The On-Line Encyclopedia of Bongard Problems

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BP813

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

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

	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`

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`

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`

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`

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`

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`

BP819

Bongard Problems with solution relating to concept: distance from center vs. Bongard Problem unrelated to this concept.

BP257

BP818

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

	CROSSREFS	`Adjacent-numbered pages: BP814 BP815 BP816 BP817 BP818 * BP820 BP821 BP822 BP823 BP824`
	KEYWORD	`meta (see left/right), links, metaconcept`
	CONCEPT	`This MBP is about BPs that feature concept: "distance_from_center"`
	WORLD	`bp [smaller \| same \| bigger]`

BP820

Shape can be combined with a copy of itself to form a convex shape vs. not so.

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

	CROSSREFS	`For the generalization of this property, see BP991.` `Adjacent-numbered pages: BP815 BP816 BP817 BP818 BP819 * BP821 BP822 BP823 BP824 BP825`
	KEYWORD	`nice, precise, allsorted`
	CONCEPT	`tiling (info \| search)`
	WORLD	`fill_shape [smaller \| same \| bigger] zoom in left`
	AUTHOR	`Isaac Hathaway`

BP821

Impossible Bongard Problems vs. possible Bongard Problems.

BP821

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

	COMMENTS	`Bongard Problems sorted left have the keyword "impossible" on the OEBP.` `"Impossible Bongard Problem" is a loose term, but it roughly means the Bongard Problem solution idea can't be displayed as an image.` `BP868, the version of this whose examples are images of Bongard Problems (miniproblems), rather than links to pages on the OEBP, is impossible. - Aaron David Fairbanks, Jul 29 2020`
	CROSSREFS	`See overriddensolution for solutions that Bongard Problems can have, but that will not be chosen by a reasonable person as the best solution.` `Adjacent-numbered pages: BP816 BP817 BP818 BP819 BP820 * BP822 BP823 BP824 BP825 BP826`
	KEYWORD	`meta (see left/right), links, keyword, right-self`
	CONCEPT	`impossible (info \| search)`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP822

Two drawn polyhedra are duals vs. not so.

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

	CROSSREFS	`Adjacent-numbered pages: BP817 BP818 BP819 BP820 BP821 * BP823 BP824 BP825 BP826 BP827`
	KEYWORD	`math, 3d, unorderedpair`
	AUTHOR	`Aaron David Fairbanks`

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