See monogon in All languages combined, or Wiktionary
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DiSessa, Turtle Geometry: The Computer As a Medium for Exploring Mathematics, →ISBN, page 262:", "text": "There are no one-sided closed polygons on a plane. On the cube, however, monogons are a diverse and interesting class of figures.", "type": "quote" }, { "text": "2003, Gordon Baker, translator and editor, Ludwig Wittgenstein and Friedrich Waismann, The Voices of Wittgenstein: The Vienna Circle, Routledge, →ISBN, page 409,\nWe explain to somebody what is a regular quadrilateral constructed within the circle; then a regular triangle and a regular bi-angle. Now we ask him to draw a regular monogon by analogy, and we probably think that he cannot do this. But what if he draws a point on the circle and says that it is a regular monogon?" } ], "glosses": [ "A one-dimensional object comprising one vertex and one (not necessarily straight) edge both of whose ends are that vertex." ], "id": "en-monogon-en-noun-XlIccm1p", "links": [ [ "geometry", "geometry" ], [ "one", "one" ], [ "dimensional", "dimensional" ], [ "vertex", "vertex" ], [ "straight", "straight" ], [ "edge", "edge" ], [ "end", "end" ] ], "raw_glosses": [ "(geometry) A one-dimensional object comprising one vertex and one (not necessarily straight) edge both of whose ends are that vertex." ], "topics": [ "geometry", "mathematics", "sciences" ] }, { "categories": [ { "kind": "topical", "langcode": "en", "name": "Geometry", "orig": "en:Geometry", "parents": [ "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "_dis": "27 49 25", "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w+disamb" }, { "_dis": "29 44 27", "kind": "other", "name": "English terms prefixed with mono-", "parents": [], "source": "w+disamb" }, { "_dis": "30 50 21", "kind": "other", "name": "English terms suffixed with -gon", "parents": [], "source": "w+disamb" }, { "_dis": "26 53 21", "kind": "other", "name": "Entries with translation boxes", "parents": [], "source": "w+disamb" }, { "_dis": "28 52 20", "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w+disamb" }, { "_dis": "26 56 19", "kind": "other", "name": "Pages with entries", "parents": [], "source": "w+disamb" }, { "_dis": "24 55 20", "kind": "other", "name": "Terms with Dutch translations", "parents": [], "source": "w+disamb" }, { "_dis": "25 55 20", "kind": "other", "name": "Terms with Finnish translations", "parents": [], "source": "w+disamb" }, { "_dis": "25 55 21", "kind": "other", "name": "Terms with German translations", "parents": [], "source": "w+disamb" }, { "_dis": "25 54 21", "kind": "other", "name": "Terms with Polish translations", "parents": [], "source": "w+disamb" }, { "_dis": "24 57 19", "kind": "other", "name": "Terms with Russian translations", "parents": [], "source": "w+disamb" }, { "_dis": "31 59 10", "kind": "other", "langcode": "en", "name": "Shapes in non-Euclidean geometry", "orig": "en:Shapes in non-Euclidean geometry", "parents": [], "source": "w+disamb" }, { "_dis": "33 42 24", "kind": "other", "langcode": "en", "name": "Sphere", "orig": "en:Sphere", "parents": [], "source": "w+disamb" }, { "_dis": "38 53 10", "kind": "topical", "langcode": "en", "name": "Polygons", "orig": "en:Polygons", "parents": [ "Shapes", "Geometry", "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w+disamb" } ], "examples": [ { "ref": "1987, Jonathan L. Gross, Thomas W. Tucker, Topological Graph Theory, Dover Publications, published 2001, →ISBN, page 231:", "text": "According to Theorem 4.1.1, such a derived imbedding could be obtained from an imbedded voltage graph with one vertex, 6s#x2B;2 edges, and 4s#x2B;2 faces. Of these faces, 4s#x2B;1 should be 3-sided and satisfy KVL. The other face should be a monogon whose net voltage has order two.", "type": "quote" }, { "text": "2002, Tao Li, \"Laminar Branched Surfaces in 3–manifolds\", Geometry & Topology 6, page 158,\nThere is no monogon in M-int(N(B)), ie, no disk D⊂M-int(N(B)) with ∂D=D∩N(B)=α∪β, where α⊂∂_(vN)(B) is in an interval fiber of ∂_(vN)(B) and β⊂∂_(hN)(B)." }, { "text": "a. 2006, Thilo Kuessner, \"A survey on simplicial volume and invariants of foliations and laminations\", in, Paweł Walczak, et al., editors, Foliations 2005, →ISBN, page 295,\nAn end-compressing monogon for F is a monogon properly embedded in the complimentary region C which is not homotopic (rel. boundary) into ∂C." } ], "glosses": [ "A two-dimensional object comprising one vertex, one edge both of whose ends are that vertex, and one face filling in the hollow formed by that edge." ], "id": "en-monogon-en-noun-ucwqiD2R", "links": [ [ "geometry", "geometry" ], [ "two", "two" ], [ "face", "face" ], [ "hollow", "hollow" ] ], "raw_glosses": [ "(geometry) A two-dimensional object comprising one vertex, one edge both of whose ends are that vertex, and one face filling in the hollow formed by that edge." ], "topics": [ "geometry", "mathematics", "sciences" ] }, { "categories": [ { "kind": "topical", "langcode": "en", "name": "Optics", "orig": "en:Optics", "parents": [ "Physics", "Sciences", "All topics", "Fundamental" ], "source": "w" } ], "examples": [ { "ref": "1991, Beam Deflection, Scanning Technologies, edited by Gerald F. Marshall, Leo Beiser, →ISBN, page 33:", "text": "A new optical scanner is described which serves as a monogon or single-facet device, providing one scan per shaft rotation.", "type": "quote" }, { "text": "1999, William L. Wolfe, Infrared Design Examples, Tutorial Texts in Optical Engineering Volume TT36, SPIE Press, →ISBN, page 133,\nThese devices also start with the monogon, a plane mirror, and include the bigon, a two-sided mirror, the trigon, quadrigon, and general n-gons." } ], "glosses": [ "A single-faceted reflector." ], "id": "en-monogon-en-noun-pau6jkq0", "links": [ [ "optics", "optics" ] ], "raw_glosses": [ "(optics) A single-faceted reflector." ], "topics": [ "engineering", "natural-sciences", "optics", "physical-sciences", "physics" ] } ], "sounds": [ { "audio": "LL-Q1860 (eng)-Rho9998-monogon.wav", "mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/7/79/LL-Q1860_%28eng%29-Rho9998-monogon.wav/LL-Q1860_%28eng%29-Rho9998-monogon.wav.mp3", "ogg_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/7/79/LL-Q1860_%28eng%29-Rho9998-monogon.wav/LL-Q1860_%28eng%29-Rho9998-monogon.wav.ogg" } ], "synonyms": [ { "_dis1": "0 0 0", "word": "henagon" } ], "translations": [ { "_dis1": "46 48 5", "code": "nl", "lang": "Dutch", "sense": "geometry", "tags": [ "masculine" ], "word": "eenhoek" }, { "_dis1": "46 48 5", "code": "fi", "lang": "Finnish", "sense": "geometry", "word": "yksikulmio" }, { "_dis1": "46 48 5", "code": "de", "lang": "German", "sense": "geometry", "tags": [ "neuter" ], "word": "Eineck" }, { "_dis1": "46 48 5", "code": "pl", "lang": "Polish", "sense": "geometry", "tags": [ "masculine" ], "word": "kształt o jednym wierzchołku" }, { "_dis1": "46 48 5", "code": "ru", "lang": "Russian", "roman": "odnougolʹnik", "sense": "geometry", "tags": [ "masculine" ], "word": "одноугольник" } ], "word": "monogon" }
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DiSessa, Turtle Geometry: The Computer As a Medium for Exploring Mathematics, →ISBN, page 262:", "text": "There are no one-sided closed polygons on a plane. On the cube, however, monogons are a diverse and interesting class of figures.", "type": "quote" }, { "text": "2003, Gordon Baker, translator and editor, Ludwig Wittgenstein and Friedrich Waismann, The Voices of Wittgenstein: The Vienna Circle, Routledge, →ISBN, page 409,\nWe explain to somebody what is a regular quadrilateral constructed within the circle; then a regular triangle and a regular bi-angle. Now we ask him to draw a regular monogon by analogy, and we probably think that he cannot do this. But what if he draws a point on the circle and says that it is a regular monogon?" } ], "glosses": [ "A one-dimensional object comprising one vertex and one (not necessarily straight) edge both of whose ends are that vertex." ], "links": [ [ "geometry", "geometry" ], [ "one", "one" ], [ "dimensional", "dimensional" ], [ "vertex", "vertex" ], [ "straight", "straight" ], [ "edge", "edge" ], [ "end", "end" ] ], "raw_glosses": [ "(geometry) A one-dimensional object comprising one vertex and one (not necessarily straight) edge both of whose ends are that vertex." ], "topics": [ "geometry", "mathematics", "sciences" ] }, { "categories": [ "English terms with quotations", "en:Geometry" ], "examples": [ { "ref": "1987, Jonathan L. Gross, Thomas W. Tucker, Topological Graph Theory, Dover Publications, published 2001, →ISBN, page 231:", "text": "According to Theorem 4.1.1, such a derived imbedding could be obtained from an imbedded voltage graph with one vertex, 6s#x2B;2 edges, and 4s#x2B;2 faces. Of these faces, 4s#x2B;1 should be 3-sided and satisfy KVL. The other face should be a monogon whose net voltage has order two.", "type": "quote" }, { "text": "2002, Tao Li, \"Laminar Branched Surfaces in 3–manifolds\", Geometry & Topology 6, page 158,\nThere is no monogon in M-int(N(B)), ie, no disk D⊂M-int(N(B)) with ∂D=D∩N(B)=α∪β, where α⊂∂_(vN)(B) is in an interval fiber of ∂_(vN)(B) and β⊂∂_(hN)(B)." }, { "text": "a. 2006, Thilo Kuessner, \"A survey on simplicial volume and invariants of foliations and laminations\", in, Paweł Walczak, et al., editors, Foliations 2005, →ISBN, page 295,\nAn end-compressing monogon for F is a monogon properly embedded in the complimentary region C which is not homotopic (rel. boundary) into ∂C." } ], "glosses": [ "A two-dimensional object comprising one vertex, one edge both of whose ends are that vertex, and one face filling in the hollow formed by that edge." ], "links": [ [ "geometry", "geometry" ], [ "two", "two" ], [ "face", "face" ], [ "hollow", "hollow" ] ], "raw_glosses": [ "(geometry) A two-dimensional object comprising one vertex, one edge both of whose ends are that vertex, and one face filling in the hollow formed by that edge." ], "topics": [ "geometry", "mathematics", "sciences" ] }, { "categories": [ "English terms with quotations", "en:Optics" ], "examples": [ { "ref": "1991, Beam Deflection, Scanning Technologies, edited by Gerald F. 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Wolfe, Infrared Design Examples, Tutorial Texts in Optical Engineering Volume TT36, SPIE Press, →ISBN, page 133,\nThese devices also start with the monogon, a plane mirror, and include the bigon, a two-sided mirror, the trigon, quadrigon, and general n-gons." } ], "glosses": [ "A single-faceted reflector." ], "links": [ [ "optics", "optics" ] ], "raw_glosses": [ "(optics) A single-faceted reflector." ], "topics": [ "engineering", "natural-sciences", "optics", "physical-sciences", "physics" ] } ], "sounds": [ { "audio": "LL-Q1860 (eng)-Rho9998-monogon.wav", "mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/7/79/LL-Q1860_%28eng%29-Rho9998-monogon.wav/LL-Q1860_%28eng%29-Rho9998-monogon.wav.mp3", "ogg_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/7/79/LL-Q1860_%28eng%29-Rho9998-monogon.wav/LL-Q1860_%28eng%29-Rho9998-monogon.wav.ogg" } ], "synonyms": [ { "word": "henagon" } ], "translations": [ { "code": "nl", "lang": "Dutch", "sense": "geometry", "tags": [ "masculine" ], "word": "eenhoek" }, { "code": "fi", "lang": "Finnish", "sense": "geometry", "word": "yksikulmio" }, { "code": "de", "lang": "German", "sense": "geometry", "tags": [ "neuter" ], "word": "Eineck" }, { "code": "pl", "lang": "Polish", "sense": "geometry", "tags": [ "masculine" ], "word": "kształt o jednym wierzchołku" }, { "code": "ru", "lang": "Russian", "roman": "odnougolʹnik", "sense": "geometry", "tags": [ "masculine" ], "word": "одноугольник" } ], "word": "monogon" }
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