EX7152 is an example of a shape than can be stretched in such a way that it no longer tessellates the plane. This is a property that is only exhibited by shapes that tessellate with rotated copies of themselves. - Leo Crabbe, Mar 05 2021

Adjacent-numbered pages:
BP330 BP331 BP332 BP333 BP334  *  BP336 BP337 BP338 BP339 BP340

nice, stretch, unstable, math, hardsort, creativeexamples, proofsrequired, perfect, pixelperfect, traditional

shape [smaller | same | bigger]
zoom in left (fill_shape)

Aaron David Fairbanks

Left examples have the keyword "pixelperfect" on the OEBP.

All examples here are perfect Bongard Problems. That is, subtle imperfections in images are meant to be considered.

When a Problem is tagged with "pixelperfect", users are reminded to make sure they do not upload images such that taking the pixelation into account would affect the sorting of that example. That is, the zoomed-in jagged blocky version of the picture should still fit the solution.

For example, in the examples of BP335, which is about tessellation, the pixels interlock properly.

Stable Bongard Problems are generally pixelperfect.

Adjacent-numbered pages:
BP942 BP943 BP944 BP945 BP946  *  BP948 BP949 BP950 BP951 BP952

meta (see left/right), links, keyword, instruction

perfect_bp [smaller | same | bigger]

Leo Crabbe

Left-sorted Bongard Problems have the keyword "proofsrequired" on the OEBP.

Right-sorted Bongard Problems have the keyword "noproofs" on the OEBP.

For every "noproofs" Bongard Problem there could be made a stricter "proofsrequired" version. This stricter version will be hardsort.

Deciding to make a Bongard Problem noproofs adds subjectivity to the sorting of examples (keyword subjective).

One interpretation of topology (a subject of mathematics -- see https://en.wikipedia.org/wiki/Topology ) is that a topology describes the observability of various properties. (The topological "neighborhoods" of a point are the subsets one could determine the point to be within using a finite number of measurements.) The analogue of restricting to just the cases where a property is observably true (i.e. "proofsrequired") corresponds to taking the topological "interior" of that property.

TO DO: It may be better to split each of these keywords up into two: "left-proofsrequired", "right-proofsrequired", "left-noproofs", "right noproofs".

See keyword hardsort.

Bongard Problems that are left-unknowable or right-unknowable will have to be "noproofs".

Adjacent-numbered pages:
BP1120 BP1121 BP1122 BP1123 BP1124  *  BP1126 BP1127 BP1128 BP1129 BP1130

In "proofsrequired" BP335 (shape tessellates the plane vs. shape does not tessellate the plane), shapes are only put in the Bongard Problem if they are known to tessellate or not to tessellate the plane. A "noproofs" version of this Bongard Problem would instead allow a shape to be put on the right if it was just (subjectively) really hard to find a way of tessellating the plane with it.

meta (see left/right), links, keyword, oebp, instruction

Aaron David Fairbanks