"apeirogon" meaning in All languages combined

{
  "etymology_templates": [
    {
      "args": {
        "1": "en",
        "2": "apeiro",
        "3": "gon"
      },
      "expansion": "apeiro- + -gon",
      "name": "confix"
    }
  ],
  "etymology_text": "apeiro- + -gon",
  "forms": [
    {
      "form": "apeirogons",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "apeirogon (plural apeirogons)",
      "name": "en-noun"
    }
  ],
  "hyphenation": [
    "apei‧ro‧gon"
  ],
  "hyponyms": [
    {
      "_dis1": "0 0",
      "english": "a specific non-regular case",
      "word": "zerogon"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "_dis1": "0 0",
      "word": "apeirohedron"
    },
    {
      "_dis1": "0 0",
      "word": "infinigon"
    },
    {
      "_dis1": "0 0",
      "word": "pseudogon"
    }
  ],
  "senses": [
    {
      "categories": [
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Geometry",
          "orig": "en:Geometry",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "_dis": "47 53",
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w+disamb"
        },
        {
          "_dis": "50 50",
          "kind": "other",
          "name": "English terms prefixed with apeiro-",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "50 50",
          "kind": "other",
          "name": "English terms suffixed with -gon",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "46 54",
          "kind": "other",
          "langcode": "en",
          "name": "Infinity",
          "orig": "en:Infinity",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "50 50",
          "kind": "other",
          "langcode": "en",
          "name": "Non-Euclidean geometry",
          "orig": "en:Non-Euclidean geometry",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "50 50",
          "kind": "other",
          "langcode": "en",
          "name": "Shapes in non-Euclidean geometry",
          "orig": "en:Shapes in non-Euclidean geometry",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "50 50",
          "kind": "topical",
          "langcode": "en",
          "name": "Polygons",
          "orig": "en:Polygons",
          "parents": [
            "Shapes",
            "Geometry",
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w+disamb"
        }
      ],
      "examples": [
        {
          "ref": "1984, Coxeter-Festschrift [Mitteilungen aus dem Mathem[atisches] Seminar Giessen], Giessen: Gießen Mathematischen Institut, Justus Liebig-Universität Gießen, page 247",
          "text": "Hence the regular polygon ABCD ... can either be a convex n-gon, a star n-gon, a horocylic apeirogon or a hypercyclic apeirogon.",
          "type": "quotation"
        },
        {
          "ref": "1994, Steven Schwartzman, The Words of Mathematics: An Etymological Dictionary of Mathematical Terms Used in English, Washington, D.C.: Mathematical Association of America, page 27",
          "text": "In geometry, an apeirogon is a limiting case of a regular polygon. The number of sides in an apeirogon is becoming infinite, so the apeirogon as a whole approaches a circle. A magnified view of a small piece of the apeirogon looks like a straight line.",
          "type": "quotation"
        },
        {
          "ref": "2002, Peter McMullen with Egon Schulte, Abstract Regular Polytopes, Cambridge: Cambridge University Press, page 217",
          "text": "[A]n apeirogon (infinite regular polygon) is a linear one {∞}, a planar (skew) one (zigzag apeirogon), which is the blend {∞} # { } with a segment, or helix, which is a blend of {∞} with a bounded regular polygon.",
          "type": "quotation"
        },
        {
          "ref": "2014, Daniel Pellicer with Egon Schulte, “Polygonal Complexes and Graphs for Crystallographic Groups”, in Robert Connelly, Asia Ivić Weiss, Walter Whiteley, editors, Rigidity and Symmetry, New York, N.Y.: Springer, page 331",
          "text": "There are exactly 12 regular apeirohedra that in some sense are reducible and have components that are regular figures of dimensions 1 and 2. These apeirohedra are blends of a planar regular apeirohedron, and a line segment { } or linear apeirogon {∞}. This explains why there are 12 = 6·2 blended (or non-pure) apeirohedra. For example, the blend of the standard square tessellation {4,4} and the infinite apeirogon {∞}, denoted {4,4}#{∞}, is an apeirohedron whose faces are helical apeirogons (over squares), rising above the squares of {4,4}, such that 4 meet at each vertex; the orthogonal projections of {4,4}#{∞} onto their component subspaces recover the original components, the square tessellation and the linear apeirogon.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A type of generalised polygon with a countably infinite number of sides and vertices;\n(in the regular case) the limit case of an n-sided regular polygon as n increases to infinity and the edge length is fixed; typically imagined as a straight line partitioned into equal segments by an infinite number of equally-spaced points.",
        "A type of generalised polygon with a countably infinite number of sides and vertices;"
      ],
      "id": "en-apeirogon-en-noun-IZByzTNo",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "geometry",
          "geometry"
        ],
        [
          "polygon",
          "polygon"
        ],
        [
          "countably infinite",
          "countably infinite"
        ],
        [
          "side",
          "side"
        ],
        [
          "vertices",
          "vertex"
        ],
        [
          "limit case",
          "limit case"
        ],
        [
          "regular polygon",
          "regular polygon"
        ],
        [
          "infinity",
          "infinity"
        ],
        [
          "edge",
          "edge"
        ],
        [
          "straight line",
          "straight line"
        ],
        [
          "partition",
          "partition"
        ],
        [
          "point",
          "point"
        ]
      ],
      "raw_glosses": [
        "(mathematics, geometry) A type of generalised polygon with a countably infinite number of sides and vertices;\n"
      ],
      "topics": [
        "geometry",
        "mathematics",
        "sciences"
      ]
    },
    {
      "categories": [
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Geometry",
          "orig": "en:Geometry",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "_dis": "47 53",
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w+disamb"
        },
        {
          "_dis": "50 50",
          "kind": "other",
          "name": "English terms prefixed with apeiro-",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "50 50",
          "kind": "other",
          "name": "English terms suffixed with -gon",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "46 54",
          "kind": "other",
          "langcode": "en",
          "name": "Infinity",
          "orig": "en:Infinity",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "50 50",
          "kind": "other",
          "langcode": "en",
          "name": "Non-Euclidean geometry",
          "orig": "en:Non-Euclidean geometry",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "50 50",
          "kind": "other",
          "langcode": "en",
          "name": "Shapes in non-Euclidean geometry",
          "orig": "en:Shapes in non-Euclidean geometry",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "50 50",
          "kind": "topical",
          "langcode": "en",
          "name": "Polygons",
          "orig": "en:Polygons",
          "parents": [
            "Shapes",
            "Geometry",
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w+disamb"
        }
      ],
      "glosses": [
        "A type of generalised polygon with a countably infinite number of sides and vertices;\n(in the regular case) the limit case of an n-sided regular polygon as n increases to infinity and the edge length is fixed; typically imagined as a straight line partitioned into equal segments by an infinite number of equally-spaced points.",
        "the limit case of an n-sided regular polygon as n increases to infinity and the edge length is fixed; typically imagined as a straight line partitioned into equal segments by an infinite number of equally-spaced points."
      ],
      "id": "en-apeirogon-en-noun-qu37Bae5",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "geometry",
          "geometry"
        ],
        [
          "polygon",
          "polygon"
        ],
        [
          "countably infinite",
          "countably infinite"
        ],
        [
          "side",
          "side"
        ],
        [
          "vertices",
          "vertex"
        ],
        [
          "limit case",
          "limit case"
        ],
        [
          "regular polygon",
          "regular polygon"
        ],
        [
          "infinity",
          "infinity"
        ],
        [
          "edge",
          "edge"
        ],
        [
          "straight line",
          "straight line"
        ],
        [
          "partition",
          "partition"
        ],
        [
          "point",
          "point"
        ]
      ],
      "raw_glosses": [
        "(mathematics, geometry) A type of generalised polygon with a countably infinite number of sides and vertices;\n"
      ],
      "raw_tags": [
        "in the regular case"
      ],
      "topics": [
        "geometry",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "sounds": [
    {
      "ipa": "/əˈpiːɹɵɡɑn/"
    },
    {
      "ipa": "/əˈpeɪ̯ɹɵɡɑn/"
    },
    {
      "audio": "LL-Q1860 (eng)-Vealhurl-apeirogon.wav",
      "mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/9/9d/LL-Q1860_%28eng%29-Vealhurl-apeirogon.wav/LL-Q1860_%28eng%29-Vealhurl-apeirogon.wav.mp3",
      "ogg_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/9/9d/LL-Q1860_%28eng%29-Vealhurl-apeirogon.wav/LL-Q1860_%28eng%29-Vealhurl-apeirogon.wav.ogg",
      "tags": [
        "Southern-England"
      ],
      "text": "Audio (Southern England)"
    }
  ],
  "translations": [
    {
      "_dis1": "46 54",
      "code": "bg",
      "lang": "Bulgarian",
      "roman": "bezkrajnoǎgǎlnik",
      "sense": "Translations",
      "tags": [
        "masculine"
      ],
      "word": "безкрайноъгълник"
    },
    {
      "_dis1": "46 54",
      "code": "fi",
      "lang": "Finnish",
      "sense": "Translations",
      "word": "ääretönkulmio"
    },
    {
      "_dis1": "46 54",
      "code": "de",
      "lang": "German",
      "sense": "Translations",
      "tags": [
        "neuter"
      ],
      "word": "Unendlicheck"
    },
    {
      "_dis1": "46 54",
      "code": "mk",
      "lang": "Macedonian",
      "roman": "beskonečnoagolnik",
      "sense": "Translations",
      "tags": [
        "masculine"
      ],
      "word": "бесконечноаголник"
    },
    {
      "_dis1": "46 54",
      "code": "pl",
      "lang": "Polish",
      "sense": "Translations",
      "tags": [
        "masculine"
      ],
      "word": "wielokąt z nieskończoną liczbą katów"
    },
    {
      "_dis1": "46 54",
      "code": "es",
      "lang": "Spanish",
      "sense": "Translations",
      "word": "apeirógono"
    }
  ],
  "word": "apeirogon"
}

{
  "categories": [
    "English 4-syllable words",
    "English countable nouns",
    "English entries with incorrect language header",
    "English lemmas",
    "English nouns",
    "English terms prefixed with apeiro-",
    "English terms suffixed with -gon",
    "English terms with IPA pronunciation",
    "English terms with audio links",
    "Translation table header lacks gloss",
    "en:Infinity",
    "en:Non-Euclidean geometry",
    "en:Polygons",
    "en:Shapes in non-Euclidean geometry"
  ],
  "etymology_templates": [
    {
      "args": {
        "1": "en",
        "2": "apeiro",
        "3": "gon"
      },
      "expansion": "apeiro- + -gon",
      "name": "confix"
    }
  ],
  "etymology_text": "apeiro- + -gon",
  "forms": [
    {
      "form": "apeirogons",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "apeirogon (plural apeirogons)",
      "name": "en-noun"
    }
  ],
  "hyphenation": [
    "apei‧ro‧gon"
  ],
  "hyponyms": [
    {
      "english": "a specific non-regular case",
      "word": "zerogon"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "apeirohedron"
    },
    {
      "word": "infinigon"
    },
    {
      "word": "pseudogon"
    }
  ],
  "senses": [
    {
      "categories": [
        "English terms with quotations",
        "en:Geometry",
        "en:Mathematics"
      ],
      "examples": [
        {
          "ref": "1984, Coxeter-Festschrift [Mitteilungen aus dem Mathem[atisches] Seminar Giessen], Giessen: Gießen Mathematischen Institut, Justus Liebig-Universität Gießen, page 247",
          "text": "Hence the regular polygon ABCD ... can either be a convex n-gon, a star n-gon, a horocylic apeirogon or a hypercyclic apeirogon.",
          "type": "quotation"
        },
        {
          "ref": "1994, Steven Schwartzman, The Words of Mathematics: An Etymological Dictionary of Mathematical Terms Used in English, Washington, D.C.: Mathematical Association of America, page 27",
          "text": "In geometry, an apeirogon is a limiting case of a regular polygon. The number of sides in an apeirogon is becoming infinite, so the apeirogon as a whole approaches a circle. A magnified view of a small piece of the apeirogon looks like a straight line.",
          "type": "quotation"
        },
        {
          "ref": "2002, Peter McMullen with Egon Schulte, Abstract Regular Polytopes, Cambridge: Cambridge University Press, page 217",
          "text": "[A]n apeirogon (infinite regular polygon) is a linear one {∞}, a planar (skew) one (zigzag apeirogon), which is the blend {∞} # { } with a segment, or helix, which is a blend of {∞} with a bounded regular polygon.",
          "type": "quotation"
        },
        {
          "ref": "2014, Daniel Pellicer with Egon Schulte, “Polygonal Complexes and Graphs for Crystallographic Groups”, in Robert Connelly, Asia Ivić Weiss, Walter Whiteley, editors, Rigidity and Symmetry, New York, N.Y.: Springer, page 331",
          "text": "There are exactly 12 regular apeirohedra that in some sense are reducible and have components that are regular figures of dimensions 1 and 2. These apeirohedra are blends of a planar regular apeirohedron, and a line segment { } or linear apeirogon {∞}. This explains why there are 12 = 6·2 blended (or non-pure) apeirohedra. For example, the blend of the standard square tessellation {4,4} and the infinite apeirogon {∞}, denoted {4,4}#{∞}, is an apeirohedron whose faces are helical apeirogons (over squares), rising above the squares of {4,4}, such that 4 meet at each vertex; the orthogonal projections of {4,4}#{∞} onto their component subspaces recover the original components, the square tessellation and the linear apeirogon.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A type of generalised polygon with a countably infinite number of sides and vertices;\n(in the regular case) the limit case of an n-sided regular polygon as n increases to infinity and the edge length is fixed; typically imagined as a straight line partitioned into equal segments by an infinite number of equally-spaced points.",
        "A type of generalised polygon with a countably infinite number of sides and vertices;"
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "geometry",
          "geometry"
        ],
        [
          "polygon",
          "polygon"
        ],
        [
          "countably infinite",
          "countably infinite"
        ],
        [
          "side",
          "side"
        ],
        [
          "vertices",
          "vertex"
        ],
        [
          "limit case",
          "limit case"
        ],
        [
          "regular polygon",
          "regular polygon"
        ],
        [
          "infinity",
          "infinity"
        ],
        [
          "edge",
          "edge"
        ],
        [
          "straight line",
          "straight line"
        ],
        [
          "partition",
          "partition"
        ],
        [
          "point",
          "point"
        ]
      ],
      "raw_glosses": [
        "(mathematics, geometry) A type of generalised polygon with a countably infinite number of sides and vertices;\n"
      ],
      "topics": [
        "geometry",
        "mathematics",
        "sciences"
      ]
    },
    {
      "categories": [
        "English terms with quotations",
        "en:Geometry",
        "en:Mathematics"
      ],
      "glosses": [
        "A type of generalised polygon with a countably infinite number of sides and vertices;\n(in the regular case) the limit case of an n-sided regular polygon as n increases to infinity and the edge length is fixed; typically imagined as a straight line partitioned into equal segments by an infinite number of equally-spaced points.",
        "the limit case of an n-sided regular polygon as n increases to infinity and the edge length is fixed; typically imagined as a straight line partitioned into equal segments by an infinite number of equally-spaced points."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "geometry",
          "geometry"
        ],
        [
          "polygon",
          "polygon"
        ],
        [
          "countably infinite",
          "countably infinite"
        ],
        [
          "side",
          "side"
        ],
        [
          "vertices",
          "vertex"
        ],
        [
          "limit case",
          "limit case"
        ],
        [
          "regular polygon",
          "regular polygon"
        ],
        [
          "infinity",
          "infinity"
        ],
        [
          "edge",
          "edge"
        ],
        [
          "straight line",
          "straight line"
        ],
        [
          "partition",
          "partition"
        ],
        [
          "point",
          "point"
        ]
      ],
      "raw_glosses": [
        "(mathematics, geometry) A type of generalised polygon with a countably infinite number of sides and vertices;\n"
      ],
      "raw_tags": [
        "in the regular case"
      ],
      "topics": [
        "geometry",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "sounds": [
    {
      "ipa": "/əˈpiːɹɵɡɑn/"
    },
    {
      "ipa": "/əˈpeɪ̯ɹɵɡɑn/"
    },
    {
      "audio": "LL-Q1860 (eng)-Vealhurl-apeirogon.wav",
      "mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/9/9d/LL-Q1860_%28eng%29-Vealhurl-apeirogon.wav/LL-Q1860_%28eng%29-Vealhurl-apeirogon.wav.mp3",
      "ogg_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/9/9d/LL-Q1860_%28eng%29-Vealhurl-apeirogon.wav/LL-Q1860_%28eng%29-Vealhurl-apeirogon.wav.ogg",
      "tags": [
        "Southern-England"
      ],
      "text": "Audio (Southern England)"
    }
  ],
  "translations": [
    {
      "code": "bg",
      "lang": "Bulgarian",
      "roman": "bezkrajnoǎgǎlnik",
      "sense": "Translations",
      "tags": [
        "masculine"
      ],
      "word": "безкрайноъгълник"
    },
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "Translations",
      "word": "ääretönkulmio"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "Translations",
      "tags": [
        "neuter"
      ],
      "word": "Unendlicheck"
    },
    {
      "code": "mk",
      "lang": "Macedonian",
      "roman": "beskonečnoagolnik",
      "sense": "Translations",
      "tags": [
        "masculine"
      ],
      "word": "бесконечноаголник"
    },
    {
      "code": "pl",
      "lang": "Polish",
      "sense": "Translations",
      "tags": [
        "masculine"
      ],
      "word": "wielokąt z nieskończoną liczbą katów"
    },
    {
      "code": "es",
      "lang": "Spanish",
      "sense": "Translations",
      "word": "apeirógono"
    }
  ],
  "word": "apeirogon"
}