Search: supworld:planar_connected_graph
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| BP562 |
| There exists a closed trail that hits each vertex exactly once vs. not so. |
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| BP576 |
| Vertices may be partitioned into two sets such that no two vertices in the same set are connected versus not so. |
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| BP788 |
| Graph contains a "loop" a.k.a. cycle (cyclic) versus graph is acyclic. |
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| BP867 |
| Bongard Problem with solution that can be naturally expressed as "___ vs. not so" vs. not so. |
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 |  | Qat | blimp | notso |
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COMMENTS
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Left-sorted BPs have the keyword "notso" on the OEBP.
This meta Bongard Problem is about Bongard Problems featuring two rules that are conceptual opposites.
Sometimes both sides could be seen as the "not" side: consider, for example, two definitions of the same Bongard Problem, "shape has hole vs. does not" and "shape is not filled vs. is". It is possible (albeit perhaps unnatural) to phrase the solution either way when the left and right sides partition all possible relevant examples cleanly into two groups (see the allsorted keyword).
When one property is "positive-seeming" and its opposite is "negative-seeming", it usually means the positive property would be recognized without counter-examples (e.g. a collection of triangles will be seen as such), while the negative property wouldn't be recognized without counter-examples (e.g. a collection of "non-triangle shapes" will just be interpreted as "shapes" unless triangles are shown opposite them).
BP513 (keyword left-narrow) is about Bongard Problems whose left side can be recognized without the right side. When a Bongard Problem is left-narrow and not "right-narrow that usually makes the property on the left seem positive and the property on the right seem negative.
The OEBP by convention has preferred the "positive-seeming" property (when there is one) to be on the left side.
All in all, the keyword "notso" should mean:
1) If the Bongard Problem is "narrow" on at least one side, then it is left-narrow.
2) The right side is the conceptual negation of the left side.
If a Bongard Problem's solution is "[Property A] vs. not so", the "not so" side is everything without [Property A] within some suitable context. A Bongard Problem "triangles vs. not so" might only include simple shapes as non-triangles; it need not include images of boats as non-triangles. It is not necessary for all the kitchen sink to be thrown on the "not so" side (although it is here). |
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CROSSREFS
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See BP1001 for a version sorting pictures of Bongard Problems (miniproblems) instead of links to pages on the OEBP. (This version is a little different. In BP1001, the kitchen sink of all other possible images is always included on the right "not so" side, rather than a context-dependent conceptual negation.)
Contrast keyword viceversa.
"[Property A] vs. not so" Bongard Problems are often allsorted, meaning they sort all relevant examples--but not always, because sometimes there exist ambiguous border cases, unclear whether they fit [Property A] or not.
Adjacent-numbered pages:
BP862 BP863 BP864 BP865 BP866 * BP868 BP869 BP870 BP871 BP872
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KEYWORD
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notso, meta (see left/right), links, keyword, left-self, funny
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WORLD
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everything [smaller | same]
zoom in left
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AUTHOR
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Aaron David Fairbanks
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| BP902 |
| This Bongard Problem vs. anything else. |
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COMMENTS
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Although this Bongard Problem is self-referential, it's only because of the specific phrasing of the solution. "BP902 vs. anything else" would also work. The number 902 could have been chosen coincidentally. |
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CROSSREFS
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See BP953, BP959.
Adjacent-numbered pages:
BP897 BP898 BP899 BP900 BP901 * BP903 BP904 BP905 BP906 BP907
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KEYWORD
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notso, meta (see left/right), links, left-self, left-narrow, left-finite, left-full, right-null, right-it, invalid, experimental, funny
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CONCEPT
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self-reference (info | search),
specificity (info | search)
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WORLD
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everything [smaller | same]
zoom in left (bp902)
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AUTHOR
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Leo Crabbe
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| BP905 |
| Graph can be redrawn such that no edges intersect vs. not so. |
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| BP932 |
| Every vertex is connected to every other vs. vertices are connected in a cycle (no other connections). |
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COMMENTS
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Complete graphs with zero, one, two, or three vertices would be ambiguously categorized (fit in overlap of both sides).
Left examples are called "fully connected graphs." Right examples are called "cycle graphs." |
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CROSSREFS
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Adjacent-numbered pages:
BP927 BP928 BP929 BP930 BP931 * BP933 BP934 BP935 BP936 BP937
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KEYWORD
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precise, left-narrow, right-narrow, both, preciseworld
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CONCEPT
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graph (info | search),
distinguishing_crossing_curves (info | search),
all (info | search),
loop (info | search)
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WORLD
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connected_graph [smaller | same | bigger]
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AUTHOR
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Aaron David Fairbanks
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REFERENCE
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Henneberg, L. (1911), Die graphische Statik der starren Systeme, Leipzig
Jackson, Bill. (2007). Notes on the Rigidity of Graphs.
Laman, Gerard. (1970), "On graphs and the rigidity of plane skeletal structures", J. Engineering Mathematics, 4 (4): 331–340.
Pollaczek‐Geiringer, Hilda (1927), "Über die Gliederung ebener Fachwerke", Zeitschrift für Angewandte Mathematik und Mechanik, 7 (1): 58–72. |
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CROSSREFS
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Adjacent-numbered pages:
BP1011 BP1012 BP1013 BP1014 BP1015 * BP1017 BP1018 BP1019 BP1020 BP1021
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KEYWORD
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nice, physics, help
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CONCEPT
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rigidity (info | search),
graph (info | search),
imagined_motion (info | search)
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WORLD
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planar_connected_graph [smaller | same | bigger]
zoom in left (rigid_planar_connected_graph)
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AUTHOR
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Aaron David Fairbanks
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