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BP1 Empty image vs. non-empty image.
(edit; present; nest [left/right]; search; history)
COMMENTS

The first Bongard Problem.

All examples in this Bongard Problem are line drawings (one or more connected figures made up of curved and non-curved lines).

REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 214.

CROSSREFS

Adjacent-numbered pages:
  *  BP2 BP3 BP4 BP5 BP6

EXAMPLE

A circle fits on the right because it is not nothing.

KEYWORD

easy, nice, precise, allsorted, unstable, world, left-narrow, left-finite, left-full, left-null, perfect, pixelperfect, finished, traditional, stableworld, deformstable, bongard

CONCEPT empty (info | search),
existence (info | search),
zero (info | search)

WORLD

zoom in left (blank_image) | zoom in right (curves_drawing)

AUTHOR

Mikhail M. Bongard

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

BP3 Hollow outline vs. filled in solid.
(edit; present; nest [left/right]; search; history)
COMMENTS

All examples in this Bongard Problem are single simple shapes.

REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 214.

CROSSREFS

Adjacent-numbered pages:
BP1 BP2  *  BP4 BP5 BP6 BP7 BP8

KEYWORD

easy, nice, precise, allsorted, world, gap, finished, traditional, preciseworld, bongard

CONCEPT outlined_filled (info | search),
texture (info | search)

WORLD

outline_or_fill_shape [smaller | same | bigger]
zoom in left (shape_outline) | zoom in right (fill_shape)

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

BP5 Is polygon vs. is smooth without straight lines or corners.
(edit; present; nest [left/right]; search; history)
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

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

BP7 Taller than wide vs. wider than tall.
(edit; present; nest [left/right]; search; history)
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.
(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

BP9 Non-wiggly outline vs. wiggly outline.
(edit; present; nest [left/right]; search; history)
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

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

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