Colin Wright (e.g., *Colin Wright*: The Mathematics of *Juggling* on Vimeo<http://vimeo.com/27998521> ) posed this at G4GX (and G9?): Dissect a disk into congruent parts at least one of which avoids the center by a positive distance. Neil just beat me to a solution. Grr. --rwg
What a great problem! I was still working through the first few minutes of "but... how... isn't..." when Jessica said "Okay, how about this?..." and solved it. But is there more than one solution? I know about the answer depicted in http://i.imgur.com/iOfRI.png, but is that unique? --Michael On Wed, Apr 18, 2012 at 10:50 PM, Bill Gosper <billgosper@gmail.com> wrote:
Colin Wright (e.g., *Colin Wright*: The Mathematics of *Juggling* on Vimeo<http://vimeo.com/27998521> )
posed this at G4GX (and G9?): Dissect a disk into congruent parts
at least one of which avoids the center by a positive distance. Neil
just beat me to a solution. Grr.
--rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Forewarned is worth an octopus in the bush.
On Thu, Apr 19, 2012 at 1:08 PM, Michael Kleber <michael.kleber@gmail.com>wrote:
What a great problem! I was still working through the first few minutes of "but... how... isn't..." when Jessica said "Okay, how about this?..." and solved it.
But is there more than one solution? I know about the answer depicted in http://i.imgur.com/iOfRI.png, but is that unique?
Ah: it's not unique, in that there are solutions like http://i.imgur.com/bxtbB.png as well. Are there any solutions that aren't a refinement of the basic dissection you get by gluing together pairs of pieces from either of the images above, though? That seems like it might be provable. --Michael
On Wed, Apr 18, 2012 at 10:50 PM, Bill Gosper <billgosper@gmail.com>wrote:
Colin Wright (e.g., *Colin Wright*: The Mathematics of *Juggling* on Vimeo<http://vimeo.com/27998521> )
posed this at G4GX (and G9?): Dissect a disk into congruent parts
at least one of which avoids the center by a positive distance. Neil
just beat me to a solution. Grr.
--rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Forewarned is worth an octopus in the bush.
-- Forewarned is worth an octopus in the bush.
Variation: Dissect a disk into congruent pieces, so that a small region around the center is within one of the pieces. -- Rich --- Quoting Michael Kleber <michael.kleber@gmail.com>:
What a great problem! I was still working through the first few minutes of "but... how... isn't..." when Jessica said "Okay, how about this?..." and solved it.
But is there more than one solution? I know about the answer depicted in http://i.imgur.com/iOfRI.png, but is that unique?
--Michael
On Wed, Apr 18, 2012 at 10:50 PM, Bill Gosper <billgosper@gmail.com> wrote:
Colin Wright (e.g., *Colin Wright*: The Mathematics of *Juggling* on Vimeo<http://vimeo.com/27998521> )
posed this at G4GX (and G9?): Dissect a disk into congruent parts
at least one of which avoids the center by a positive distance. Neil
just beat me to a solution. Grr.
--rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Forewarned is worth an octopus in the bush. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Do you know this is possible? --Michael On Apr 29, 2012 8:56 PM, <rcs@xmission.com> wrote:
Variation: Dissect a disk into congruent pieces, so that a small region around the center is within one of the pieces. -- Rich
--- Quoting Michael Kleber <michael.kleber@gmail.com>:
What a great problem! I was still working through the first few minutes
of "but... how... isn't..." when Jessica said "Okay, how about this?..." and solved it.
But is there more than one solution? I know about the answer depicted in http://i.imgur.com/iOfRI.png, but is that unique?
--Michael
On Wed, Apr 18, 2012 at 10:50 PM, Bill Gosper <billgosper@gmail.com> wrote:
Colin Wright (e.g.,
*Colin Wright*: The Mathematics of *Juggling* on Vimeo<http://vimeo.com/**27998521 <http://vimeo.com/27998521>> )
posed this at G4GX (and G9?): Dissect a disk into congruent parts
at least one of which avoids the center by a positive distance. Neil
just beat me to a solution. Grr.
--rwg ______________________________**_________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/**cgi-bin/mailman/listinfo/math-**fun<http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun>
-- Forewarned is worth an octopus in the bush. ______________________________**_________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/**cgi-bin/mailman/listinfo/math-**fun<http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun>
______________________________**_________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/**cgi-bin/mailman/listinfo/math-**fun<http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun>
I don't know a solution. There might be something with gluing together pieces from the original puzzle. It stikes me as an interesting local-global problem, in that the boundary of the shape might affect what's possible in the center. Rich --- Quoting Michael Kleber <michael.kleber@gmail.com>:
Do you know this is possible?
--Michael On Apr 29, 2012 8:56 PM, <rcs@xmission.com> wrote:
Variation: Dissect a disk into congruent pieces, so that a small region around the center is within one of the pieces. -- Rich
--- Quoting Michael Kleber <michael.kleber@gmail.com>:
What a great problem! I was still working through the first few minutes
of "but... how... isn't..." when Jessica said "Okay, how about this?..." and solved it.
But is there more than one solution? I know about the answer depicted in http://i.imgur.com/iOfRI.png, but is that unique?
--Michael
On Wed, Apr 18, 2012 at 10:50 PM, Bill Gosper <billgosper@gmail.com> wrote:
Colin Wright (e.g.,
*Colin Wright*: The Mathematics of *Juggling* on Vimeo<http://vimeo.com/**27998521 <http://vimeo.com/27998521>> )
posed this at G4GX (and G9?): Dissect a disk into congruent parts
at least one of which avoids the center by a positive distance. Neil
just beat me to a solution. Grr.
--rwg ______________________________**_________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/**cgi-bin/mailman/listinfo/math-**fun<http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun>
-- Forewarned is worth an octopus in the bush. ______________________________**_________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/**cgi-bin/mailman/listinfo/math-**fun<http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun>
______________________________**_________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/**cgi-bin/mailman/listinfo/math-**fun<http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun>
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (3)
-
Bill Gosper -
Michael Kleber -
rcs＠xmission.com