The On-Line Encyclopedia of Bongard Problems

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Thin elongated convex hull vs. compact convex hull.

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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: BP7 BP8 BP9 BP10 BP11 * BP13 BP14 BP15 BP16 BP17`
	KEYWORD	`nice, fuzzy, spectrum, stretch, finished, traditional, bongard`
	CONCEPT	`convex_hull (info \| search),` `elongated_compact (info \| search)`
	WORLD	`shape_outline [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

Closed shape outline vs. non-closed curve.

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	COMMENTS	`All examples in this Bongard Problem are non-self-intersecting curves.`
	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 218.`
	CROSSREFS	`Adjacent-numbered pages: BP10 BP11 BP12 BP13 BP14 * BP16 BP17 BP18 BP19 BP20`
	KEYWORD	`nice, unstable, world, finished, traditional, bongard`
	CONCEPT	`closed_open (info \| search),` `hole (info \| search),` `loop (info \| search)`
	WORLD	`curve_or_outline [smaller \| same \| bigger] zoom in left (shape_outline) \| zoom in right (curve)`
	AUTHOR	`Mikhail M. Bongard`

Clockwise spiraling curve vs. counter-clockwise spiraling curve.

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	COMMENTS	`All examples in this Bongard Problem are non-self-intersecting spiraling curves, perhaps wiggly, perhaps with corners.`
	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 219.`
	CROSSREFS	`Adjacent-numbered pages: BP11 BP12 BP13 BP14 BP15 * BP17 BP18 BP19 BP20 BP21`
	KEYWORD	`nice, handed, gap, finished, traditional, bongard`
	CONCEPT	`turn_orientation (info \| search),` `tracing_line_or_curve (info \| search),` `rotational_direction (info \| search),` `direction (info \| search)`
	WORLD	`spiral [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

Both dots touching same bulb vs. dots on opposite bulbs.

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	COMMENTS	`All examples in this Bongard Problem are outlines of smooth shapes with a pinch in the middle and with two tiny black circles attached to the outside of the shape (tangent).` `A shape with either dot tangent to the the valley section would be ambiguous.`
	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 220.`
	CROSSREFS	`Adjacent-numbered pages: BP15 BP16 BP17 BP18 BP19 * BP21 BP22 BP23 BP24 BP25`
	KEYWORD	`nice, finished, traditional, bongard`
	CONCEPT	`near_far (info \| search),` `neck_narrowing (info \| search),` `separation_of_joined_objects (info \| search)`
	AUTHOR	`Mikhail M. Bongard`

One vs. two figures.

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	COMMENTS	`All examples in this Problem comprise one or two shape outlines.`
	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 221.`
	CROSSREFS	`Adjacent-numbered pages: BP18 BP19 BP20 BP21 BP22 * BP24 BP25 BP26 BP27 BP28`
	KEYWORD	`easy, nice, precise, number, world, gap, finished, traditional, bongard`
	CONCEPT	`number (info \| search),` `one (info \| search),` `two (info \| search)`
	WORLD	`outlines [smaller \| same \| bigger] zoom in left (shape_outline) \| zoom in right (two_outlines)`
	AUTHOR	`Mikhail M. Bongard`

A curve with one self-crossing vs. a curve without a self-crossing.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 223.`
	CROSSREFS	`BP1232 is almost exactly the same, but allowing for multiple curves and multiple self-crossings.` `Adjacent-numbered pages: BP25 BP26 BP27 BP28 BP29 * BP31 BP32 BP33 BP34 BP35`
	KEYWORD	`nice, finished, traditional, bongard`
	CONCEPT	`x-crossing (info \| search),` `existence (info \| search)`
	WORLD	`crosscurve [smaller \| same \| bigger] zoom in right (curve_or_outline)`
	AUTHOR	`Mikhail M. Bongard`

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`

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`

Two circles close to each other vs. no two circles close to each other.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 230.`
	CROSSREFS	`Adjacent-numbered pages: BP46 BP47 BP48 BP49 BP50 * BP52 BP53 BP54 BP55 BP56`
	KEYWORD	`nice, finished, traditional, bongard`
	CONCEPT	`near_far (info \| search)`
	WORLD	`four_dot_outlines [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

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