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BP2 Big vs. small.
(edit; present; nest [left/right]; search; history)
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

BP4 Convex vs. concave.
(edit; present; nest [left/right]; search; history)
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

BP6 Triangle vs. quadrilateral.
(edit; present; nest [left/right]; search; history)
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

BP8 Positioned right vs. positioned left.
(edit; present; nest [left/right]; search; history)
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

BP10 Approximately triangular outline vs. approximately convex quadrilateral outline.
(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:
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

BP12 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

BP14 All big individual figures vs. all small individual figures.
(edit; present; nest [left/right]; search; history)
COMMENTS

All examples in this Problem show one or more connected figures made up of lines.

Some big shapes and some small shapes would be ambiguous.

REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 218.

CROSSREFS

See BP2 for the same idea using one shape.

Adjacent-numbered pages:
BP9 BP10 BP11 BP12 BP13  *  BP15 BP16 BP17 BP18 BP19

KEYWORD

fuzzy, size, stable, finished, traditional, bongard

CONCEPT all (info | search),
length_line_or_curve (info | search),
size (info | search)

WORLD

curves_drawing [smaller | same | bigger]

AUTHOR

Mikhail M. Bongard

BP16 Clockwise spiraling curve vs. counter-clockwise spiraling curve.
(edit; present; nest [left/right]; search; history)
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

BP18 "Pinched" shape (drastically thinner somewhere in the middle than on the ends) vs. non-pinched shape.
(edit; present; nest [left/right]; search; history)
COMMENTS

All examples in this Bongard Problem are oblong outlines of shapes.

REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 219.

CROSSREFS

Adjacent-numbered pages:
BP13 BP14 BP15 BP16 BP17  *  BP19 BP20 BP21 BP22 BP23

KEYWORD

finished, traditional, bongard

CONCEPT neck_narrowing (info | search)

WORLD

elongated_outline [smaller | same | bigger]

AUTHOR

Mikhail M. Bongard

BP20 Both dots touching same bulb vs. dots on opposite bulbs.
(edit; present; nest [left/right]; search; history)
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

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