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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

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

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

BP13 Tall rectangle OR wide ellipse vs. wide rectangle OR tall ellipse.
(edit; present; nest [left/right]; search; history)
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

BP23 One vs. two figures.
(edit; present; nest [left/right]; search; history)
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

BP31 One line vs. two lines.
(edit; present; nest [left/right]; search; history)
REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 224.

CROSSREFS

Adjacent-numbered pages:
BP26 BP27 BP28 BP29 BP30  *  BP32 BP33 BP34 BP35 BP36

KEYWORD

easy, precise, allsorted, left-narrow, right-narrow, pixelperfect, traditional, bongard

CONCEPT distinguishing_crossing_curves (info | search),
one (info | search),
two (info | search)

WORLD

smooth_crosscurves [smaller | same | bigger]

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

BP72 Ends of the curve are parallel vs. ends of the curve are perpendicular.
(edit; present; nest [left/right]; search; history)
REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 237.

CROSSREFS

Adjacent-numbered pages:
BP67 BP68 BP69 BP70 BP71  *  BP73 BP74 BP75 BP76 BP77

KEYWORD

nice, precise, unstable, ignoreimperfections, finished, traditional, bongard

CONCEPT slope_at_endpoint (info | search),
tracing_line_or_curve (info | search),
parallel (info | search),
perpendicular (info | search)

WORLD

curve [smaller | same | bigger]

AUTHOR

Mikhail M. Bongard

BP103 Isosceles triangle vs. scalene triangle.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP98 BP99 BP100 BP101 BP102  *  BP104 BP105 BP106 BP107 BP108

KEYWORD

precise, allsorted, stretch, orderedpair, traditional, preciseworld

CONCEPT line_or_curve_endpoint (info | search),
length_line_or_curve (info | search),
imagined_line_or_curve (info | search),
imagined_entity (info | search),
same_feature (info | search),
same (info | search),
isosceles_triangle (info | search),
triangle (info | search)

AUTHOR

Douglas R. Hofstadter

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