The On-Line Encyclopedia of Bongard Problems

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A dark circle is closer to the outline circle than to the triangle vs. a dark circle is closer to the triangle than to the outline circle.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 240.`
	CROSSREFS	`Adjacent-numbered pages: BP74 BP75 BP76 BP77 BP78 * BP80 BP81 BP82 BP83 BP84`
	KEYWORD	`spectrum, finished, traditional, continuous, viceversa, bongard`
	CONCEPT	`length_line_or_curve (info \| search),` `near_far (info \| search),` `outlined_filled (info \| search),` `texture (info \| search),` `triangle (info \| search)`
	AUTHOR	`Mikhail M. Bongard`

Points located at the same distances from a cross vs. points located at different distances from a cross.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 240.`
	CROSSREFS	`Adjacent-numbered pages: BP75 BP76 BP77 BP78 BP79 * BP81 BP82 BP83 BP84 BP85`
	KEYWORD	`stretch, finished, traditional, bongard`
	CONCEPT	`length_line_or_curve (info \| search),` `same_feature (info \| search),` `same (info \| search),` `isosceles_triangle (info \| search),` `triangle (info \| search)`
	AUTHOR	`Mikhail M. Bongard`

The convex hull of the crosses forms an equilateral triangle vs. the convex hull of the crosses does not form an equilateral triangle.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 241.`
	CROSSREFS	`Adjacent-numbered pages: BP77 BP78 BP79 BP80 BP81 * BP83 BP84 BP85 BP86 BP87`
	KEYWORD	`noisy, notso, finished, traditional, bongard`
	CONCEPT	`convex_hull (info \| search),` `equilateral_triangle (info \| search),` `triangle (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

Isosceles triangle vs. scalene triangle.

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	CROSSREFS	`Adjacent-numbered pages: BP98 BP99 BP100 BP101 BP102 * BP104 BP105 BP106 BP107 BP108`
	KEYWORD	`precise, allsorted, stretch, orderedpair, traditional, preciseworld`
	CONCEPT	`line_or_curve_endpoint (info \| search),` `length_line_or_curve (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search),` `same_feature (info \| search),` `same (info \| search),` `isosceles_triangle (info \| search),` `triangle (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

Middle shape is a triangle vs. middle shape is not a triangle.

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	CROSSREFS	`Adjacent-numbered pages: BP106 BP107 BP108 BP109 BP110 * BP112 BP113 BP114 BP115 BP116`
	KEYWORD	`traditional`
	CONCEPT	`between (info \| search),` `inside (info \| search),` `triangle (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

Triangle points to center of circle vs. triangle does not point to center of circle.

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	CROSSREFS	`Adjacent-numbered pages: BP112 BP113 BP114 BP115 BP116 * BP118 BP119 BP120 BP121 BP122`
	KEYWORD	`traditional`
	CONCEPT	`between (info \| search),` `on_line_or_curve (info \| search),` `midpoint (info \| search),` `pointing_to (info \| search),` `center_of_circle (info \| search),` `center (info \| search),` `imagined_point (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search),` `triangle_arrow (info \| search),` `triangle (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

Objects below match their "symbols" above, according to one "code" versus objects below match their "symbols" above, according to another "code."

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	COMMENTS	`Circle: VV; square: VΛ; triangle: ΛΛ ; blank: ΛV vs. circle: ΛΛ; square: ΛV; triangle: VV; blank: VΛ.`
	CROSSREFS	`Adjacent-numbered pages: BP116 BP117 BP118 BP119 BP120 * BP122 BP123 BP124 BP125 BP126`
	KEYWORD	`arbitrary, consistentsymbols, traditional`
	CONCEPT	`absence_as_presence (info \| search),` `correspondence (info \| search),` `sides_of_line (info \| search),` `triangle (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

Dots are vertices of a triangle standing on a side vs. dots are vertices of a triangle standing on a vertex.

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	CROSSREFS	`Adjacent-numbered pages: BP127 BP128 BP129 BP130 BP131 * BP133 BP134 BP135 BP136 BP137`
	KEYWORD	`noisy, traditional`
	CONCEPT	`base (info \| search),` `horizontal (info \| search),` `vertex_of_meeting_lines (info \| search),` `triangle (info \| search),` `vertical (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

A shape contains a square if and only if it is a circle vs. a shape contains a square if and only if it is a triangle.

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	CROSSREFS	`Adjacent-numbered pages: BP141 BP142 BP143 BP144 BP145 * BP147 BP148 BP149 BP150 BP151`
	KEYWORD	`traditional`
	CONCEPT	`iff (info \| search),` `inside (info \| search),` `triangle (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

If the circle closest to the cross is removed, the rest form an equilateral triangle vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP146 BP147 BP148 BP149 BP150 * BP152 BP153 BP154 BP155 BP156`
	KEYWORD	`traditional`
	CONCEPT	`correspondence (info \| search),` `length_line_or_curve (info \| search),` `near_far (info \| search),` `number (info \| search),` `mentally_remove_object (info \| search),` `equilateral_triangle (info \| search),` `triangle (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

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