The On-Line Encyclopedia of Bongard Problems

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BP35

The axis of the hole is parallel to the figure axis vs. the axis of the hole is perpendicular to the figure axis.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 225.`
	CROSSREFS	`Adjacent-numbered pages: BP30 BP31 BP32 BP33 BP34 * BP36 BP37 BP38 BP39 BP40`
	KEYWORD	`finished, traditional, bongard`
	CONCEPT	`hole (info \| search),` `line_slope (info \| search),` `same (info \| search),` `texture (info \| search),` `parallel (info \| search),` `perpendicular (info \| search)`
	WORLD	`elongated_shape_one_small_elongated_centered_hole [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

BP50

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`

BP62

Ends of the curve are far apart vs. ends of the curve are close together.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 234.`
	CROSSREFS	`Adjacent-numbered pages: BP57 BP58 BP59 BP60 BP61 * BP63 BP64 BP65 BP66 BP67`
	KEYWORD	`nice, fuzzy, spectrum, stretch, stable, finished, traditional, continuous, bongard`
	CONCEPT	`line_or_curve_endpoint (info \| search),` `near_far (info \| search)`
	WORLD	`curve [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

BP72

Ends of the curve are parallel vs. ends of the curve are perpendicular.

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

	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 237.`
	CROSSREFS	`Adjacent-numbered pages: BP67 BP68 BP69 BP70 BP71 * BP73 BP74 BP75 BP76 BP77`
	KEYWORD	`nice, precise, unstable, ignoreimperfections, finished, traditional, bongard`
	CONCEPT	`slope_at_endpoint (info \| search),` `tracing_line_or_curve (info \| search),` `parallel (info \| search),` `perpendicular (info \| search)`
	WORLD	`curve [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

BP322

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`

BP335

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`

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`

BP391

There exists an edge such that removing it yields two disconnected graphs (i.e., the minimum number of edges whose removal results in two disconnected graphs is 1) vs. the minimum number of edges whose removal results in two disconnected graphs is 2.

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	CROSSREFS	`Adjacent-numbered pages: BP386 BP387 BP388 BP389 BP390 * BP392 BP393 BP394 BP395 BP396`
	KEYWORD	`nice, precise, traditional, preciseworld`
	CONCEPT	`graph (info \| search),` `distinguishing_crossing_curves (info \| search),` `existence (info \| search),` `imagined_shape (info \| search),` `imagined_entity (info \| search)`
	WORLD	`connected_graph [smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

BP533

Contains smaller copy of itself vs. doesn't.

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	CROSSREFS	`Adjacent-numbered pages: BP528 BP529 BP530 BP531 BP532 * BP534 BP535 BP536 BP537 BP538`
	EXAMPLE	`A smaller copy of EX6409 (the black area) can be located within itself, but some of the white space inside it is not retained in this smaller copy.`
	KEYWORD	`perfect, infinitedetail, contributepairs`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	WORLD	`connected_built_from_self_tile_fractals [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP935

Shapes have equal area vs. not so.

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

	CROSSREFS	`Adjacent-numbered pages: BP930 BP931 BP932 BP933 BP934 * BP936 BP937 BP938 BP939 BP940`
	KEYWORD	`nice, precise, allsorted, unstable, left-narrow, perfect, pixelperfect, unorderedpair`
	CONCEPT	`area (info \| search)`
	WORLD	`2_fill_shapes [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

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