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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

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

BP15 Closed shape outline vs. non-closed curve.
(edit; present; nest [left/right]; search; history)
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

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

BP45 Outline figure on top of solid black figure vs. black figure on top of outline figure.
(edit; present; nest [left/right]; search; history)
REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 228.

CROSSREFS

Adjacent-numbered pages:
BP40 BP41 BP42 BP43 BP44  *  BP46 BP47 BP48 BP49 BP50

KEYWORD

dual, finished, traditional, viceversa, bongard

CONCEPT 3d_front_back (info | search),
outlined_filled (info | search),
objects_overlap (info | search),
overlap (info | search),
texture (info | search)

AUTHOR

Mikhail M. Bongard

BP98 Triangles vs. quadrangles.
(edit; present; nest [left/right]; search; history)
REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 246.

CROSSREFS

Adjacent-numbered pages:
BP93 BP94 BP95 BP96 BP97  *  BP99 BP100 BP101 BP102 BP103

KEYWORD

easy, nice, noisy, number, finished, traditional, bongard

CONCEPT number (info | search)

AUTHOR

Mikhail M. Bongard

BP157 White background vs. black background.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP152 BP153 BP154 BP155 BP156  *  BP158 BP159 BP160 BP161 BP162

KEYWORD

dual, boundingbox, blackwhite, traditional, bordercontent

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

WORLD

zoom in left (curves_and_fill_shapes_drawing)

AUTHOR

Harry E. Foundalis

BP240 Straight line joining the curve ends does not cut the curve vs. straight line joining the curve ends intersects the curve.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP235 BP236 BP237 BP238 BP239  *  BP241 BP242 BP243 BP244 BP245

KEYWORD

traditional

CONCEPT x-crossing (info | search),
line_or_curve_endpoint (info | search),
imagined_line_or_curve (info | search),
imagined_entity (info | search)

AUTHOR

Matthew J. Howells

BP322 One outer outline vs. more than one outer outline.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP317 BP318 BP319 BP320 BP321  *  BP323 BP324 BP325 BP326 BP327

KEYWORD

nice, precise, allsorted, traditional

CONCEPT separated_regions (info | search),
interior_exterior (info | search),
outer_outline (info | search),
recursion (info | search),
one (info | search)

WORLD

nest_shapes [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP327 Straight line tangent to curve vs. straight line not tangent to curve.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP322 BP323 BP324 BP325 BP326  *  BP328 BP329 BP330 BP331 BP332

KEYWORD

math, traditional

CONCEPT tangent (info | search)

AUTHOR

Aaron David Fairbanks

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