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Robin also found a more complicated formula for the general paper bag, which gives 0.2017, below the bounds given by Kepert (i.e., 0.2055+ ≤ maximum volume ≤ 0.217+).
320:(This latter formula assumes that the corners at the bottom of the bag are linked by a single edge, and that the base of the bag is not a more complex shape such as a
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403:, an upper bound for this version of the teabag problem is 0.217+, and he has made a construction that appears to give a volume of 0.2055+.
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is to calculate the maximum possible inflated volume of an initially flat sealed rectangular bag which has the same shape as a
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310:{\displaystyle V=w^{3}\left(h/\left(\pi w\right)-0.071\left(1-10^{\left(-2h/w\right)}\right)\right)}
166:{\displaystyle V=w^{3}\left(h/\left(\pi w\right)-0.142\left(1-10^{\left(-h/w\right)}\right)\right),}
47:
According to
Anthony C. Robin, an approximate formula for the capacity of a sealed expanded bag is:
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is the maximum volume. The approximation ignores the crimping round the equator of the bag.
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For the special case where the bag is sealed on all edges and is square with unit sides,
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A very rough approximation to the capacity of a bag that is open at one edge is:
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A numerical simulation of an inflated teabag (with crimping smoothed out)
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A numerical approach to the teabag problem by
Andreas Gammel
357:
348:= 1, the first formula estimates a volume of roughly
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Andrew Kepert's work on the teabag problem (mirror)
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399:or roughly 0.19. According to Andrew Kepert at the
389:{\displaystyle V={\frac {1}{\pi }}-0.142\cdot 0.9}
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180:is the width of the bag (the shorter dimension),
460:Robin, Anthony C (2004). "Paper Bag Problem".
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472:Institute of Mathematics and its Applications
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515:The original statement of the teabag problem
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184:is the height (the longer dimension), and
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811:Geometric Exercises in Paper Folding
832:A History of Folding in Mathematics
525:Curved folds for the teabag problem
401:University of Newcastle, Australia
14:
732:Alexandrov's uniqueness theorem
20:A cushion filled with stuffing
1:
670:Regular paperfolding sequence
818:Geometric Folding Algorithms
585:Mathematics of paper folding
995:
868:Margherita Piazzola Beloch
979:Mathematical optimization
639:Yoshizawa–Randlett system
839:Origami Polyhedra Design
422:Mylar balloon (geometry)
629:Napkin folding problem
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789:Fold-and-cut theorem
745:Steffen's polyhedron
609:Huzita–Hatori axioms
599:Big-little-big lemma
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737:Flexible polyhedron
540:"Paper Bag Surface"
918:Toshikazu Kawasaki
741:Bricard octahedron
716:Yoshimura buckling
614:Kawasaki's theorem
537:Weisstein, Eric W.
488:Weisstein, Eric W.
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22:
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825:Geometric Origami
696:Paper bag problem
619:Maekawa's theorem
463:Mathematics Today
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328:The square teabag
30:paper bag problem
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974:Geometric shapes
898:David A. Huffman
863:Roger C. Alperin
766:Source unfolding
634:Pureland origami
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499:. Archived from
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771:Star unfolding
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604:Crease pattern
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509:External links
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503:on 2011-06-29.
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34:teabag problem
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794:Lill's method
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701:Rigid origami
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679:3d structures
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953:Eve Torrence
883:Erik Demaine
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803:Publications
695:
665:Möbius strip
655:Dragon curve
592:Flat folding
543:
501:the original
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938:KĹŤryĹŤ Miura
933:Jun Maekawa
908:KĂ´di Husimi
624:Map folding
491:"Paper Bag"
474:: 104–107.
968:Categories
928:Anna Lubiw
761:Common net
686:Miura fold
454:References
444:Robin 2004
846:Origamics
725:Polyhedra
545:MathWorld
496:MathWorld
480:1361-2042
381:⋅
375:−
370:π
274:−
261:−
247:−
236:π
130:−
117:−
103:−
92:π
903:Tom Hull
873:Yan Chen
756:Blooming
660:Flexagon
416:Biscornu
410:See also
26:geometry
38:cushion
856:People
711:Sonobe
478:
176:where
42:pillow
28:, the
428:Notes
378:0.142
250:0.071
106:0.142
476:ISSN
468:June
322:lens
751:Net
384:0.9
324:).
40:or
32:or
24:In
970::
743:,
542:.
493:.
470:.
466:.
436:^
344:=
265:10
121:10
747:)
739:(
577:e
570:t
563:v
548:.
482:.
446:.
367:1
362:=
359:V
346:w
342:h
304:)
299:)
292:)
288:w
284:/
280:h
277:2
270:(
258:1
254:(
243:)
239:w
232:(
227:/
223:h
219:(
213:3
209:w
205:=
202:V
186:V
182:h
178:w
161:,
157:)
152:)
145:)
141:w
137:/
133:h
126:(
114:1
110:(
99:)
95:w
88:(
83:/
79:h
75:(
69:3
65:w
61:=
58:V
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