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BP171 Angle bisectors meet at the incenter vs. perpendicular bisectors meet at the orthocenter.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP166 BP167 BP168 BP169 BP170  *  BP172 BP173 BP174 BP175 BP176

KEYWORD

nice, math, traditional

CONCEPT triangle_incenter (info | search),
triangle_orthocenter (info | search),
triangle (info | search)

AUTHOR

Harry E. Foundalis

BP266 At least one touch or cross point vs. no touch or cross point.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP261 BP262 BP263 BP264 BP265  *  BP267 BP268 BP269 BP270 BP271

CONCEPT x-crossing (info | search),
or (info | search),
existence (info | search),
t-point (info | search)

WORLD

arial_font_centered_symbol [smaller | same | bigger]

AUTHOR

Merse E. Gáspár

BP999 The collection of collections obeys the same rule as the individual collections vs. it does not.
(edit; present; nest [left/right]; search; history)
COMMENTS

Rhetorical question: Where would the collection of left examples of this Bongard Problem be sorted by this Bongard Problem? (The question is whether these examples considered together satisfy the pattern that all the parts do, namely that the whole satisfies the pattern that all the parts do.)

See BP793 and BP1004 for similar paradoxes.

CROSSREFS

See BP1005 for the version about only numerical properties; examples in that BP would be sorted the same way here that they are there.

See BP1003 for a similar idea. Rather than the collection of collections imitating the individual collections, BP1003 is about the total combined collection imitating the individual collections. A picture showing (for example) an odd number of even-numbered groups would be sorted differently by these two BPs.

Also see BP1004, which is likewise about the whole satisfying the same rule as its parts, but there the parts don't themselves have to be collections; there the parts are just plain individual objects. The panels in BP999 (this BP) should be sorted the same way in BP1004.

See BP1002, which is about only visual self-similarity instead of more general conceptual "self-similarity".

Adjacent-numbered pages:
BP994 BP995 BP996 BP997 BP998  *  BP1000 BP1001 BP1002 BP1003 BP1004

KEYWORD

nice, abstract, creativeexamples, left-narrow, rules, miniworlds

CONCEPT recursion (info | search),
self-reference (info | search)

WORLD

[smaller | same | bigger]
zoom in left | zoom in right

AUTHOR

Aaron David Fairbanks

BP219 Parallel curves vs. non-parallel curves.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP214 BP215 BP216 BP217 BP218  *  BP220 BP221 BP222 BP223 BP224

KEYWORD

traditional

CONCEPT all (info | search)

AUTHOR

Giuseppe Insana

BP181 One concavity vs. two concavities.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP176 BP177 BP178 BP179 BP180  *  BP182 BP183 BP184 BP185 BP186

KEYWORD

noisy, traditional

CONCEPT indentation (info | search),
number (info | search),
one (info | search),
two (info | search)

AUTHOR

Harry E. Foundalis

BP1291 Black points are the set of vertices that are some shortest-distance away from some white vertex vs. not so.
(edit; present; nest [left/right]; search; history)
COMMENTS

Left hand examples can be thought of as "graph circles".

CROSSREFS

https://en.wikipedia.org/wiki/Level_structure

Adjacent-numbered pages:
BP1286 BP1287 BP1288 BP1289 BP1290  *  BP1292

KEYWORD

precise, unwordable, notso, left-narrow

CONCEPT graph (info | search)

AUTHOR

Leo Crabbe

BP1219 Blank image (square) vs. image of blank square.
(edit; present; nest [left/right]; search; history)
CROSSREFS

See also BP1056, "blank image vs. nothing".


BP1 is also a (less specific) solution to this.

BP1209 (flipped) is also a (less specific) solution to this.

Adjacent-numbered pages:
BP1214 BP1215 BP1216 BP1217 BP1218  *  BP1220 BP1221 BP1222 BP1223 BP1224

KEYWORD

minimal, gap, left-narrow, right-narrow, left-finite, right-finite, left-full, right-full, left-null, funny, unstableworld

CONCEPT empty (info | search),
square (info | search)

AUTHOR

Aaron David Fairbanks

BP1145 Polygon that can be achieved by folding a square once vs. other polygons.
(edit; present; nest [left/right]; search; history)
COMMENTS

Although it is tempting at first to make a version of this Bongard Problem with the solution "Shape can be achieved by folding a square a finite amount of times vs. other shapes", this alternate Bongard Problem would just amount to having the solution "Convex shape with straight edges vs. concave shape or convex shape with at least one curved edge."

CROSSREFS

Adjacent-numbered pages:
BP1140 BP1141 BP1142 BP1143 BP1144  *  BP1146 BP1147 BP1148 BP1149 BP1150

KEYWORD

precise, notso, stretch, left-narrow, finishedexamples, preciseworld

CONCEPT square (info | search)

AUTHOR

Leo Crabbe

BP43 The vibration amplitude increases from left to right vs. the vibration amplitude decreases from left to right.
(edit; present; nest [left/right]; search; history)
REFERENCE

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

CROSSREFS

Adjacent-numbered pages:
BP38 BP39 BP40 BP41 BP42  *  BP44 BP45 BP46 BP47 BP48

KEYWORD

dual, handed, leftright, finished, traditional, viceversa, bongard

CONCEPT size_increase_decrease (info | search),
horizontal (info | search),
leftward_rightward (info | search),
regular_irregular_change (info | search),
tracing_line_or_curve (info | search),
wave (info | search)

WORLD

wave_horizontal_increase_or_decrease [smaller | same | bigger]

AUTHOR

Mikhail M. Bongard

BP176 Line that connects dots avoiding obstacles is short vs. line that connects dots avoiding obstacles is long.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP171 BP172 BP173 BP174 BP175  *  BP177 BP178 BP179 BP180 BP181

KEYWORD

nice, spectrum, traditional, continuous

CONCEPT length_line_or_curve (info | search),
path (info | search)

AUTHOR

Harry E. Foundalis

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