The On-Line Encyclopedia of Bongard Problems

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BP803

Image of Bongard Problem such that rotating by a half-turn leaves the solution invariant versus not so.

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

	CROSSREFS	`Adjacent-numbered pages: BP798 BP799 BP800 BP801 BP802 * BP804 BP805 BP806 BP807 BP808`
	KEYWORD	`nice, meta (see left/right), miniproblems, creativeexamples, presentationmatters, assumesfamiliarity, structure`
	WORLD	`boxes_bpimage_three_per_side [smaller \| same \| bigger] zoom in left (half_turn_invariant_bp_image_3_per_side)`
	AUTHOR	`Aaron David Fairbanks`

BP804

Bongard Problem with solution relating to concept: vertical vs. Bongard Problem unrelated to this concept.

BP7	BP13	BP19	BP65	BP66	BP95
BP116	BP132	BP147	BP192	BP206	BP268
BP270	BP280	BP281	BP1087	BP1206

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

	CROSSREFS	`Adjacent-numbered pages: BP799 BP800 BP801 BP802 BP803 * BP805 BP806 BP807 BP808 BP809`
	KEYWORD	`meta (see left/right), links, metaconcept`
	CONCEPT	`This MBP is about BPs that feature concept: "vertical"`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Harry E. Foundalis`

BP805

Bongard Problem sorts example below on the left versus Bongard Problem sorts example below on the right.

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

	COMMENTS	`See BP372 for the version of this with BPs with black shapes as examples instead of boxes.`
	CROSSREFS	`Adjacent-numbered pages: BP800 BP801 BP802 BP803 BP804 * BP806 BP807 BP808 BP809 BP810`
	KEYWORD	`nice, dual, handed, leftright, creativeexamples, structure, contributepairs, rules`
	CONCEPT	`bongard_problem (info \| search),` `categorization (info \| search),` `choice (info \| search)`
	WORLD	`boxes_bdimage_six_per_side_extra_below_clear_sort [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP806

Image of repeating wallpaper with only 3-fold rotational symmetries versus image of repeating wallpaper with some other symmetries.

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

	COMMENTS	`Left examples have wallpaper symmetry group p3 (a.k.a. 333).`
	CROSSREFS	`Adjacent-numbered pages: BP801 BP802 BP803 BP804 BP805 * BP807 BP808 BP809 BP810 BP811`
	KEYWORD	`nice, math, bordercontent`
	CONCEPT	`rotational_symmetry (info \| search),` `three (info \| search)`
	WORLD	`wallpaper [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP807

Bongard Problem with solution relating to concept: direction vs. Bongard Problem unrelated to this concept.

BP16	BP54	BP55	BP199	BP206	BP208
BP215	BP226	BP234	BP238	BP273	BP274
BP1087

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

	CROSSREFS	`Adjacent-numbered pages: BP802 BP803 BP804 BP805 BP806 * BP808 BP809 BP810 BP811 BP812`
	KEYWORD	`meta (see left/right), links, metaconcept, primitive`
	CONCEPT	`This MBP is about BPs that feature concept: "direction"`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Harry E. Foundalis`

BP808

Bongard Problem with solution relating to concept: flow of liquid vs. Bongard Problem unrelated to this concept.

BP274

BP896

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

	CROSSREFS	`Adjacent-numbered pages: BP803 BP804 BP805 BP806 BP807 * BP809 BP810 BP811 BP812 BP813`
	KEYWORD	`meta (see left/right), links, metaconcept`
	CONCEPT	`This MBP is about BPs that feature concept: "liquid_flow"`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP809

Figures can be transformed into one another by smooth stretching (before and after there are the same crossroad-points; there is a curve connecting points before if and only if there is a curve connecting those points after) vs. not so.

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

	COMMENTS	`Left examples are topologically homeomorphic figures.` `For some examples one can imagine pulling the shape "out of" the 2d square in 3d in order to transform it, and then laying it flat back in the 2d square. See BP810 for the version where this is not allowed.`
	CROSSREFS	`Adjacent-numbered pages: BP804 BP805 BP806 BP807 BP808 * BP810 BP811 BP812 BP813 BP814`
	KEYWORD	`nice, math, unorderedpair, traditional`
	CONCEPT	`topological_transformation (info \| search)`
	WORLD	`two_figures_made_of_curves [smaller \| same \| bigger] zoom in left (two_homeomorphic_figures_made_of_curves)`
	AUTHOR	`Aaron David Fairbanks`

BP810

Figures can be transformed into one another by smooth stretching (intersection points stay constant; paths connecting those points remain), while remaining within the 2d box vs. movement out of the plane required.

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

	CROSSREFS	`All examples here fit left in BP809, a version where the figures are allowed to pass through themselves while being deformed.` `Adjacent-numbered pages: BP805 BP806 BP807 BP808 BP809 * BP811 BP812 BP813 BP814 BP815`
	KEYWORD	`nice, math, unorderedpair, traditional`
	CONCEPT	`topological_transformation (info \| search)`
	WORLD	`two_homeomorphic_figures_made_of_curves [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP811

Archimedean tiling (regular polygons, all vertices look the same) versus two-uniform tiling (regular polygons, two different kinds of vertex).

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

	CROSSREFS	`Adjacent-numbered pages: BP806 BP807 BP808 BP809 BP810 * BP812 BP813 BP814 BP815 BP816`
	KEYWORD	`nice, math`
	CONCEPT	`infinite_plane (info \| search),` `tiling (info \| search),` `symmetry (info \| search)`
	WORLD	`wallpaper_tiling [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP812

Aesthetically pleasing vs. not so.

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

	CROSSREFS	`Adjacent-numbered pages: BP807 BP808 BP809 BP810 BP811 * BP813 BP814 BP815 BP816 BP817`
	KEYWORD	`easy, fuzzy, abstract, notso, stretch, anticomputer, subjective, invalid, experimental, funny, dithering`
	AUTHOR	`Aaron David Fairbanks`

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