The On-Line Encyclopedia of Bongard Problems

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Vertical axis of symmetry vs. no axis of symmetry.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 230.`
	CROSSREFS	`BP152 is the same solution (with the sides switched), using connected shapes and without black filling.` `BP1206 was created to be a slightly different version of this: "vertical axis of symmetry vs. no vertical axis of symmetry." (That less specific solution fits this Bongard Problem as well.)` `Adjacent-numbered pages: BP45 BP46 BP47 BP48 BP49 * BP51 BP52 BP53 BP54 BP55`
	KEYWORD	`nice, stretch, left-narrow, finished, traditional, bongard`
	CONCEPT	`symmetry_axis (info \| search),` `symmetry (info \| search)`
	WORLD	`curves_and_fill_shapes_separate_drawing [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

No axis of symmetry vs. vertical axis of symmetry.

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	CROSSREFS	`BP50 is the same solution (with the sides switched), using multiple shapes and with some shapes filled in black.` `BP1206 is like BP50 but instead of "no axis of symmetry at all" it uses "no vertical axis of symmetry".` `Adjacent-numbered pages: BP147 BP148 BP149 BP150 BP151 * BP153 BP154 BP155 BP156 BP157`
	KEYWORD	`rotate, stretch, traditional`
	CONCEPT	`existence (info \| search),` `symmetry_axis (info \| search),` `symmetry (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

Rotationally symmetric vs. not.

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	COMMENTS	`The rotational symmetry axis is about the center of the object, not the bounding box. Positioning within the bounding box is noise.`
	CROSSREFS	`Adjacent-numbered pages: BP167 BP168 BP169 BP170 BP171 * BP173 BP174 BP175 BP176 BP177`
	KEYWORD	`traditional`
	CONCEPT	`rotational_symmetry (info \| search),` `symmetry (info \| search)`
	AUTHOR	`Harry E. Foundalis`

Axis of symmetry vs. no axis of symmetry.

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	CROSSREFS	`Adjacent-numbered pages: BP260 BP261 BP262 BP263 BP264 * BP266 BP267 BP268 BP269 BP270`
	CONCEPT	`symmetry_axis (info \| search),` `symmetry (info \| search)`
	WORLD	`arial_font_centered_connected_symbol [smaller \| same \| bigger]`
	AUTHOR	`Merse E. Gáspár`

Center of symmetry vs. no center of symmetry.

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	CROSSREFS	`Adjacent-numbered pages: BP264 BP265 BP266 BP267 BP268 * BP270 BP271 BP272 BP273 BP274`
	CONCEPT	`symmetry (info \| search)`
	WORLD	`arial_font_centered_connected_symbol [smaller \| same \| bigger]`
	AUTHOR	`Merse E. Gáspár`

Exactly one axis of symmetry vs. either zero or more than one axis of symmetry.

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	CROSSREFS	`Adjacent-numbered pages: BP337 BP338 BP339 BP340 BP341 * BP343 BP344 BP345 BP346 BP347`
	KEYWORD	`traditional, finishedexamples`
	CONCEPT	`exists_one (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search),` `symmetry_axis (info \| search),` `symmetry (info \| search)`
	WORLD	`shape_outline [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

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

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	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`

Image of a Bongard Problem with solution about a geometrical symmetry (invariance under spatial transformation) vs. not so.

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	COMMENTS	`Every Bongard Problem on the left shows invariance under some transformation in left sub-examples.` `Some Bongard Problems on the right are symmetrical or have sub-examples that are symmetrical.`
	CROSSREFS	`See BP760 for the version with links to pages on the OEBP instead of images of Bongard Problems.` `Adjacent-numbered pages: BP831 BP832 BP833 BP834 BP835 * BP837 BP838 BP839 BP840 BP841`
	KEYWORD	`meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, presentationinvariant`
	CONCEPT	`symmetry (info \| search)`
	WORLD	`boxes_bpimage_three_per_side [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Evokes the idea of symmetry vs. not so.

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	COMMENTS	`Or, perhaps more concretely, "Depiction of object with some symmetry (invariance under transformation) vs. depiction of object with no simple symmetries."`
	CROSSREFS	`Adjacent-numbered pages: BP842 BP843 BP844 BP845 BP846 * BP848 BP849 BP850 BP851 BP852`
	KEYWORD	`nice, fuzzy, abstract, math, concept, collective, dithering`
	CONCEPT	`symmetry (info \| search)`
	AUTHOR	`Leo Crabbe`

Approximately symmetric vs. asymmetric.

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	COMMENTS	`Or, "evokes idea of symmetry (see BP760) vs. not so," which is also a solution for BP847. - Aaron David Fairbanks, Jul 29 2020`
	CROSSREFS	`Adjacent-numbered pages: BP864 BP865 BP866 BP867 BP868 * BP870 BP871 BP872 BP873 BP874`
	KEYWORD	`abstract, spectrum, anticomputer, subjective, concept, perfect`
	CONCEPT	`imperfection_small (info \| search),` `symmetry (info \| search)`
	AUTHOR	`Leo Crabbe`

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