See Euler's formula on Wiktionary
Download JSON data for Euler's formula meaning in All languages combined (15.6kB)
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"expansion": "Named after Swiss mathematician Leonhard Euler (1707–1783)",
"name": "named-after"
}
],
"etymology_text": "Named after Swiss mathematician Leonhard Euler (1707–1783).",
"head_templates": [
{
"args": {},
"expansion": "Euler's formula",
"name": "en-proper noun"
}
],
"hyponyms": [
{
"word": "Euler's identity"
}
],
"lang": "English",
"lang_code": "en",
"pos": "name",
"related": [
{
"word": "Euler's totient function"
}
],
"senses": [
{
"categories": [
"en:Complex analysis"
],
"examples": [
{
"text": "eⁱᶿ= cos θ+i sin θ"
}
],
"glosses": [
"Formula which links complex exponentiation with trigonometric functions:",
"Formula which links complex exponentiation with trigonometric functions"
],
"links": [
[
"complex analysis",
"complex analysis"
],
[
"trigonometric function",
"trigonometric function"
]
],
"raw_glosses": [
"(complex analysis) Formula which links complex exponentiation with trigonometric functions:"
],
"topics": [
"complex-analysis",
"mathematics",
"sciences"
]
},
{
"categories": [
"en:Differential geometry"
],
"examples": [
{
"text": "κₙ(θ)=κ₁ cos ²θ+κ₂ sin ²θ"
}
],
"glosses": [
"Formula which calculates the normal curvature of an arbitrary direction in the tangent plane in terms of the principal curvatures κ₁ and κ₂ and the angle θ which that direction makes with the first principal direction:",
"Formula which calculates the normal curvature of an arbitrary direction in the tangent plane in terms of the principal curvatures κ₁ and κ₂ and the angle θ which that direction makes with the first principal direction"
],
"links": [
[
"differential geometry",
"differential geometry"
],
[
"normal curvature",
"normal curvature"
],
[
"tangent plane",
"tangent plane"
],
[
"principal curvature",
"principal curvature"
],
[
"principal direction",
"principal direction"
]
],
"qualifier": "differential geometry",
"raw_glosses": [
"(differential geometry) Formula which calculates the normal curvature of an arbitrary direction in the tangent plane in terms of the principal curvatures κ₁ and κ₂ and the angle θ which that direction makes with the first principal direction:"
]
}
],
"translations": [
{
"code": "af",
"lang": "Afrikaans",
"sense": "Euler's formula",
"word": "Euler se formule"
},
{
"code": "ar",
"lang": "Arabic",
"roman": "ṣīḡat ʔoyler",
"sense": "Euler's formula",
"tags": [
"feminine"
],
"word": "صِيغَة أُويْلِر"
},
{
"code": "bg",
"lang": "Bulgarian",
"roman": "formula na Ojler",
"sense": "Euler's formula",
"tags": [
"feminine"
],
"word": "формула на Ойлер"
},
{
"code": "ca",
"lang": "Catalan",
"sense": "Euler's formula",
"tags": [
"feminine"
],
"word": "fórmula d'Euler"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "Euler's formula",
"word": "歐拉公式"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "Ōulā gōngshì",
"sense": "Euler's formula",
"word": "欧拉公式"
},
{
"code": "cs",
"lang": "Czech",
"sense": "Euler's formula",
"tags": [
"masculine"
],
"word": "Eulerův vzorec"
},
{
"code": "da",
"lang": "Danish",
"sense": "Euler's formula",
"tags": [
"common-gender"
],
"word": "Eulers formel"
},
{
"code": "nl",
"lang": "Dutch",
"sense": "Euler's formula",
"word": "formule van Euler"
},
{
"code": "eo",
"lang": "Esperanto",
"sense": "Euler's formula",
"word": "Eŭlera formulo"
},
{
"code": "et",
"lang": "Estonian",
"sense": "Euler's formula",
"word": "Euleri valem"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "Euler's formula",
"word": "Eulerin lause"
},
{
"code": "fr",
"lang": "French",
"sense": "Euler's formula",
"tags": [
"feminine"
],
"word": "formule d’Euler"
},
{
"code": "de",
"lang": "German",
"sense": "Euler's formula",
"tags": [
"feminine"
],
"word": "eulersche Formel"
},
{
"code": "he",
"lang": "Hebrew",
"sense": "Euler's formula",
"word": "נוסחת אוילר"
},
{
"code": "hi",
"lang": "Hindi",
"roman": "yūlar kā sūtra",
"sense": "Euler's formula",
"word": "यूलर का सूत्र"
},
{
"code": "is",
"lang": "Icelandic",
"sense": "Euler's formula",
"word": "jafna Eulers"
},
{
"code": "id",
"lang": "Indonesian",
"sense": "Euler's formula",
"word": "rumus Euler"
},
{
"code": "it",
"lang": "Italian",
"sense": "Euler's formula",
"tags": [
"feminine"
],
"word": "formula di Eulero"
},
{
"alt": "オイラーのこうしき",
"code": "ja",
"lang": "Japanese",
"roman": "oirā no kōshiki",
"sense": "Euler's formula",
"word": "オイラーの公式"
},
{
"code": "km",
"lang": "Khmer",
"roman": "ruup mʊən aylaa",
"sense": "Euler's formula",
"word": "រូបមន្តអយល័រ"
},
{
"code": "ko",
"lang": "Korean",
"roman": "oilleoui gongsik",
"sense": "Euler's formula",
"word": "오일러의 공식"
},
{
"code": "lt",
"lang": "Lithuanian",
"sense": "Euler's formula",
"word": "Oilerio formulė"
},
{
"code": "no",
"lang": "Norwegian",
"sense": "Euler's formula",
"word": "Eulers formel"
},
{
"code": "fa",
"lang": "Persian",
"sense": "Euler's formula",
"word": "فرمول اولر"
},
{
"code": "pl",
"lang": "Polish",
"sense": "Euler's formula",
"tags": [
"masculine"
],
"word": "wzór Eulera"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "Euler's formula",
"tags": [
"feminine"
],
"word": "fórmula de Euler"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "Euler's formula",
"tags": [
"feminine"
],
"word": "formula lui Euler"
},
{
"code": "ru",
"lang": "Russian",
"roman": "fórmula Ejlera",
"sense": "Euler's formula",
"tags": [
"feminine"
],
"word": "фо́рмула Эйлера"
},
{
"code": "ru",
"lang": "Russian",
"roman": "fórmula Ejlera",
"sense": "Euler's formula",
"tags": [
"feminine"
],
"word": "фо́рмула Эйлера"
},
{
"code": "sh",
"lang": "Serbo-Croatian",
"sense": "Euler's formula",
"tags": [
"Cyrillic",
"feminine"
],
"word": "Еулерова формула"
},
{
"code": "sh",
"lang": "Serbo-Croatian",
"sense": "Euler's formula",
"tags": [
"Cyrillic",
"feminine"
],
"word": "Ојлерова формула"
},
{
"code": "sh",
"lang": "Serbo-Croatian",
"sense": "Euler's formula",
"tags": [
"Roman",
"feminine"
],
"word": "Eulerova formula"
},
{
"code": "sh",
"lang": "Serbo-Croatian",
"sense": "Euler's formula",
"tags": [
"Roman",
"feminine"
],
"word": "Ojlerova formula"
},
{
"code": "sl",
"lang": "Slovene",
"sense": "Euler's formula",
"tags": [
"feminine"
],
"word": "Eulerjeva formula"
},
{
"code": "es",
"lang": "Spanish",
"sense": "Euler's formula",
"tags": [
"feminine"
],
"word": "fórmula de Euler"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "Euler's formula",
"tags": [
"common-gender"
],
"word": "Eulers formel"
},
{
"code": "th",
"lang": "Thai",
"roman": "sòot kŏng oyler",
"sense": "Euler's formula",
"word": "สูตรของออยเลอร์"
},
{
"code": "cy",
"lang": "Welsh",
"sense": "Euler's formula",
"word": "fformwla Euler"
}
],
"wikipedia": [
"Euler's formula"
],
"word": "Euler's formula"
}
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-06-23 from the enwiktionary dump dated 2024-06-20 using wiktextract (1b9bfc5 and 0136956). 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.
If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.