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Search: concept:x-crossing
Displaying 1-9 of 9 results found.     page 1
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BP30 A curve with one self-crossing vs. a curve without a self-crossing.
(edit; present; nest [left/right]; search; history)
REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 223.

CROSSREFS

BP1232 is almost exactly the same, but allowing for multiple curves and multiple self-crossings.

Adjacent-numbered pages:
BP25 BP26 BP27 BP28 BP29  *  BP31 BP32 BP33 BP34 BP35

KEYWORD

nice, finished, traditional, bongard

CONCEPT x-crossing (info | search),
existence (info | search)

WORLD

crosscurve [smaller | same | bigger]
zoom in right (curve_or_outline)

AUTHOR

Mikhail M. Bongard

BP99 Outlines made by triangles and circles intersect vs. outlines made by triangles and circles do not intersect.
(edit; present; nest [left/right]; search; history)
REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 246.

CROSSREFS

Adjacent-numbered pages:
BP94 BP95 BP96 BP97 BP98  *  BP100 BP101 BP102 BP103 BP104

KEYWORD

finished, traditional, bongard

CONCEPT collinear (info | search),
x-crossing (info | search),
cluster (info | search)

AUTHOR

Mikhail M. Bongard

BP114 Four X-like points vs. two X-like points.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP109 BP110 BP111 BP112 BP113  *  BP115 BP116 BP117 BP118 BP119

KEYWORD

traditional

CONCEPT x-crossing (info | search),
number (info | search)

AUTHOR

Douglas R. Hofstadter

BP213 The tightest-curved section, out of all sections of curve that make a complete turn (360 degrees), contains an x-crossing point vs. not so.
(edit; present; nest [left/right]; search; history)
COMMENTS

All examples are connected smooth curves allowed to self-intersect that must curve in only one direction (starting at one end, either clockwise or counter-clockwise), i.e. there is no inflection point.

CROSSREFS

Adjacent-numbered pages:
BP208 BP209 BP210 BP211 BP212  *  BP214 BP215 BP216 BP217 BP218

KEYWORD

less, convoluted, perfect, traditional

CONCEPT x-crossing (info | search)

AUTHOR

Giuseppe Insana

BP240 Straight line joining the curve ends does not cut the curve vs. straight line joining the curve ends intersects the curve.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP235 BP236 BP237 BP238 BP239  *  BP241 BP242 BP243 BP244 BP245

KEYWORD

traditional

CONCEPT x-crossing (info | search),
line_or_curve_endpoint (info | search),
imagined_line_or_curve (info | search),
imagined_entity (info | search)

AUTHOR

Matthew J. Howells

BP261 Straight lines that join filled and outlined circles intersect vs. straight lines that join filled and outlined circles do not intersect.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP256 BP257 BP258 BP259 BP260  *  BP262 BP263 BP264 BP265 BP266

KEYWORD

noisy, traditional

CONCEPT lines_coincide (info | search),
x-crossing (info | search),
outlined_filled (info | search),
feature_cluster (info | search),
cluster (info | search),
imagined_line_or_curve (info | search),
imagined_entity (info | search),
texture (info | search)

AUTHOR

Michael Ihde

BP266 At least one touch or cross point vs. no touch or cross point.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP261 BP262 BP263 BP264 BP265  *  BP267 BP268 BP269 BP270 BP271

CONCEPT x-crossing (info | search),
or (info | search),
existence (info | search),
t-point (info | search)

WORLD

arial_font_centered_symbol [smaller | same | bigger]

AUTHOR

Merse E. Gáspár

BP1232 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

BP1233 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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