The On-Line Encyclopedia of Bongard Problems

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BP790

The leftmost two add (as vectors) to the right versus no two add to a third.

(edit; present; nest [left/right]; search; history)

	CROSSREFS	`Adjacent-numbered pages: BP785 BP786 BP787 BP788 BP789 * BP791 BP792 BP793 BP794 BP795`
	KEYWORD	`math, structure, orderedtriplet, traditional`
	CONCEPT	`addition (info \| search),` `2_inputs_1_output (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP34

A large hole vs. a small hole.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 225.`
	CROSSREFS	`Adjacent-numbered pages: BP29 BP30 BP31 BP32 BP33 * BP35 BP36 BP37 BP38 BP39`
	KEYWORD	`spectrum, stable, finished, traditional, bongard`
	CONCEPT	`hole (info \| search),` `size (info \| search),` `texture (info \| search)`
	WORLD	`shape_one_hole [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

BP170

Pi-like shape vs. x-like shape.

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	CROSSREFS	`Adjacent-numbered pages: BP165 BP166 BP167 BP168 BP169 * BP171 BP172 BP173 BP174 BP175`
	KEYWORD	`nice, arbitrary, anticomputer, traditional, blackwhiteinvariant`
	CONCEPT	`specific_shape (info \| search),` `specificity (info \| search)`
	AUTHOR	`Harry E. Foundalis`

BP240

Straight line joining the curve ends does not cut the curve vs. straight line joining the curve ends intersects the curve.

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	CROSSREFS	`Adjacent-numbered pages: BP235 BP236 BP237 BP238 BP239 * BP241 BP242 BP243 BP244 BP245`
	KEYWORD	`traditional`
	CONCEPT	`x-crossing (info \| search),` `line_or_curve_endpoint (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search)`
	AUTHOR	`Matthew J. Howells`

BP992

Concave shapes with concave cavities vs. convex cavities

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	COMMENTS	`All examples in this Problem are solid concave black shapes. In this Problem, the "cavities" of a concave shape are defined to be the convex hull of the shape minus the shape itself. For example, if you take a bite out of the edge of a piece of paper, the piece of paper in your mouth is the cavity of the bitten piece of paper. The idea may be indefinitely extended, considering whether the cavities of the cavities are concave or convex, and so on.`
	CROSSREFS	`Adjacent-numbered pages: BP987 BP988 BP989 BP990 BP991 * BP993 BP994 BP995 BP996 BP997`
	KEYWORD	`nice, precise, perfect, traditional`
	CONCEPT	`recursion_number (info \| search),` `recursion (info \| search)`
	WORLD	`concave_fill_shape [smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

BP5

Is polygon vs. is smooth without straight lines or corners.

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	COMMENTS	`All examples in this Bongard Problem are outlines of shapes.`
	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 215.`
	CROSSREFS	`Adjacent-numbered pages: BP1 BP2 BP3 BP4 * BP6 BP7 BP8 BP9 BP10`
	KEYWORD	`easy, nice, ignoreimperfections, finished, traditional, bongard`
	CONCEPT	`curved_straight (info \| search)`
	WORLD	`shape_outline [smaller \| same \| bigger] zoom in left (polygon_outline)`
	AUTHOR	`Mikhail M. Bongard`

BP1098

Concave shapes whose cavities are similar to the shape vs. concave shape whose cavities are not similar to the shape.

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	COMMENTS	`"I am agnostic on whether to let this world include examples such as EX8932, where pixelation is used, or examples such as suggested by EX8928 similar to the "Topologist's Comb" (link in references) which are not locally path-connected. These two examples were provided by Aaron David Fairbanks." - Jago Collins 28th January 2021`
	REFERENCE	`https://en.wikipedia.org/wiki/Similarity_(geometry)` `https://en.wikipedia.org/wiki/Self-similarity` `https://en.wikipedia.org/wiki/Comb_space`
	CROSSREFS	`Adjacent-numbered pages: BP1093 BP1094 BP1095 BP1096 BP1097 * BP1099 BP1100 BP1101 BP1102 BP1103`
	EXAMPLE	`A circle with a circle cut out of it does not fit left, because with the circle cut out of it, our shape is no longer a circle.`
	KEYWORD	`stub, precise, allsorted, left-narrow, perfect, infinitedetail`
	CONCEPT	`self-reference (info \| search)`
	AUTHOR	`Jago Collins`

BP388

White dot can see (in straight lines) all black points vs. white dot cannot see (in straight lines) all black points.

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	CROSSREFS	`See BP368 for whether ALL points can see all points.` `Adjacent-numbered pages: BP383 BP384 BP385 BP386 BP387 * BP389 BP390 BP391 BP392 BP393`
	KEYWORD	`nice, traditional`
	CONCEPT	`all (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search)`
	WORLD	`fill_shape_white_dot [smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

BP249

Dashed lines form the same shape centered inside vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP244 BP245 BP246 BP247 BP248 * BP250 BP251 BP252 BP253 BP254`
	KEYWORD	`traditional`
	CONCEPT	`inside (info \| search),` `imagined_point (info \| search),` `imagined_entity (info \| search),` `similar_shape (info \| search),` `similar (info \| search),` `curve_texture (info \| search),` `texture (info \| search)`
	AUTHOR	`Andreas Gunnarsson`

BP821

Impossible Bongard Problems vs. possible Bongard Problems.

BP821

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	COMMENTS	`Bongard Problems sorted left have the keyword "impossible" on the OEBP.` `"Impossible Bongard Problem" is a loose term, but it roughly means the Bongard Problem solution idea can't be displayed as an image.` `BP868, the version of this whose examples are images of Bongard Problems (miniproblems), rather than links to pages on the OEBP, is impossible. - Aaron David Fairbanks, Jul 29 2020`
	CROSSREFS	`See overriddensolution for solutions that Bongard Problems can have, but that will not be chosen by a reasonable person as the best solution.` `Adjacent-numbered pages: BP816 BP817 BP818 BP819 BP820 * BP822 BP823 BP824 BP825 BP826`
	KEYWORD	`meta (see left/right), links, keyword, right-self`
	CONCEPT	`impossible (info \| search)`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

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