The On-Line Encyclopedia of Bongard Problems

Search: subworld:curves_drawing

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Triangle located at the concave side of an arc vs. triangle located at the convex side of an arc.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 238.`
	CROSSREFS	`Adjacent-numbered pages: BP70 BP71 BP72 BP73 BP74 * BP76 BP77 BP78 BP79 BP80`
	KEYWORD	`finished, traditional, bongard`
	CONCEPT	`concave_convex_region (info \| search),` `on_sides_of_curve (info \| search),` `triangle (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

Long sides concave vs. long sides convex.

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

	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 239.`
	CROSSREFS	`Adjacent-numbered pages: BP71 BP72 BP73 BP74 BP75 * BP77 BP78 BP79 BP80 BP81`
	KEYWORD	`nice, stretch, finished, traditional, viceversa, bongard`
	CONCEPT	`indentation (info \| search),` `size (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

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`

Extensions of segments cross at one point vs. extensions of segments do not cross at one point.

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

	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 239.`
	CROSSREFS	`Adjacent-numbered pages: BP73 BP74 BP75 BP76 BP77 * BP79 BP80 BP81 BP82 BP83`
	KEYWORD	`finished, unorderedtriplet, traditional, bongard`
	CONCEPT	`all (info \| search),` `lines_coincide (info \| search),` `imagined_point (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search)`
	WORLD	`three_segments [smaller \| same \| bigger]`
	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.

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

	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`

A circle is inside of a figure made by crosses vs. a circle is outside of figures made by crosses.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 241.`
	CROSSREFS	`Adjacent-numbered pages: BP78 BP79 BP80 BP81 BP82 * BP84 BP85 BP86 BP87 BP88`
	KEYWORD	`finished, traditional, bongard`
	CONCEPT	`convex_hull (info \| search),` `inside (info \| search),` `cluster_of_one (info \| search),` `cluster (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

A small correction will result in a single circle vs. no small correction will result in a single circle.

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

	CROSSREFS	`Adjacent-numbered pages: BP114 BP115 BP116 BP117 BP118 * BP120 BP121 BP122 BP123 BP124`
	KEYWORD	`fuzzy, traditional`
	CONCEPT	`existence (info \| search),` `imperfection_small (info \| search)`
	WORLD	`curves_drawing [smaller \| same \| bigger]`
	AUTHOR	`Douglas R. Hofstadter`

Number of objects is one less than sides of each object vs. number of objects is one more than sides of each object.

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	CROSSREFS	`Adjacent-numbered pages: BP159 BP160 BP161 BP162 BP163 * BP165 BP166 BP167 BP168 BP169`
	KEYWORD	`nice, traditional`
	CONCEPT	`subtraction (info \| search),` `number (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Harry E. Foundalis`

Object thinner at top vs. object thicker at top.

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	CROSSREFS	`Adjacent-numbered pages: BP174 BP175 BP176 BP177 BP178 * BP180 BP181 BP182 BP183 BP184`
	KEYWORD	`traditional`
	CONCEPT	`size_increase_decrease (info \| search),` `downward_upward (info \| search),` `regular_irregular_change (info \| search),` `tracing_line_or_curve (info \| search),` `uppermost_lowermost (info \| search)`
	WORLD	`shape_outline [smaller \| same \| bigger]`
	AUTHOR	`Harry E. Foundalis`

Same curvature close to the middle vs. change of curvature close to the middle.

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

	CROSSREFS	`Adjacent-numbered pages: BP178 BP179 BP180 BP181 BP182 * BP184 BP185 BP186 BP187 BP188`
	KEYWORD	`noisy, traditional`
	CONCEPT	`sides_of_line (info \| search),` `tangent (info \| search),` `imagined_point (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search)`
	WORLD	`curve [smaller \| same \| bigger]`
	AUTHOR	`Harry E. Foundalis`

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