See Morley triangle on Wiktionary
{
"etymology_text": "Named for Anglo-American mathematician Frank Morley.",
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"lang_code": "en",
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"derived": [
{
"word": "second Morley triangle"
},
{
"word": "third Morley triangle"
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"examples": [
{
"ref": "2009, Marcel Berger, Geometry I, page 276:",
"text": "Show that the sides of the Morley triangle of T (cf. 10.3.10) lie on three of those lines (notice that each vertex of the Morley triangle is the center of a cardioid lying inside T and tangent to all its sides, one of them twice.)",
"type": "quote"
},
{
"ref": "2013, Dragoslav S. Mitrinovic, J. Pecaric, V. Volenec, Recent Advances in Geometric Inequalities, page 276:",
"text": "The length of a side of the Morley triangle of a given triangle T is less than one third the length of the smallest side of T.\nRemark. The Morley triangle of T is the equilateral triangle formed by the intersection in pairs of the angle trisectors of T.",
"type": "quote"
},
{
"ref": "2016, Erik Seligman, Math Mutation Classics, page 27:",
"text": "There are a total of 18 Morley triangles that can be constructed. One amusing article I spotted on the web was from a math enthusiast who wrote a computer program trying to illustrate the central Morley triangle we started with, but due to a bug actually trisected the exterior angles in come cases... and was surprised to produce equilateral Morley triangles anyway!",
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"glosses": [
"Any of a number of triangles described in Morley's trisector theorem, especially the equilateral triangle formed from the points of intersection of adjacent angle trisectors of a given triangle."
],
"id": "en-Morley_triangle-en-noun-n8fIsKVA",
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"raw_glosses": [
"(geometry) Any of a number of triangles described in Morley's trisector theorem, especially the equilateral triangle formed from the points of intersection of adjacent angle trisectors of a given triangle."
],
"related": [
{
"word": "Morley centre"
},
{
"word": "Morley center"
},
{
"word": "Hofstadter point"
}
],
"synonyms": [
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"sense": "first Morley triangle, Morley's triangle",
"word": "equilateral triangle formed by intersection points of adjacent trisectors"
}
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{
"code": "fr",
"lang": "French",
"sense": "triangle formed by intersection points of adjacent trisectors",
"tags": [
"masculine"
],
"word": "triangle de Morley"
},
{
"code": "de",
"lang": "German",
"sense": "triangle formed by intersection points of adjacent trisectors",
"tags": [
"neuter"
],
"word": "Morley-Dreieck"
},
{
"code": "it",
"lang": "Italian",
"sense": "triangle formed by intersection points of adjacent trisectors",
"tags": [
"masculine"
],
"word": "primo triangolo di Morley"
},
{
"code": "it",
"lang": "Italian",
"sense": "triangle formed by intersection points of adjacent trisectors",
"tags": [
"masculine"
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"word": "triangolo di Morley"
}
],
"wikipedia": [
"Frank Morley",
"Morley's trisector theorem"
]
}
],
"word": "Morley triangle"
}
{
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"word": "second Morley triangle"
},
{
"word": "third Morley triangle"
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"etymology_text": "Named for Anglo-American mathematician Frank Morley.",
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"word": "Morley centre"
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"word": "Morley center"
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"examples": [
{
"ref": "2009, Marcel Berger, Geometry I, page 276:",
"text": "Show that the sides of the Morley triangle of T (cf. 10.3.10) lie on three of those lines (notice that each vertex of the Morley triangle is the center of a cardioid lying inside T and tangent to all its sides, one of them twice.)",
"type": "quote"
},
{
"ref": "2013, Dragoslav S. Mitrinovic, J. Pecaric, V. Volenec, Recent Advances in Geometric Inequalities, page 276:",
"text": "The length of a side of the Morley triangle of a given triangle T is less than one third the length of the smallest side of T.\nRemark. The Morley triangle of T is the equilateral triangle formed by the intersection in pairs of the angle trisectors of T.",
"type": "quote"
},
{
"ref": "2016, Erik Seligman, Math Mutation Classics, page 27:",
"text": "There are a total of 18 Morley triangles that can be constructed. One amusing article I spotted on the web was from a math enthusiast who wrote a computer program trying to illustrate the central Morley triangle we started with, but due to a bug actually trisected the exterior angles in come cases... and was surprised to produce equilateral Morley triangles anyway!",
"type": "quote"
}
],
"glosses": [
"Any of a number of triangles described in Morley's trisector theorem, especially the equilateral triangle formed from the points of intersection of adjacent angle trisectors of a given triangle."
],
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"raw_glosses": [
"(geometry) Any of a number of triangles described in Morley's trisector theorem, especially the equilateral triangle formed from the points of intersection of adjacent angle trisectors of a given triangle."
],
"topics": [
"geometry",
"mathematics",
"sciences"
],
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],
"synonyms": [
{
"sense": "first Morley triangle, Morley's triangle",
"word": "equilateral triangle formed by intersection points of adjacent trisectors"
}
],
"translations": [
{
"code": "fr",
"lang": "French",
"sense": "triangle formed by intersection points of adjacent trisectors",
"tags": [
"masculine"
],
"word": "triangle de Morley"
},
{
"code": "de",
"lang": "German",
"sense": "triangle formed by intersection points of adjacent trisectors",
"tags": [
"neuter"
],
"word": "Morley-Dreieck"
},
{
"code": "it",
"lang": "Italian",
"sense": "triangle formed by intersection points of adjacent trisectors",
"tags": [
"masculine"
],
"word": "primo triangolo di Morley"
},
{
"code": "it",
"lang": "Italian",
"sense": "triangle formed by intersection points of adjacent trisectors",
"tags": [
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],
"word": "triangolo di Morley"
}
],
"word": "Morley triangle"
}
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This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-12-15 from the enwiktionary dump dated 2024-12-04 using wiktextract (8a39820 and 4401a4c). 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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