there strong programmers who could extend our 50-term file? The last two terms have respectively 4 and 6 digits (!): 5412/178596 = 0.03030303030... (q) 178596/5412 = 33 (r) {1;2;4;5;6;7;8;9} vs {0;3} And this: Is this seq infinite? Thank you, Best, É. (and C.)
Example 1: 2/3 = 0,6666... (q) 3/2 = 1,5 (r) The sets {2;3} and {0;1;5;6} are disjoint.
I'll point out that Eric sees a zero in front of the decimal mark as significant. Since of the two divisions one will always have this zero, the terms of his sequence can never have a zero digit. There's a different sequence that sees the zero in front of the decimal mark as insignificant: 2, 3, 5, 6, 8, 4, 11, 40, 12, 400, 22, ...
"I'll point out that Eric sees a zero in front of the decimal mark as significant. Since of the two divisions one will always have this zero, the terms of his sequence can never have a zero digit. There's a different sequence that sees the zero in front of the decimal mark as insignificant: 2, 3, 5, 6, 8, 4, 11, 40, 12, 400, 22, ..." I've persuaded Eric to invest in my version: https://oeis.org/A333480 The question of this sequence being infinite remains, awaiting perhaps an emerging pattern or roadblock as the sequence evolves.
Thanks! In the clip, the problem was formulated as finding a polyhedron with more holes than faces. On Fri, Mar 20, 2020 at 11:06 AM Marc LeBrun <mlb@well.com> wrote:
IIRC the "holyhedron" problem (assuming that's the same thing as you're referring to) was broached here on math-fun back in the late 90's, possibly by John Conway, and discussed here for a while (eg the "stella octangula" was ruled out). Then I think Conway and Jade Vinson found the first solution, and perhaps even offered a prize for a simpler one. I too would love to see a picture of a simple solution!
On Mar 19, 2020, at 9:44 PM, Leo Broukhis <leob@mailcom.com> wrote:
I've just heard on a Russian YouTube stream (streamed live yesterday) that a polyhedron with 24 sides and 25 holes has been found, instead of the previously known 4095-sided polyhedron with 4096 holes.
No picture was shown, unfortunately.
Who posed the problem and when? Is a picture of the new solution available?
Thanks, Leo _______________________________________________ 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
participants (5)
-
Hans Havermann -
James Buddenhagen -
Leo Broukhis -
Marc LeBrun -
Éric Angelini