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BP4 Convex vs. concave.
(edit; present; nest [left/right]; search; history)
COMMENTS

All examples in this Problem are outlines of shapes or solid black shapes.

REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 215.

CROSSREFS

BP136 is the same solution (flipped) but with only polygonal outlines and also with extraneous dots distracting from the solution.

Adjacent-numbered pages:
BP1 BP2 BP3  *  BP5 BP6 BP7 BP8 BP9

KEYWORD

easy, nice, precise, unstable, right-narrow, finished, traditional, bongard

CONCEPT concave_convex_angle (info | search)

WORLD

outline_or_fill_shape [smaller | same | bigger]

AUTHOR

Mikhail M. Bongard

BP866 Bongard Problems that admit examples fitting the solution in various creative ways vs. not so.
BP200
BP335
BP344
BP346
BP350
BP351
BP352
BP353
BP354
BP355
BP356
BP357
BP361
BP362
BP372
BP373
BP380
BP548
BP792
BP793
BP796
BP802
BP803
BP805
BP827
BP828
BP829
BP831
BP833
BP834
BP835
BP836
BP843
BP845
BP846

. . .

BP1
BP4
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COMMENTS

Left-sorted Bongard Problems have the keyword "creativeexamples" on the OEBP.

Be encouraged to contribute new interesting examples to Bongard Problems with this keyword.


There is much overlap with the keyword hardsort.



This is what it usually means to say examples fit on (e.g.) the left of a Bongard Problem in various creative ways: there is no (obvious) general method to determine a left-fitting example fits left.


There is a related idea in computability theory: a "non recursively enumerable" property is one that cannot in general be checked by a computer algorithm.

But keep in mind the tag "creativeexamples" is supposed to mean something less formal. For example, it requires no ingenuity for a human being to check when a simple shape is convex or concave (so BP4 is not labelled "creativeexamples"). However, it is not as if we use an algorithm to do this, like a computer. (It is not even clear what an "algorithm" would mean in this context, since it is ambiguous both what class of shapes the Bongard Problem sorts and how that would be encoded into a computer program's input. There are usually many options and ambiguities like this whenever one tries to formalize the content of a Bongard Problem.)

CROSSREFS

Adjacent-numbered pages:
BP861 BP862 BP863 BP864 BP865  *  BP867 BP868 BP869 BP870 BP871

KEYWORD

notso, meta (see left/right), links, keyword

WORLD

bp [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP136 Concave shape vs. convex shape.
(edit; present; nest [left/right]; search; history)
CROSSREFS

BP4 is the same solution (flipped) but without the distracting dots (and also with some shapes filled in black and/or curvy instead of just polygon outlines).

Adjacent-numbered pages:
BP131 BP132 BP133 BP134 BP135  *  BP137 BP138 BP139 BP140 BP141

KEYWORD

noisy, ignoreimperfections, traditional

CONCEPT concave_convex_angle (info | search)

AUTHOR

Douglas R. Hofstadter

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