The On-Line Encyclopedia of Bongard Problems

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BP818

Dot's position within square is center of square's position within panel vs. not so.

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

	COMMENTS	`All examples in this problem are dots inside square outlines.`
	CROSSREFS	`Similar to BP1122 (the "fractal" version).` `Adjacent-numbered pages: BP813 BP814 BP815 BP816 BP817 * BP819 BP820 BP821 BP822 BP823`
	KEYWORD	`nice, notso, boundingbox, absoluteposition`
	CONCEPT	`bounding_box (info \| search),` `self-reference (info \| search),` `center (info \| search),` `distance_from_center (info \| search)`
	WORLD	`point_inside_square [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP817

Bongard Problems with solution relating to concept: cross section vs. Bongard Problem unrelated to this concept.

BP559

BP816

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

	COMMENTS	`Bongard Problems with solutions related to cross sections of 3D shapes.`
	CROSSREFS	`Adjacent-numbered pages: BP812 BP813 BP814 BP815 BP816 * BP818 BP819 BP820 BP821 BP822`
	KEYWORD	`meta (see left/right), links, metaconcept`
	CONCEPT	`This MBP is about BPs that feature concept: "cross_section"`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP816

Cross section of a cylinder vs. not cross section of a cylinder

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

	CROSSREFS	`Adjacent-numbered pages: BP811 BP812 BP813 BP814 BP815 * BP817 BP818 BP819 BP820 BP821`
	KEYWORD	`precise, notso, stretch, unstable, perfect`
	CONCEPT	`cross_section (info \| search)`
	WORLD	`fill_shapes [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP815

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

BP148

BP218

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

	CROSSREFS	`See BP668.` `Adjacent-numbered pages: BP810 BP811 BP812 BP813 BP814 * BP816 BP817 BP818 BP819 BP820`
	KEYWORD	`meta (see left/right), links, metaconcept`
	CONCEPT	`This MBP is about BPs that feature concept: "extra_part"`
	AUTHOR	`Harry E. Foundalis`

BP814

Bongard Problems with solution "object features concept: ___" vs. other BP pages.

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

	COMMENTS	`Left examples have the keyword "concept" on the OEBP.` `Each concept has a corresponding metaconcept page, which describes that concept and catalogues Bongard Problems featuring that concept.`
	CROSSREFS	`Adjacent-numbered pages: BP809 BP810 BP811 BP812 BP813 * BP815 BP816 BP817 BP818 BP819`
	KEYWORD	`meta (see left/right), links, keyword`
	WORLD	`bppage [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP813

Representations of natural mathematical objects vs. representations of arbitrary objects.

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	COMMENTS	`This is a very fuzzy definition. Some left examples arguably should be placed on the right, since the particular way they are represented is arbitrary--the Platonic solids EX6730 and primes EX6734 especially, as these show arbitrary placement and arrangement of objects. Furthermore if arbitrary representations are allowed one cannot be sure for example the right hand drawing of random numbers EX6740 does not represent "numbers" in general. Still this Bongard Problem has been solved by people.`
	CROSSREFS	`Adjacent-numbered pages: BP808 BP809 BP810 BP811 BP812 * BP814 BP815 BP816 BP817 BP818`
	KEYWORD	`fuzzy, abstract, stretch, math, solved, collective, experimental, dithering`
	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`

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`

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`

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`

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