The On-Line Encyclopedia of Bongard Problems

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A sharp projection vs. no sharp projection.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 224.`
	CROSSREFS	`Adjacent-numbered pages: BP27 BP28 BP29 BP30 BP31 * BP33 BP34 BP35 BP36 BP37`
	KEYWORD	`nice, notso, finished, traditional, bongard`
	CONCEPT	`acute (info \| search),` `angle (info \| search),` `cusp (info \| search),` `protrusion (info \| search)`
	WORLD	`shape_outline [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

Acute angle vs. no acute angle.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 224.`
	CROSSREFS	`Adjacent-numbered pages: BP28 BP29 BP30 BP31 BP32 * BP34 BP35 BP36 BP37 BP38`
	KEYWORD	`nice, stretch, finished, traditional, bongard`
	CONCEPT	`acute (info \| search),` `angle (info \| search),` `existence (info \| search)`
	WORLD	`Multiple options: mediumsize_centered_outline [smaller \| same \| bigger], shape_outline [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

Long sides concave vs. long sides convex.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 239.`
	CROSSREFS	`Adjacent-numbered pages: BP71 BP72 BP73 BP74 BP75 * BP77 BP78 BP79 BP80 BP81`
	KEYWORD	`nice, stretch, finished, traditional, viceversa, bongard`
	CONCEPT	`indentation (info \| search),` `size (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

Object thinner at top vs. object thicker at top.

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	CROSSREFS	`Adjacent-numbered pages: BP174 BP175 BP176 BP177 BP178 * BP180 BP181 BP182 BP183 BP184`
	KEYWORD	`traditional`
	CONCEPT	`size_increase_decrease (info \| search),` `downward_upward (info \| search),` `regular_irregular_change (info \| search),` `tracing_line_or_curve (info \| search),` `uppermost_lowermost (info \| search)`
	WORLD	`shape_outline [smaller \| same \| bigger]`
	AUTHOR	`Harry E. Foundalis`

At least one (interior or exterior) right angle vs. no right angle (either interior or exterior).

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	CROSSREFS	`Adjacent-numbered pages: BP299 BP300 BP301 BP302 BP303 * BP305 BP306 BP307 BP308 BP309`
	KEYWORD	`traditional, finishedexamples`
	WORLD	`polygon_outline [smaller \| same \| bigger]`
	AUTHOR	`"Lewis"`

All sides are equal vs. all angles are equal.

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	CROSSREFS	`Adjacent-numbered pages: BP323 BP324 BP325 BP326 BP327 * BP329 BP330 BP331 BP332 BP333`
	KEYWORD	`nice, stretch, left-narrow, right-narrow, traditional, finishedexamples, both`
	CONCEPT	`angle (info \| search),` `length_line_or_curve (info \| search),` `same_feature (info \| search),` `same (info \| search)`
	WORLD	`polygon_outline [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Regular polygon vs. not regular polygon.

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	CROSSREFS	`Adjacent-numbered pages: BP324 BP325 BP326 BP327 BP328 * BP330 BP331 BP332 BP333 BP334`
	KEYWORD	`precise, allsorted, stretch, traditional, finishedexamples, preciseworld`
	CONCEPT	`angle (info \| search),` `same_feature (info \| search),` `same (info \| search)`
	WORLD	`polygon_outline [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Exactly one axis of symmetry vs. either zero or more than one axis of symmetry.

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	CROSSREFS	`Adjacent-numbered pages: BP337 BP338 BP339 BP340 BP341 * BP343 BP344 BP345 BP346 BP347`
	KEYWORD	`traditional, finishedexamples`
	CONCEPT	`exists_one (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search),` `symmetry_axis (info \| search),` `symmetry (info \| search)`
	WORLD	`shape_outline [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Nothing vs. nothing.

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	CROSSREFS	`Adjacent-numbered pages: BP849 BP850 BP851 BP852 BP853 * BP855 BP856 BP857 BP858 BP859`
	KEYWORD	`left-finite, right-finite, left-full, right-full, finished, experimental, funny`
	WORLD	`nothing [same \| bigger] zoom in left (nothing) \| zoom in right (nothing)`
	AUTHOR	`Aaron David Fairbanks`

Polygons where all sides are different lengths vs. Polygons where not all sides are different lengths.

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	COMMENTS	`All examples in this Problem are outlines of convex polygons.` `This is a generalisation of scalene triangles to any polygon.`
	CROSSREFS	`The left side implies the right side of BP329 (regular vs. irregular polygons), but the converse is not true.` `The left side of BP329 implies the right side, but the converse is not true.` `Adjacent-numbered pages: BP919 BP920 BP921 BP922 BP923 * BP925 BP926 BP927 BP928 BP929`
	EXAMPLE	`Any scalene triangle will fit on the left, because no two sides are equal.` `However, any regular polygon will not fit on the left, because all of its sides are equal.` `A random convex polygon will "almost surely" fit on the left.`
	KEYWORD	`nice, stretch, right-narrow, traditional`
	CONCEPT	`all (info \| search)`
	WORLD	`polygon_outline [smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

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