The On-Line Encyclopedia of Bongard Problems

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Big vs. small.

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	COMMENTS	`The meaning of "big" left intentionally vague. There are various specific ways to define size, such as diameter, minimum distance between points on edge, and size of smallest bounding circle.` `All examples in this Bongard Problem are single simple shapes, either outlines or solid black.` `All examples on the same side are approximately the same size.`
	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 214.`
	CROSSREFS	`Adjacent-numbered pages: BP1 * BP3 BP4 BP5 BP6 BP7`
	KEYWORD	`easy, nice, fuzzy, spectrum, size, stable, finished, traditional, continuous, bongard`
	CONCEPT	`size (info \| search)`
	WORLD	`outline_or_fill_shape [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

Hollow outline vs. filled in solid.

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	COMMENTS	`All examples in this Bongard Problem are single simple shapes.`
	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 214.`
	CROSSREFS	`Adjacent-numbered pages: BP1 BP2 * BP4 BP5 BP6 BP7 BP8`
	KEYWORD	`easy, nice, precise, allsorted, world, gap, finished, traditional, preciseworld, bongard`
	CONCEPT	`outlined_filled (info \| search),` `texture (info \| search)`
	WORLD	`outline_or_fill_shape [smaller \| same \| bigger] zoom in left (shape_outline) \| zoom in right (fill_shape)`
	AUTHOR	`Mikhail M. Bongard`

Convex vs. concave.

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	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`

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`

Vertical axis of symmetry vs. no axis of symmetry.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 230.`
	CROSSREFS	`BP152 is the same solution (with the sides switched), using connected shapes and without black filling.` `BP1206 was created to be a slightly different version of this: "vertical axis of symmetry vs. no vertical axis of symmetry." (That less specific solution fits this Bongard Problem as well.)` `Adjacent-numbered pages: BP45 BP46 BP47 BP48 BP49 * BP51 BP52 BP53 BP54 BP55`
	KEYWORD	`nice, stretch, left-narrow, finished, traditional, bongard`
	CONCEPT	`symmetry_axis (info \| search),` `symmetry (info \| search)`
	WORLD	`curves_and_fill_shapes_separate_drawing [smaller \| same \| bigger]`
	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`

Two of the shapes make tiles along their border lines vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP196 BP197 BP198 BP199 BP200 * BP202 BP203 BP204 BP205 BP206`
	KEYWORD	`noisy, traditional`
	CONCEPT	`rotation_required (info \| search),` `tiling (info \| search),` `imagined_motion (info \| search),` `motion (info \| search)`
	WORLD	`fill_shapes [smaller \| same \| bigger]`
	AUTHOR	`Giuseppe Insana`

One outer outline vs. more than one outer outline.

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	CROSSREFS	`Adjacent-numbered pages: BP317 BP318 BP319 BP320 BP321 * BP323 BP324 BP325 BP326 BP327`
	KEYWORD	`nice, precise, allsorted, traditional`
	CONCEPT	`separated_regions (info \| search),` `interior_exterior (info \| search),` `outer_outline (info \| search),` `recursion (info \| search),` `one (info \| search)`
	WORLD	`nest_shapes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Tessellates the plane vs. does not tessellate the plane.

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	COMMENTS	`EX7152 is an example of a shape than can be stretched in such a way that it no longer tessellates the plane. This is a property that is only exhibited by shapes that tessellate with rotated copies of themselves. - Leo Crabbe, Mar 05 2021`
	CROSSREFS	`Adjacent-numbered pages: BP330 BP331 BP332 BP333 BP334 * BP336 BP337 BP338 BP339 BP340`
	KEYWORD	`nice, stretch, unstable, math, hardsort, creativeexamples, proofsrequired, perfect, pixelperfect, traditional`
	CONCEPT	`infinite_plane (info \| search),` `tessellation (info \| search),` `tiling (info \| search)`
	WORLD	`shape [smaller \| same \| bigger] zoom in left (fill_shape)`
	AUTHOR	`Aaron David Fairbanks`

No two shapes are the same vs. at least two shapes are the same.

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	CROSSREFS	`BP57 is the same solution except all examples have two shapes.` `Adjacent-numbered pages: BP338 BP339 BP340 BP341 BP342 * BP344 BP345 BP346 BP347 BP348`
	KEYWORD	`traditional, collection`
	CONCEPT	`existence (info \| search),` `identical (info \| search),` `same_shape (info \| search),` `same (info \| search),` `two (info \| search)`
	WORLD	`shapes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

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