The On-Line Encyclopedia of Bongard Problems

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BP7

Taller than wide vs. wider than tall.

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	COMMENTS	`All examples in this Bongard Problem are oblong connected figures made up of some curves.` `Shapes as tall as they are wide would be ambiguous.`
	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 216.`
	CROSSREFS	`Adjacent-numbered pages: BP2 BP3 BP4 BP5 BP6 * BP8 BP9 BP10 BP11 BP12`
	KEYWORD	`easy, nice, dual, handed, rotate, stretch, finished, traditional, bongard`
	CONCEPT	`horizontal (info \| search),` `line_slope (info \| search),` `vertical (info \| search),` `quantity_comparison (info \| search)`
	WORLD	`Multiple options: figure_made_of_curves [smaller \| same \| bigger], oblong_axis_aligned_figure_made_of_curves [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

BP8

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`

BP16

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`

BP36

Triangle above circle vs. circle above triangle.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 225.`
	CROSSREFS	`Adjacent-numbered pages: BP31 BP32 BP33 BP34 BP35 * BP37 BP38 BP39 BP40 BP41`
	KEYWORD	`spectrum, dual, handed, updown, rotate, finished, orderedpair, traditional, continuous, viceversa, bongard`
	CONCEPT	`above_below (info \| search),` `triangle (info \| search),` `quantity_comparison (info \| search)`
	WORLD	`one_circle_one_eq-tri_small_outlines [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

BP43

The vibration amplitude increases from left to right vs. the vibration amplitude decreases from left to right.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 228.`
	CROSSREFS	`Adjacent-numbered pages: BP38 BP39 BP40 BP41 BP42 * BP44 BP45 BP46 BP47 BP48`
	KEYWORD	`dual, handed, leftright, finished, traditional, viceversa, bongard`
	CONCEPT	`size_increase_decrease (info \| search),` `horizontal (info \| search),` `leftward_rightward (info \| search),` `regular_irregular_change (info \| search),` `tracing_line_or_curve (info \| search),` `wave (info \| search)`
	WORLD	`wave_horizontal_increase_or_decrease [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

BP54

A cross, circle, and triangle arranged counterclockwise vs. a cross, circle, and triangle arranged clockwise.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 231.`
	CROSSREFS	`Adjacent-numbered pages: BP49 BP50 BP51 BP52 BP53 * BP55 BP56 BP57 BP58 BP59`
	KEYWORD	`dual, handed, finished, orderedtriplet, traditional, bongard`
	CONCEPT	`turn_orientation (info \| search),` `rotational_direction (info \| search),` `triangle (info \| search),` `direction (info \| search)`
	AUTHOR	`Mikhail M. Bongard`

BP55

A circle is at the left of the cavity if you look from inside the figure vs. a circle is at the right of the cavity if you look from inside the figure.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 232.`
	CROSSREFS	`Adjacent-numbered pages: BP50 BP51 BP52 BP53 BP54 * BP56 BP57 BP58 BP59 BP60`
	KEYWORD	`dual, handed, finished, traditional, bongard`
	CONCEPT	`indentation (info \| search),` `on_line_or_curve (info \| search),` `separation_of_joined_objects (info \| search),` `tracing_line_or_curve (info \| search),` `rotational_direction (info \| search),` `direction (info \| search)`
	AUTHOR	`Mikhail M. Bongard`

BP63

Shading thicker on the right side vs. shading thicker on the left side.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 234.`
	CROSSREFS	`Adjacent-numbered pages: BP58 BP59 BP60 BP61 BP62 * BP64 BP65 BP66 BP67 BP68`
	KEYWORD	`dual, handed, finished, traditional, viceversa, bongard`
	CONCEPT	`left_right (info \| search),` `curve_texture (info \| search),` `texture (info \| search)`
	AUTHOR	`Mikhail M. Bongard`

BP67

The right branch begins at a higher point than the left branch vs. the right branch begins at a lower point than the left branch.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 236.`
	CROSSREFS	`Adjacent-numbered pages: BP62 BP63 BP64 BP65 BP66 * BP68 BP69 BP70 BP71 BP72`
	KEYWORD	`precise, spectrum, dual, handed, leftright, finished, traditional, continuous, viceversa, bongard`
	CONCEPT	`above_below (info \| search),` `branch_point (info \| search),` `left_right (info \| search),` `on_sides_of_curve (info \| search),` `tracing_line_or_curve (info \| search)`
	WORLD	`curve_tree_one_branch_per_side [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

BP106

Negative slope vs. positive slope.

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	COMMENTS	`All examples feature a white circle and a black circle. The answer refers to the slope of the line connecting the two circles.` `The coloring of the circles is irrelevant.`
	CROSSREFS	`Adjacent-numbered pages: BP101 BP102 BP103 BP104 BP105 * BP107 BP108 BP109 BP110 BP111`
	KEYWORD	`nice, noisy, dual, handed, rotate, orderedpair, traditional`
	CONCEPT	`positive_negative_slope (info \| search),` `line_slope (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

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