The On-Line Encyclopedia of Bongard Problems

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

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

	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`

Curves with at least one crossing vs. curves do not cross.

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

	COMMENTS	`Based on BP30, "curve with exactly one self-crossing vs. curve without a self-crossing". This is just a slightly more general version.`
	CROSSREFS	`Adjacent-numbered pages: BP1227 BP1228 BP1229 BP1230 BP1231 * BP1233 BP1234 BP1235 BP1236 BP1237`
	EXAMPLE	`EX6881`
	KEYWORD	`stub, notso, traditional`
	CONCEPT	`x-crossing (info \| search),` `existence (info \| search)`
	WORLD	`crosscurves [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Different curves cross each other vs. curves only cross themselves (or do not cross at all).

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

	CROSSREFS	`Adjacent-numbered pages: BP1228 BP1229 BP1230 BP1231 BP1232 * BP1234 BP1235 BP1236 BP1237 BP1238`
	KEYWORD	`notso, traditional`
	CONCEPT	`distinguishing_crossing_curves (info \| search),` `x-crossing (info \| search)`
	WORLD	`smooth_crosscurves [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

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