The On-Line Encyclopedia of Bongard Problems

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Angle divided in half vs. angle not divided in half.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 239.`
	CROSSREFS	`Adjacent-numbered pages: BP72 BP73 BP74 BP75 BP76 * BP78 BP79 BP80 BP81 BP82`
	KEYWORD	`nice, notso, stretch, finished, traditional, bongard`
	CONCEPT	`angle (info \| search),` `half (info \| search),` `same_feature (info \| search),` `same (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

At least one (interior or exterior) right angle vs. no right angle (either interior or exterior).

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	CROSSREFS	`Adjacent-numbered pages: BP299 BP300 BP301 BP302 BP303 * BP305 BP306 BP307 BP308 BP309`
	KEYWORD	`traditional, finishedexamples`
	WORLD	`polygon_outline [smaller \| same \| bigger]`
	AUTHOR	`"Lewis"`

All sides are equal vs. all angles are equal.

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	CROSSREFS	`Adjacent-numbered pages: BP323 BP324 BP325 BP326 BP327 * BP329 BP330 BP331 BP332 BP333`
	KEYWORD	`nice, stretch, left-narrow, right-narrow, traditional, finishedexamples, both`
	CONCEPT	`angle (info \| search),` `length_line_or_curve (info \| search),` `same_feature (info \| search),` `same (info \| search)`
	WORLD	`polygon_outline [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Regular polygon vs. not regular polygon.

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	CROSSREFS	`Adjacent-numbered pages: BP324 BP325 BP326 BP327 BP328 * BP330 BP331 BP332 BP333 BP334`
	KEYWORD	`precise, allsorted, stretch, traditional, finishedexamples, preciseworld`
	CONCEPT	`angle (info \| search),` `same_feature (info \| search),` `same (info \| search)`
	WORLD	`polygon_outline [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Regular star polygon vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP335 BP336 BP337 BP338 BP339 * BP341 BP342 BP343 BP344 BP345`
	KEYWORD	`math, traditional`
	CONCEPT	`tracing_line_or_curve (info \| search),` `vertex_of_meeting_lines (info \| search),` `write_in_single_stroke (info \| search)`
	WORLD	`figure_made_of_segments [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Nothing vs. nothing.

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	CROSSREFS	`Adjacent-numbered pages: BP849 BP850 BP851 BP852 BP853 * BP855 BP856 BP857 BP858 BP859`
	KEYWORD	`left-finite, right-finite, left-full, right-full, finished, experimental, funny`
	WORLD	`nothing [same \| bigger] zoom in left (nothing) \| zoom in right (nothing)`
	AUTHOR	`Aaron David Fairbanks`

Wide angles connected to narrow angles vs. not so.

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	COMMENTS	`Another way to phrase this solution is that right examples can be folded down flat onto one isosceles triangle while left examples cannot.` `All examples in this Problem feature four isosceles triangles connected by corners and/or edges.`
	CROSSREFS	`This was conceived as a false solution for BP898.` `Adjacent-numbered pages: BP892 BP893 BP894 BP895 BP896 * BP898 BP899 BP900 BP901 BP902`
	KEYWORD	`nice, precise, allsorted, notso, traditional, preciseworld`
	CONCEPT	`triangle (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Molly C Klenzak, Aaron David Fairbanks`

Can fold into tetragonal disphenoid ("isosceles tetrahedron") vs. cannot.

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	COMMENTS	`Which two sides are the long sides and which side is the short side, or equivalently which angles are the wider angles and which angle is the narrower angle, is the only relevant information to consider for each triangle. Triangles are all assumed isosceles and congruent to one another.` `All examples in this Problem feature four of these triangles connected by corners and/or edges.`
	CROSSREFS	`BP897 was conceived as a false solution for this.` `Adjacent-numbered pages: BP893 BP894 BP895 BP896 BP897 * BP899 BP900 BP901 BP902 BP903`
	KEYWORD	`hard, precise, allsorted, notso, math, preciseworld`
	CONCEPT	`triangle (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Molly C Klenzak`

Polygons where all sides are different lengths vs. Polygons where not all sides are different lengths.

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	COMMENTS	`All examples in this Problem are outlines of convex polygons.` `This is a generalisation of scalene triangles to any polygon.`
	CROSSREFS	`The left side implies the right side of BP329 (regular vs. irregular polygons), but the converse is not true.` `The left side of BP329 implies the right side, but the converse is not true.` `Adjacent-numbered pages: BP919 BP920 BP921 BP922 BP923 * BP925 BP926 BP927 BP928 BP929`
	EXAMPLE	`Any scalene triangle will fit on the left, because no two sides are equal.` `However, any regular polygon will not fit on the left, because all of its sides are equal.` `A random convex polygon will "almost surely" fit on the left.`
	KEYWORD	`nice, stretch, right-narrow, traditional`
	CONCEPT	`all (info \| search)`
	WORLD	`polygon_outline [smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

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