The On-Line Encyclopedia of Bongard Problems

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Triangle vs. quadrilateral.

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	COMMENTS	`All examples in this Problem are outlines of polygons or solid black polygons.`
	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 215.`
	CROSSREFS	`BP1211 is "triangle vs. anything else".` `Adjacent-numbered pages: BP1 BP2 BP3 BP4 BP5 * BP7 BP8 BP9 BP10 BP11`
	KEYWORD	`easy, nice, precise, number, ignoreimperfections, finished, traditional, preciseworld, bongard`
	CONCEPT	`number (info \| search),` `triangle (info \| search),` `three (info \| search),` `four (info \| search)`
	WORLD	`Multiple options: polygon_outline_or_fill [smaller \| same \| bigger], triangle_or_quadrilateral_outline_or_fill [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

Approximately triangular outline vs. approximately convex quadrilateral outline.

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	COMMENTS	`All examples in this Bongard Problem are shape outlines.`
	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 217.`
	CROSSREFS	`Adjacent-numbered pages: BP5 BP6 BP7 BP8 BP9 * BP11 BP12 BP13 BP14 BP15`
	KEYWORD	`easy, fuzzy, noisy, number, finished, traditional, bongard`
	CONCEPT	`number (info \| search),` `three (info \| search),` `four (info \| search)`
	WORLD	`shape_outline [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

Three points on a straight line vs. no three points on a straight line.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 227.`
	CROSSREFS	`Adjacent-numbered pages: BP35 BP36 BP37 BP38 BP39 * BP41 BP42 BP43 BP44 BP45`
	KEYWORD	`noisy, finished, traditional, bongard`
	CONCEPT	`collinear (info \| search),` `three (info \| search),` `four (info \| search)`
	WORLD	`four_dots [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

Four parts vs. five parts.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 242.`
	CROSSREFS	`Adjacent-numbered pages: BP82 BP83 BP84 BP85 BP86 * BP88 BP89 BP90 BP91 BP92`
	KEYWORD	`number, finished, traditional, bongard`
	CONCEPT	`number (info \| search),` `four (info \| search),` `five (info \| search)`
	AUTHOR	`Mikhail M. Bongard`

Three parts vs. four parts.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 243.`
	CROSSREFS	`Adjacent-numbered pages: BP85 BP86 BP87 BP88 BP89 * BP91 BP92 BP93 BP94 BP95`
	KEYWORD	`number, finished, traditional, bongard`
	CONCEPT	`number (info \| search),` `outlined_filled (info \| search),` `separation_of_joined_objects (info \| search),` `feature_cluster (info \| search),` `cluster_of_one (info \| search),` `cluster (info \| search),` `texture (info \| search),` `three (info \| search),` `four (info \| search)`
	AUTHOR	`Mikhail M. Bongard`

Three identical elements vs. four identical elements.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 244.`
	CROSSREFS	`BP1226 is "three identical elements vs. other number of identical elements".` `Adjacent-numbered pages: BP86 BP87 BP88 BP89 BP90 * BP92 BP93 BP94 BP95 BP96`
	KEYWORD	`number, ignoreimperfections, finished, traditional, bongard`
	CONCEPT	`indentation (info \| search),` `on_line_or_curve (info \| search),` `number (info \| search),` `protrusion (info \| search),` `separation_of_joined_objects (info \| search),` `same (info \| search),` `three (info \| search),` `four (info \| search)`
	WORLD	`curves_and_fill_shapes_drawing [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

Different ways of grouping yield same 4-1 split vs. different ways of grouping yield different 4-1 splits.

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	CROSSREFS	`Adjacent-numbered pages: BP140 BP141 BP142 BP143 BP144 * BP146 BP147 BP148 BP149 BP150`
	KEYWORD	`traditional, miniworlds`
	CONCEPT	`and (info \| search),` `number (info \| search),` `feature_cluster (info \| search),` `cluster (info \| search),` `same_shape (info \| search),` `same (info \| search),` `similar_shape (info \| search),` `similar (info \| search),` `one (info \| search),` `four (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

5 collinear objects, of which the 3rd is moved elsewhere vs. 5 collinear objects, of which the 2nd/4th is moved elsewhere.

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	CROSSREFS	`Adjacent-numbered pages: BP297 BP298 BP299 BP300 BP301 * BP303 BP304 BP305 BP306 BP307`
	KEYWORD	`traditional`
	CONCEPT	`collinear (info \| search),` `ordinal_orering (info \| search),` `two (info \| search),` `three (info \| search),` `four (info \| search),` `five (info \| search)`
	AUTHOR	`"Lewis"`

Vertical, horizontal, and both diagonal axes of symmetry vs. not (more specifically, one or fewer axes of symmetry).

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	CROSSREFS	`Adjacent-numbered pages: BP1205 BP1206 BP1207 BP1208 BP1209 * BP1211 BP1212 BP1213 BP1214 BP1215`
	KEYWORD	`stub, left-narrow, traditional`
	CONCEPT	`symmetry_axis (info \| search),` `symmetry (info \| search),` `four (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

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