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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

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

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

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

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

BP30 A curve with one self-crossing vs. a curve without a self-crossing.
(edit; present; nest [left/right]; search; history)
REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 223.

CROSSREFS

BP1232 is almost exactly the same, but allowing for multiple curves and multiple self-crossings.

Adjacent-numbered pages:
BP25 BP26 BP27 BP28 BP29  *  BP31 BP32 BP33 BP34 BP35

KEYWORD

nice, finished, traditional, bongard

CONCEPT x-crossing (info | search),
existence (info | search)

WORLD

crosscurve [smaller | same | bigger]
zoom in right (curve_or_outline)

AUTHOR

Mikhail M. Bongard

BP32 A sharp projection vs. no sharp projection.
(edit; present; nest [left/right]; search; history)
REFERENCE

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

CROSSREFS

Adjacent-numbered pages:
BP27 BP28 BP29 BP30 BP31  *  BP33 BP34 BP35 BP36 BP37

KEYWORD

nice, notso, finished, traditional, bongard

CONCEPT acute (info | search),
angle (info | search),
cusp (info | search),
protrusion (info | search)

WORLD

shape_outline [smaller | same | bigger]

AUTHOR

Mikhail M. Bongard

BP33 Acute angle vs. no acute angle.
(edit; present; nest [left/right]; search; history)
REFERENCE

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

CROSSREFS

Adjacent-numbered pages:
BP28 BP29 BP30 BP31 BP32  *  BP34 BP35 BP36 BP37 BP38

KEYWORD

nice, stretch, finished, traditional, bongard

CONCEPT acute (info | search),
angle (info | search),
existence (info | search)

WORLD

Multiple options:
mediumsize_centered_outline [smaller | same | bigger],
shape_outline [smaller | same | bigger]

AUTHOR

Mikhail M. Bongard

BP50 Vertical axis of symmetry vs. no axis of symmetry.
(edit; present; nest [left/right]; search; history)
REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 230.

CROSSREFS

BP152 is the same solution (with the sides switched), using connected shapes and without black filling.

BP1206 was created to be a slightly different version of this: "vertical axis of symmetry vs. no vertical axis of symmetry." (That less specific solution fits this Bongard Problem as well.)

Adjacent-numbered pages:
BP45 BP46 BP47 BP48 BP49  *  BP51 BP52 BP53 BP54 BP55

KEYWORD

nice, stretch, left-narrow, finished, traditional, bongard

CONCEPT symmetry_axis (info | search),
symmetry (info | search)

WORLD

curves_and_fill_shapes_separate_drawing [smaller | same | bigger]

AUTHOR

Mikhail M. Bongard

BP51 Two circles close to each other vs. no two circles close to each other.
(edit; present; nest [left/right]; search; history)
REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 230.

CROSSREFS

Adjacent-numbered pages:
BP46 BP47 BP48 BP49 BP50  *  BP52 BP53 BP54 BP55 BP56

KEYWORD

nice, finished, traditional, bongard

CONCEPT near_far (info | search)

WORLD

four_dot_outlines [smaller | same | bigger]

AUTHOR

Mikhail M. Bongard

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