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BP1098 Concave shapes whose cavities are similar to the shape vs. concave shape whose cavities are not similar to the shape.
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(edit; present; nest [left/right]; search; history)
COMMENTS

"I am agnostic on whether to let this world include examples such as EX8932, where pixelation is used, or examples such as suggested by EX8928 similar to the "Topologist's Comb" (link in references) which are not locally path-connected. These two examples were provided by Aaron David Fairbanks." - Jago Collins 28th January 2021

REFERENCE

https://en.wikipedia.org/wiki/Similarity_(geometry)

https://en.wikipedia.org/wiki/Self-similarity

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

CROSSREFS

Adjacent-numbered pages:
BP1093 BP1094 BP1095 BP1096 BP1097  *  BP1099 BP1100 BP1101 BP1102 BP1103

EXAMPLE

A circle with a circle cut out of it does not fit left, because with the circle cut out of it, our shape is no longer a circle.

KEYWORD

stub, precise, allsorted, left-narrow, perfect, infinitedetail

CONCEPT self-reference (info | search)

AUTHOR

Jago Collins

BP1137 Constructible Polygon vs. Non-constructible Polygon
(edit; present; nest [left/right]; search; history)
REFERENCE

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


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

CROSSREFS

Adjacent-numbered pages:
BP1132 BP1133 BP1134 BP1135 BP1136  *  BP1138 BP1139 BP1140 BP1141 BP1142

KEYWORD

stub, precise, math, hardsort, proofsrequired, preciseworld

AUTHOR

Jago Collins

BP1206 Vertical axis of symmetry vs. no vertical axis of symmetry.
(edit; present; nest [left/right]; search; history)
COMMENTS

The solution for this Bongard Problem is also a (less specific) solution for BP500, "vertical axis of symmetry vs. no axis of symmetry".

CROSSREFS

BP1207 is the same solution but using the horizontal axis instead of the vertical axis.

BP1215 is the same solution but with the NW/SE diagonal instead of the vertical axis.

Adjacent-numbered pages:
BP1201 BP1202 BP1203 BP1204 BP1205  *  BP1207 BP1208 BP1209 BP1210 BP1211

KEYWORD

stub, notso, stretch, left-narrow, traditional

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

AUTHOR

Aaron David Fairbanks

BP1207 Horizontal axis of symmetry vs. no horizontal axis of symmetry.
(edit; present; nest [left/right]; search; history)
CROSSREFS

BP1206 is the same solution but using the vertical axis instead of the horizontal axis.

BP1215 is the same solution but with the NW/SE diagonal instead of the vertical axis.

Adjacent-numbered pages:
BP1202 BP1203 BP1204 BP1205 BP1206  *  BP1208 BP1209 BP1210 BP1211 BP1212

KEYWORD

stub, notso, stretch, left-narrow, traditional

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

AUTHOR

Aaron David Fairbanks

BP1208 More triangles left than right vs. more triangles right than left.
(edit; present; nest [left/right]; search; history)
COMMENTS

The triangles vary in size in order to make the solution clearly about quantity, not "total mass".

CROSSREFS

Adjacent-numbered pages:
BP1203 BP1204 BP1205 BP1206 BP1207  *  BP1209 BP1210 BP1211 BP1212 BP1213

KEYWORD

stub, precise, spectrum, dual, handed, leftright, traditional

CONCEPT number (info | search),
triangle (info | search),
quantity_comparison (info | search)

AUTHOR

Aaron David Fairbanks

BP1209 Empty square present vs. no square present.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Nearly identical to BP1221, which is the same except non-empty squares are allowed.

See BP24 for "circle present vs. not".

Adjacent-numbered pages:
BP1204 BP1205 BP1206 BP1207 BP1208  *  BP1210 BP1211 BP1212 BP1213 BP1214

KEYWORD

stub, left-narrow, traditional

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

AUTHOR

Aaron David Fairbanks

BP1210 Vertical, horizontal, and both diagonal axes of symmetry vs. not (more specifically, one or fewer axes of symmetry).
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP1205 BP1206 BP1207 BP1208 BP1209  *  BP1211 BP1212 BP1213 BP1214 BP1215

KEYWORD

stub, left-narrow, traditional, blackwhiteinvariant

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

AUTHOR

Aaron David Fairbanks

BP1211 Triangle vs. anything else.
(edit; present; nest [left/right]; search; history)
CROSSREFS

See BP6 for "triangle vs. quadrilateral".

Adjacent-numbered pages:
BP1206 BP1207 BP1208 BP1209 BP1210  *  BP1212 BP1213 BP1214 BP1215 BP1216

KEYWORD

stub, notso, left-narrow, traditional

CONCEPT triangle (info | search)

AUTHOR

Aaron David Fairbanks

BP1213 Axis of symmetry along the NW/SE diagonal vs. axis of symmetry along the NE/SW diagonal
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP1208 BP1209 BP1210 BP1211 BP1212  *  BP1214 BP1215 BP1216 BP1217 BP1218

KEYWORD

stub, dual, handed, leftright, updown, rotate, stretch, left-narrow, right-narrow, traditional, both

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

AUTHOR

Aaron David Fairbanks

BP1214 Left shape is bigger than right shape vs. right shape is bigger than left shape.
(edit; present; nest [left/right]; search; history)
CROSSREFS

BP1217 has the same solution but rotated a quarter-turn counter-clockwise.

Adjacent-numbered pages:
BP1209 BP1210 BP1211 BP1212 BP1213  *  BP1215 BP1216 BP1217 BP1218 BP1219

KEYWORD

stub, dual, handed, leftright, traditional

CONCEPT size (info | search),
quantity_comparison (info | search)

AUTHOR

Aaron David Fairbanks

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