The On-Line Encyclopedia of Bongard Problems

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BP330

1-D curve vs. 2-D shape.

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

	CROSSREFS	`Adjacent-numbered pages: BP325 BP326 BP327 BP328 BP329 * BP331 BP332 BP333 BP334 BP335`
	KEYWORD	`traditional`
	CONCEPT	`dimensionality (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP331

Image of something 2-D vs. image of something 3-D.

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

	CROSSREFS	`Adjacent-numbered pages: BP326 BP327 BP328 BP329 BP330 * BP332 BP333 BP334 BP335 BP336`
	KEYWORD	`abstract, anticomputer, collective, traditional, dithering`
	CONCEPT	`dimensionality (info \| search),` `3d_solid (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP332

Wireframe drawing of solid vs. drawing of opaque solid.

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

	CROSSREFS	`Adjacent-numbered pages: BP327 BP328 BP329 BP330 BP331 * BP333 BP334 BP335 BP336 BP337`
	KEYWORD	`projectionmatters, contributepairs, traditional`
	AUTHOR	`Aaron David Fairbanks`

BP348

Shape on the right is the convex hull of shape on the left vs. not so.

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

	CROSSREFS	`Adjacent-numbered pages: BP343 BP344 BP345 BP346 BP347 * BP349 BP350 BP351 BP352 BP353`
	KEYWORD	`precise, unstable, perfect, orderedpair, traditional`
	CONCEPT	`convex_hull (info \| search)`
	WORLD	`2_fill_shapes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP363

Counterclockwise along the curve following the arrow vs. clockwise along the curve following the arrow.

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

	CROSSREFS	`Adjacent-numbered pages: BP358 BP359 BP360 BP361 BP362 * BP364 BP365 BP366 BP367 BP368`
	KEYWORD	`easy, nice, dual, handed, leftright, updown, gap, traditional`
	CONCEPT	`arrow (info \| search),` `turn_orientation (info \| search),` `tracing_line_or_curve (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP367

Center of mass within the black area of the shape vs. center of mass out of the black area of the shape.

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

	CROSSREFS	`Adjacent-numbered pages: BP362 BP363 BP364 BP365 BP366 * BP368 BP369 BP370 BP371 BP372`
	KEYWORD	`precise, unstable, physics, perfect, pixelperfect, traditional`
	CONCEPT	`inside (info \| search),` `center_of_mass (info \| search)`
	WORLD	`shape [smaller \| same \| bigger] zoom in left (shape_center_of_mass_falls_inside)`
	AUTHOR	`Aaron David Fairbanks`

BP368

There is a point that can see (in straight lines) all points vs. there is no point that can see (in straight lines) all points.

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

	COMMENTS	`Left examples are called "star domains."`
	CROSSREFS	`See BP388 for whether a distinguished point can see all points.` `Adjacent-numbered pages: BP363 BP364 BP365 BP366 BP367 * BP369 BP370 BP371 BP372 BP373`
	KEYWORD	`nice, precise, unstable, perfect, traditional`
	CONCEPT	`all (info \| search),` `existence (info \| search),` `imagined_point (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search)`
	WORLD	`shape [smaller \| same \| bigger] zoom in left (fill_shape_with_seeing_point)`
	AUTHOR	`Aaron David Fairbanks`

BP369

All points (small white circles) on one figure can be glued together to make the other figure vs. not so.

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

	CROSSREFS	`See BP851 for a version where the figure must stay within the 2D plane and cannot pass through itself while being deformed.` `Adjacent-numbered pages: BP364 BP365 BP366 BP367 BP368 * BP370 BP371 BP372 BP373 BP374`
	KEYWORD	`nice, math, traditional`
	CONCEPT	`topological_transformation (info \| search),` `imagined_motion (info \| search),` `motion (info \| search)`
	WORLD	`zoom in left (figure_made_of_curves_and_quotient_by_hollow_dots)`
	AUTHOR	`Aaron David Fairbanks`

BP389

Loops are entangled (in 3-D) vs. loops can be separated (in 3-D).

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

	CROSSREFS	`Adjacent-numbered pages: BP384 BP385 BP386 BP387 BP388 * BP390 BP391 BP392 BP393 BP394`
	KEYWORD	`nice, precise, allsorted, contributepairs, traditional`
	CONCEPT	`knot (info \| search),` `topological_transformation (info \| search),` `imagined_motion (info \| search),` `motion (info \| search)`
	WORLD	`link_two_knots [smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

BP809

Figures can be transformed into one another by smooth stretching (before and after there are the same crossroad-points; there is a curve connecting points before if and only if there is a curve connecting those points after) vs. not so.

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

	COMMENTS	`Left examples are topologically homeomorphic figures.` `For some examples one can imagine pulling the shape "out of" the 2d square in 3d in order to transform it, and then laying it flat back in the 2d square. See BP810 for the version where this is not allowed.`
	CROSSREFS	`Adjacent-numbered pages: BP804 BP805 BP806 BP807 BP808 * BP810 BP811 BP812 BP813 BP814`
	KEYWORD	`nice, math, unorderedpair, traditional`
	CONCEPT	`topological_transformation (info \| search)`
	WORLD	`two_figures_made_of_curves [smaller \| same \| bigger] zoom in left (two_homeomorphic_figures_made_of_curves)`
	AUTHOR	`Aaron David Fairbanks`

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