See Euler line in All languages combined, or Wiktionary
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{
"etymology_text": "Named for Swiss mathematician Leonhard Euler.",
"forms": [
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"name": "Geometry",
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"examples": [
{
"ref": "1983, The American Mathematical Monthly, volume 40, page 199",
"text": "Since the line joining the circumcenter and orthocenter of a triangle is its Euler line, we see that this parabola is the envelope of the Euler lines of the triangles Aᵢ.",
"type": "quotation"
},
{
"ref": "2000, Alfred S. Posamentier, Making Geometry Come Alive: Student Activities and Teacher Notes, page 147",
"text": "The Euler line in the preceding figure is OH. N, the center of the nine-point circle, not only lies on the Euler line, but is also its midpoint.",
"type": "quotation"
},
{
"text": "2011, Derek Allan Holton, A Second Step to Mathematical Olympiad Problems, World Scientific Publishing, Mathematical Olympiad Series, Volume 7, page 57,\nShow that the perpendicular bisector of LM in Figure 2.5 meets the Euler line halfway between the orthocentre and the circumcentre of ΔABC."
}
],
"glosses": [
"A line that, for a given triangle, passes through several important points, including the circumcentre, orthocentre and centroid; an analogous line for certain other 2- and 3-dimensional geometric figures."
],
"id": "en-Euler_line-en-noun-0oJtSpmK",
"links": [
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"geometry",
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"circumcentre",
"circumcentre"
],
[
"orthocentre",
"orthocentre"
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[
"centroid",
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],
"raw_glosses": [
"(geometry) A line that, for a given triangle, passes through several important points, including the circumcentre, orthocentre and centroid; an analogous line for certain other 2- and 3-dimensional geometric figures."
],
"related": [
{
"_dis1": "66 34",
"word": "Hamiltonian path"
}
],
"synonyms": [
{
"_dis1": "66 34",
"word": "Euler's line"
}
],
"topics": [
"geometry",
"mathematics",
"sciences"
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"translations": [
{
"_dis1": "91 9",
"code": "hu",
"lang": "Hungarian",
"sense": "geometry",
"word": "Euler-egyenes"
}
]
},
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"kind": "topical",
"langcode": "en",
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{
"ref": "1961, Yale University, Graphs and Their Uses, page 25",
"text": "Theorem 2.1 A connected graph with even local degrees has an Euler line.",
"type": "quotation"
},
{
"ref": "2009, J. P. Chauhan, Krishna's Applied Discrete Mathematics, page 279",
"text": "In defining an Euler graph, some authors drop the requirement that the Euler line be closed.",
"type": "quotation"
},
{
"ref": "2013, Bhavanari Satyanarayana, Kuncham Syam Prasad, Near Rings, Fuzzy Ideals, and Graph Theory, page 372",
"text": "Euler lines mainly deal with the nature of connectivity in graphs. The concept of an Euler line is used to solve several puzzles and games.[…]A closed walk running through every edge of the graph G exactly once is called an Euler line.",
"type": "quotation"
}
],
"glosses": [
"An Eulerian path, a looped path through a graph that passes along every edge exactly once."
],
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"raw_glosses": [
"(graph theory) An Eulerian path, a looped path through a graph that passes along every edge exactly once."
],
"topics": [
"graph-theory",
"mathematics",
"sciences"
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}
],
"wikipedia": [
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"word": "Euler line"
}
{
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"etymology_text": "Named for Swiss mathematician Leonhard Euler.",
"forms": [
{
"form": "Euler lines",
"tags": [
"plural"
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"lang_code": "en",
"pos": "noun",
"related": [
{
"word": "Hamiltonian path"
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"examples": [
{
"ref": "1983, The American Mathematical Monthly, volume 40, page 199",
"text": "Since the line joining the circumcenter and orthocenter of a triangle is its Euler line, we see that this parabola is the envelope of the Euler lines of the triangles Aᵢ.",
"type": "quotation"
},
{
"ref": "2000, Alfred S. Posamentier, Making Geometry Come Alive: Student Activities and Teacher Notes, page 147",
"text": "The Euler line in the preceding figure is OH. N, the center of the nine-point circle, not only lies on the Euler line, but is also its midpoint.",
"type": "quotation"
},
{
"text": "2011, Derek Allan Holton, A Second Step to Mathematical Olympiad Problems, World Scientific Publishing, Mathematical Olympiad Series, Volume 7, page 57,\nShow that the perpendicular bisector of LM in Figure 2.5 meets the Euler line halfway between the orthocentre and the circumcentre of ΔABC."
}
],
"glosses": [
"A line that, for a given triangle, passes through several important points, including the circumcentre, orthocentre and centroid; an analogous line for certain other 2- and 3-dimensional geometric figures."
],
"links": [
[
"geometry",
"geometry"
],
[
"triangle",
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],
[
"circumcentre",
"circumcentre"
],
[
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],
[
"centroid",
"centroid"
]
],
"raw_glosses": [
"(geometry) A line that, for a given triangle, passes through several important points, including the circumcentre, orthocentre and centroid; an analogous line for certain other 2- and 3-dimensional geometric figures."
],
"topics": [
"geometry",
"mathematics",
"sciences"
]
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{
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"examples": [
{
"ref": "1961, Yale University, Graphs and Their Uses, page 25",
"text": "Theorem 2.1 A connected graph with even local degrees has an Euler line.",
"type": "quotation"
},
{
"ref": "2009, J. P. Chauhan, Krishna's Applied Discrete Mathematics, page 279",
"text": "In defining an Euler graph, some authors drop the requirement that the Euler line be closed.",
"type": "quotation"
},
{
"ref": "2013, Bhavanari Satyanarayana, Kuncham Syam Prasad, Near Rings, Fuzzy Ideals, and Graph Theory, page 372",
"text": "Euler lines mainly deal with the nature of connectivity in graphs. The concept of an Euler line is used to solve several puzzles and games.[…]A closed walk running through every edge of the graph G exactly once is called an Euler line.",
"type": "quotation"
}
],
"glosses": [
"An Eulerian path, a looped path through a graph that passes along every edge exactly once."
],
"links": [
[
"graph theory",
"graph theory"
],
[
"Eulerian path",
"Eulerian path"
],
[
"graph",
"graph"
],
[
"edge",
"edge"
]
],
"raw_glosses": [
"(graph theory) An Eulerian path, a looped path through a graph that passes along every edge exactly once."
],
"topics": [
"graph-theory",
"mathematics",
"sciences"
]
}
],
"synonyms": [
{
"word": "Euler's line"
}
],
"translations": [
{
"code": "hu",
"lang": "Hungarian",
"sense": "geometry",
"word": "Euler-egyenes"
}
],
"wikipedia": [
"Euler line",
"Leonhard Euler"
],
"word": "Euler line"
}
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-03 from the enwiktionary dump dated 2024-05-02 using wiktextract (f4fd8c9 and c9440ce). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
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