The On-Line Encyclopedia of Bongard Problems

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Triangle above circle vs. circle above triangle.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 225.`
	CROSSREFS	`Adjacent-numbered pages: BP31 BP32 BP33 BP34 BP35 * BP37 BP38 BP39 BP40 BP41`
	KEYWORD	`spectrum, dual, handed, updown, rotate, finished, orderedpair, traditional, continuous, viceversa, bongard`
	CONCEPT	`above_below (info \| search),` `triangle (info \| search),` `quantity_comparison (info \| search)`
	WORLD	`one_circle_one_eq-tri_small_outlines [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

Triangle larger than circle vs. triangle smaller than circle.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 226.`
	CROSSREFS	`Adjacent-numbered pages: BP33 BP34 BP35 BP36 BP37 * BP39 BP40 BP41 BP42 BP43`
	KEYWORD	`spectrum, finished, orderedpair, traditional, continuous, viceversa, bongard`
	CONCEPT	`size (info \| search),` `triangle (info \| search),` `quantity_comparison (info \| search)`
	WORLD	`one_circle_outline_one_triangle_outline_nest [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

Isosceles triangle vs. scalene triangle.

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	CROSSREFS	`Adjacent-numbered pages: BP98 BP99 BP100 BP101 BP102 * BP104 BP105 BP106 BP107 BP108`
	KEYWORD	`precise, allsorted, stretch, orderedpair, traditional, preciseworld`
	CONCEPT	`line_or_curve_endpoint (info \| search),` `length_line_or_curve (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search),` `same_feature (info \| search),` `same (info \| search),` `isosceles_triangle (info \| search),` `triangle (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

Negative slope vs. positive slope.

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	COMMENTS	`All examples feature a white circle and a black circle. The answer refers to the slope of the line connecting the two circles.` `The coloring of the circles is irrelevant.`
	CROSSREFS	`Adjacent-numbered pages: BP101 BP102 BP103 BP104 BP105 * BP107 BP108 BP109 BP110 BP111`
	KEYWORD	`nice, noisy, dual, handed, rotate, orderedpair, traditional`
	CONCEPT	`positive_negative_slope (info \| search),` `line_slope (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

Line perpendicular to one side of the object vs. line parallel to one side of the object.

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	CROSSREFS	`Adjacent-numbered pages: BP160 BP161 BP162 BP163 BP164 * BP166 BP167 BP168 BP169 BP170`
	KEYWORD	`noisy, orderedpair, traditional`
	CONCEPT	`parallel (info \| search),` `perpendicular (info \| search)`
	AUTHOR	`Harry E. Foundalis`

Small object can glide in the bay vs. small object cannot glide in the bay.

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	CROSSREFS	`Adjacent-numbered pages: BP170 BP171 BP172 BP173 BP174 * BP176 BP177 BP178 BP179 BP180`
	KEYWORD	`orderedpair, traditional`
	CONCEPT	`entrance_exit (info \| search),` `indentation (info \| search),` `rotation_required (info \| search),` `imagined_motion (info \| search),` `motion (info \| search),` `specific_shape (info \| search),` `physically_fitting (info \| search)`
	AUTHOR	`Harry E. Foundalis`

Shape on the right is the convex hull of shape on the left vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP343 BP344 BP345 BP346 BP347 * BP349 BP350 BP351 BP352 BP353`
	KEYWORD	`precise, unstable, perfect, orderedpair, traditional`
	CONCEPT	`convex_hull (info \| search)`
	WORLD	`2_fill_shapes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Lower shape can be used as a tile to build the upper one vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP381 BP382 BP383 BP384 BP385 * BP387 BP388 BP389 BP390 BP391`
	KEYWORD	`nice, precise, allsorted, left-narrow, perfect, pixelperfect, orderedpair, traditional, preciseworld, left-listable, right-listable`
	CONCEPT	`tiling (info \| search)`
	AUTHOR	`Jago Collins`

Black shape is a valid shadow (2D projection) of 3D shape vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP895 BP896 BP897 BP898 BP899 * BP901 BP902 BP903 BP904 BP905`
	KEYWORD	`3d, orderedpair`
	CONCEPT	`3d_solid (info \| search),` `projection (info \| search)`
	AUTHOR	`Leo Crabbe`

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