About: Boy's surface

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In geometry, Boy's surface is an immersion of the real projective plane in 3-dimensional space found by Werner Boy in 1901. He discovered it on assignment from David Hilbert to prove that the projective plane could not be immersed in 3-space. Boy's surface was first parametrized explicitly by Bernard Morin in 1978. Another parametrization was discovered by Rob Kusner and Robert Bryant. Boy's surface is one of the two possible immersions of the real projective plane which have only a single triple point.

Attributes	Values
rdf:type	school yago:Artifact100021939 yago:Object100002684 yago:PhysicalEntity100001930 yago:Surface104362025 yago:Whole100003553 yago:WikicatSurfaces
rdfs:label	Boysche Fläche (de) Boy's surface (en) Superficie de Boy (es) Superficie di Boy (it) Surface de Boy (fr) ボーイ・サーフェス (ja) Поверхность Боя (ru) Поверхня Боя (uk)
rdfs:comment	Die Boysche Fläche ist ein geometrisches Objekt. Sie ist eine Immersion der reellen projektiven Ebene in den dreidimensionalen Raum. Werner Boy entdeckte die nach ihm benannte Fläche 1901. Wie die Kleinsche Flasche besitzt sie Selbstüberschneidungen, zudem aber auch einen Tripelpunkt. (de) ボーイ・サーフェス（ボーイ曲面）は、二次元実射影空間 RP2 のR3 へのはめ込みの一種である。が二次元実射影空間RP2がR3 へはめ込み可能であることを発見した。ボーイは具体的にはめ込みを構成することでその発見をした。ボーイのこの業績に敬意を表してこの図形をボーイ・サーフェスと呼ぶ。 (ja) Поверхность Боя — первый известный пример погружения вещественной проективной плоскости в трёхмерное евклидово пространство. (ru) У геометрії поверхня Боя — приклад занурення дійсної проєктивної площини в 3-вимірному просторі. На відміну від та плівки Мебіуса, вона не має інших особливих точок, крім самоперетину. (uk) In geometry, Boy's surface is an immersion of the real projective plane in 3-dimensional space found by Werner Boy in 1901. He discovered it on assignment from David Hilbert to prove that the projective plane could not be immersed in 3-space. Boy's surface was first parametrized explicitly by Bernard Morin in 1978. Another parametrization was discovered by Rob Kusner and Robert Bryant. Boy's surface is one of the two possible immersions of the real projective plane which have only a single triple point. (en) En matemática, concretamente en el ámbito de la geometría, la superficie de Boy es una inmersión del plano proyectivo real en un espacio tridimensional, descubierta por Werner Boy en 1901, a raíz del encargo de David Hilbert para demostrar que el plano proyectivo no podía embeberse en el espacio tridimensional. A diferencia de la superficie romana y de la gorra cruzada, no tiene otras singularidades que las (es decir, no tiene puntos de pellizco). (es) La surface de Boy, du nom de Werner Boy, mathématicien ayant été le premier à imaginer son existence en 1902, est une immersion du plan projectif réel dans l'espace usuel de dimension 3. Le plan projectif se définit comme l'espace quotient de par la relation d'équivalence qu'est la colinéarité. (fr) La superficie di Boy è un'immersione del piano proiettivo reale in uno spazio tridimensionale. È una varietà non orientabile scoperta nel 1901 da Werner Boy. Al 1981 risale il primo studio analitico della superficie di Boy con metodo semiempirico. La superficie Boy è discussa (ed illustrata) nel Le Topologicon di Jean-Pierre Petit. La superficie di Boy ha una curva di autointersezione a forma di elica con tre pale che si incontrano in un punto triplo, il fatto che tale curva sia assicura che la superficie stessa rappresenti una del piano proiettivo reale nello spazio affine tridimensionale. (it)
foaf:depiction
dct:subject	Surfaces Geometric topology
Wikipage page ID	61361 (xsd:integer)
Wikipage revision ID	1111440240 (xsd:integer)
Link from a Wikipage to another Wikipage	Cartesian coordinates Projective plane End (topology) Morin surface Cross-cap Bernard Morin David Hilbert Algebraic surface Surfaces Robert Bryant (mathematician) Three-space Constructive Solid Geometry Mathematical Research Institute of Oberwolfach Geometry Möbius strip Congruence (geometry) Smooth function Complex conjugate Perimeter Pinch point (mathematics) Symmetry Three-dimensional space Werner Boy Minimal surface Rational surface Euclidean space Sphere eversion Rational function Geometric topology Willmore energy Polar coordinate system Mercedes-Benz Magnitude (mathematics) Real projective plane Immersion (mathematics) Singular point of an algebraic variety Rotational symmetry Roman surface Half-way model Self-intersection Parametrized Generic fiber dbr:File:Surface_de_Boy.stl
Link from a Wikipage to an external page	http://surfaces.gotfork.net/boy_jv.html http://www.andrewlipson.com/boys.htm http://www.maths.warwick.ac.uk/~bjs/proj.pdf https://mathcurve.com/surfaces.gb/boy/boy.shtml https://www.mfo.de/about-the-institute/history/boy-surface/karcher_pinkallboy_surface.pdf https://www.ams.org/notices/200710/200710-about-the-cover.pdf https://www.ams.org/notices/200710/tx071001306p.pdf http://www.math.univ-toulouse.fr/~cheritat/boy-surface/index.html https://web.archive.org/web/20160712171217/http:/www.mfo.de/about-the-institute/history/Boy-Surface/the-boy-surface-at-oberwolfach https://web.archive.org/web/20160827051210/http:/teach.hilderbuild.com/tiki-index.php%3Fpage=Paper%20Boy%27s https://www.youtube.com/watch%3Fv=9gRx66xKXek http://www.maths.ed.ac.uk/~aar/surgery/boy.pdf http://www.maths.ed.ac.uk/~aar/surgery/notes.htm http://plus.maths.org/issue27/features/mathart/BoyUnfold.html
sameAs	Boy's surface Boy's surface Boy's surface Boy's surface Boy's surface Boy's surface Boy's surface Boy's surface Boy's surface

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