The On-Line Encyclopedia of Bongard Problems

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Is polygon vs. is smooth without straight lines or corners.

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	COMMENTS	`All examples in this Bongard Problem are outlines of shapes.`
	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 215.`
	CROSSREFS	`Adjacent-numbered pages: BP1 BP2 BP3 BP4 * BP6 BP7 BP8 BP9 BP10`
	KEYWORD	`easy, nice, ignoreimperfections, finished, traditional, bongard`
	CONCEPT	`curved_straight (info \| search)`
	WORLD	`shape_outline [smaller \| same \| bigger] zoom in left (polygon_outline)`
	AUTHOR	`Mikhail M. Bongard`

Positioned right vs. positioned left.

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	COMMENTS	`Center of shape's x coordinate is higher than zero (where zero is the middle of the picture).` `All examples in this Bongard Problem are small shape outlines.` `This is the first Bongard Problem in which absolute positioning is relevant.` `Shapes close to the middle would be ambiguous.`
	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 216.`
	CROSSREFS	`Adjacent-numbered pages: BP3 BP4 BP5 BP6 BP7 * BP9 BP10 BP11 BP12 BP13`
	KEYWORD	`easy, nice, dual, handed, leftright, boundingbox, finished, traditional, absoluteposition, bongard`
	CONCEPT	`absolute_position (info \| search),` `bounding_box (info \| search),` `coordinate (info \| search),` `left_right (info \| search)`
	WORLD	`small_outline [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

Non-wiggly outline vs. wiggly outline.

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	COMMENTS	`"Wiggly" means a high number of small concavities adjacent to one another all around the outline.` `All examples in this Bongard Problem are shape outlines.` `Shapes with outlines that are only wiggly within partial sections would be ambiguous. Shapes with outlines that have many medium-size concavities would be ambiguous.`
	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 216.`
	CROSSREFS	`Adjacent-numbered pages: BP4 BP5 BP6 BP7 BP8 * BP10 BP11 BP12 BP13 BP14`
	KEYWORD	`easy, nice, fuzzy, stable, world, finished, traditional, bongard`
	CONCEPT	`curve_texture (info \| search),` `texture (info \| search)`
	WORLD	`Multiple options: mediumsize_centered_outline [smaller \| same \| bigger], shape_outline [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`

Thin and elongated vs. compact.

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

	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: BP6 BP7 BP8 BP9 BP10 * BP12 BP13 BP14 BP15 BP16`
	KEYWORD	`nice, fuzzy, spectrum, stretch, stable, world, finished, traditional, bongard`
	CONCEPT	`elongated_compact (info \| search)`
	WORLD	`shape_outline [smaller \| same \| bigger] zoom in left (elongated_outline)`
	AUTHOR	`Mikhail M. Bongard`

Thin elongated convex hull vs. compact convex hull.

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

	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`

Tall rectangle OR wide ellipse vs. wide rectangle OR tall ellipse.

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	COMMENTS	`All examples in this Bongard Problem are outlines of ellipses or rectangles aligned to the x-y-axes.`
	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 218.`
	CROSSREFS	`Adjacent-numbered pages: BP8 BP9 BP10 BP11 BP12 * BP14 BP15 BP16 BP17 BP18`
	KEYWORD	`precise, stretch, finished, traditional, preciseworld, bongard`
	CONCEPT	`or (info \| search),` `horizontal (info \| search),` `line_slope (info \| search),` `vertical (info \| search)`
	WORLD	`rectangle_or_ellipse_outline_axis_aligned [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`

Shape with a reflex corner vs. shape without a reflex corner.

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	COMMENTS	`All examples in this Bongard Problem are outlines of shapes.`
	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 219.`
	CROSSREFS	`Adjacent-numbered pages: BP12 BP13 BP14 BP15 BP16 * BP18 BP19 BP20 BP21 BP22`
	KEYWORD	`finished, traditional, bongard`
	CONCEPT	`acute (info \| search),` `angle (info \| search),` `indentation (info \| search)`
	WORLD	`shape_outline [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

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