Angular eccentricity (original) (raw)
Angular eccentricity is one of many parameters which arise in the study of the ellipse or ellipsoid. It is denoted here by α (alpha). It may be defined in terms of the eccentricity, e, or the aspect ratio, b/a (the ratio of the semi-minor axis and the semi-major axis): Angular eccentricity is not currently used in English language publications on mathematics, geodesy or map projections but it does appear in older literature. The alternative expressions for the flattenings would guard against large cancellations in numerical work.
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| dbo:abstract | Angular eccentricity is one of many parameters which arise in the study of the ellipse or ellipsoid. It is denoted here by α (alpha). It may be defined in terms of the eccentricity, e, or the aspect ratio, b/a (the ratio of the semi-minor axis and the semi-major axis): Angular eccentricity is not currently used in English language publications on mathematics, geodesy or map projections but it does appear in older literature. Any non-dimensional parameter of the ellipse may be expressed in terms of the angular eccentricity. Such expressions are listed in the following table after the conventional definitions. in terms of the semi-axes. The notation for these parameters varies. Here we follow Rapp: The alternative expressions for the flattenings would guard against large cancellations in numerical work. (en) De hoekexcentriciteit is een van de vele parameters voor het karakteriseren van een ellips of een ellipsoide. De hoekexcentriciteit kan gedefinieerd worden in termen van de excentriciteit e, of de beeldverhouding b/a (de verhouding van de halve korte as en de halve lange as). De term 'hoekexcentriciteit' is een verouderd begrip dat tegenwoordig niet of nauwelijks meer gebruikt wordt, maar vooral voorkomt in oudere literatuur over wiskunde, geodesie en kaartprojectie. Elke dimensieloze parameter van de ellips kan uitgedrukt worden in de hoekexcentriciteit. De onderstaande tabel geeft voor de gebruikelijke parameters de uitdrukking in de halve assen en de hoekexcentriciteit. (nl) A excentricidade angular é um dos diversos parâmetros que surgem no estudo da elipse ou elipsoide. É aqui denotada por α (alfa). Pode ser definida em termos da excentricidade, e, ou a razão de aspeto, b/a (a razão entre o e o semieixo maior): A excentricidade angular não é usada atualmente nas publicações de língua inglesa em matemática, geodésia ou projeções de mapas, mas ela aparece em literatura mais antiga. Qualquer parâmetro adimensional da elipse pode ser expresso em termos de excentricidade angular. Estas expressões são listadas na tabela a seguir após as definições convencionais. em termos de os semi-eixos. A notação para esses parâmetros variam. Aqui se segue Rapp As expressões alternativas para partes planas visam proteger contra grandes cancelamentos de trabalho numérico. (pt) |
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| dbo:wikiPageExternalLink | https://web.archive.org/web/20070401052928/http:/www.oc.nps.navy.mil/~garfield/ellipse_app2.pdf https://web.archive.org/web/20070928080949/http:/www.ec-gis.org/sdi/publist/pdfs/annoni-etal2003eur.pdf |
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| rdfs:comment | Angular eccentricity is one of many parameters which arise in the study of the ellipse or ellipsoid. It is denoted here by α (alpha). It may be defined in terms of the eccentricity, e, or the aspect ratio, b/a (the ratio of the semi-minor axis and the semi-major axis): Angular eccentricity is not currently used in English language publications on mathematics, geodesy or map projections but it does appear in older literature. The alternative expressions for the flattenings would guard against large cancellations in numerical work. (en) De hoekexcentriciteit is een van de vele parameters voor het karakteriseren van een ellips of een ellipsoide. De hoekexcentriciteit kan gedefinieerd worden in termen van de excentriciteit e, of de beeldverhouding b/a (de verhouding van de halve korte as en de halve lange as). De term 'hoekexcentriciteit' is een verouderd begrip dat tegenwoordig niet of nauwelijks meer gebruikt wordt, maar vooral voorkomt in oudere literatuur over wiskunde, geodesie en kaartprojectie. (nl) A excentricidade angular é um dos diversos parâmetros que surgem no estudo da elipse ou elipsoide. É aqui denotada por α (alfa). Pode ser definida em termos da excentricidade, e, ou a razão de aspeto, b/a (a razão entre o e o semieixo maior): A excentricidade angular não é usada atualmente nas publicações de língua inglesa em matemática, geodésia ou projeções de mapas, mas ela aparece em literatura mais antiga. As expressões alternativas para partes planas visam proteger contra grandes cancelamentos de trabalho numérico. (pt) |
| rdfs:label | Angular eccentricity (en) Hoekexcentriciteit (nl) Excentricidade angular (pt) |
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