Re: [math-fun] Radial disk-dissection
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Subject: [math-fun] Radial disk-dissection Date: 2018-04-13 07:49 From: James Propp <jamespropp@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Reply-To: math-fun <math-fun@mailman.xmission.com>
If you dissect a unit disk radially into a large number of equal wedges, it’s well known that you can reassemble them to form a shape that in the limit converges to a 1-by-pi rectangle.
gosper.org/picfzoom.gif gosper.org/semizoom.gif --rwg I don't see how to get anything other than allowing unequal wedges.
What other limiting shapes can we form in the limit from patterns that join the wedges edge-to-edge?
I’m guessing that you get a class of curvy pseudoquadrilaterals ABCD where AB is a unit segment, CD is a unit segment, and the curves BC and AD satisfy some sort of curvature-compatibility condition.
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
UUDUUDUUDUUD followed by DDUDDUDDUDDU (where U stands for a skinny wedge pointing one way and D stands for a skinny wedge pointing the other way) shows the kind of thing I mean. UDUUDUUUDUUUUD followed by DUDDUDDDUDDDDU shows another. Would a sketch be helpful? Jim On Wednesday, April 18, 2018, Bill Gosper <billgosper@gmail.com> wrote:
-------- Original Message -------
Subject: [math-fun] Radial disk-dissection Date: 2018-04-13 07:49 From: James Propp <jamespropp@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Reply-To: math-fun <math-fun@mailman.xmission.com>
If you dissect a unit disk radially into a large number of equal wedges, it’s well known that you can reassemble them to form a shape that in the limit converges to a 1-by-pi rectangle.
gosper.org/picfzoom.gif gosper.org/semizoom.gif --rwg I don't see how to get anything other than allowing unequal wedges.
What other limiting shapes can we form in the limit from patterns that
join
the wedges edge-to-edge?
I’m guessing that you get a class of curvy pseudoquadrilaterals ABCD where AB is a unit segment, CD is a unit segment, and the curves BC and AD satisfy some sort of curvature-compatibility condition.
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
participants (2)
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Bill Gosper -
James Propp