The On-Line Encyclopedia of Bongard Problems

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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`

BP810

Figures can be transformed into one another by smooth stretching (intersection points stay constant; paths connecting those points remain), while remaining within the 2d box vs. movement out of the plane required.

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

	CROSSREFS	`All examples here fit left in BP809, a version where the figures are allowed to pass through themselves while being deformed.` `Adjacent-numbered pages: BP805 BP806 BP807 BP808 BP809 * BP811 BP812 BP813 BP814 BP815`
	KEYWORD	`nice, math, unorderedpair, traditional`
	CONCEPT	`topological_transformation (info \| search)`
	WORLD	`two_homeomorphic_figures_made_of_curves [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

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