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In mathematics, hyperbolic coordinates are a method of locating points in quadrant I of the Cartesian plane . Hyperbolic coordinates take values in the hyperbolic plane defined as: . These coordinates in HP are useful for studying logarithmic comparisons of direct proportion in Q and measuring deviations from direct proportion. For in take and . The parameter u is the hyperbolic angle to (x, y) and v is the geometric mean of x and y. The inverse mapping is . The function is a continuous mapping, but not an analytic function.

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rdf:type	yago:WikicatCoordinateSystems yago:Abstraction100002137 yago:Arrangement105726596 yago:Cognition100023271 yago:CoordinateSystem105728024 yago:PsychologicalFeature100023100 yago:Structure105726345
rdfs:label	نظام إحداثيات قطعي زائدي (ar) Coordenadas hiperbólicas (es) Hyperbolic coordinates (en) 쌍곡 좌표계 (ko) Coordenadas hiperbólicas (pt) Гиперболическая система координат (ru) 雙曲坐標系 (zh)
rdfs:comment	في الرياضيات، نظام الإحداثيات القطعي الزائدي، هو طريقة لتحديد أماكن النقاط ضمن رباعيات في المستوي الديكارتي. . تأخذ الإحداثيات القطعية الزائدية قيماً في . من أجل في تأخذ القيمة و . بعض الأحيان يطلق على اسم ، و هو المتوسط الهندسي. (ar) In mathematics, hyperbolic coordinates are a method of locating points in quadrant I of the Cartesian plane . Hyperbolic coordinates take values in the hyperbolic plane defined as: . These coordinates in HP are useful for studying logarithmic comparisons of direct proportion in Q and measuring deviations from direct proportion. For in take and . The parameter u is the hyperbolic angle to (x, y) and v is the geometric mean of x and y. The inverse mapping is . The function is a continuous mapping, but not an analytic function. (en) En matemáticas, las coordenadas hiperbólicas son un método útil para la localización de puntos en el primer cuadrante de un plano cartesiano. Las coordenadas hiperbólicas asumen los valores tales que: Para un punto en tenemos y El parámetro algumas veces es llamado ángulo hiperbólico y es la media geométrica. La transformación inversa es Esta es una transformación continua, pero no es una función analítica. (es) 수학에서 쌍곡 좌표계(영어: hyperbolic coordinates)는 직교 좌표 평면의 제 1사분면에 있는 점들을 위치시키는 방법이다 . 쌍곡 좌표계는 다음과 같이 정의된 쌍곡면의 값을 가진다: . HP에 있는 이 좌표계는 Q에 있는 정비례의 비교 연구와 정비례의 편차 측정 연구에서 유용하다. 에 있는 에 대해서 u와 v는 다음과 같다: 매개변수 u는 (x, y)의 이고 v는 x와 y의 기하 평균이다. 역 변환은 다음과 같다: . 함수 는 연속 함수지만 해석 함수는 아니다. (ko) Em matemática, as coordenadas hiperbólicas são um método útil para a localização de pontos no primeiro quadrante do plano cartesiano. As coordenadas hiperbólicas assumem valores tais que Para um ponto em temos e O parâmetro algumas vezes é chamado ângulo hiperbólico e a média geométrica. A transformação inversa é Esta é uma transformação contínua, mas não é uma função analítica. (pt) 在數學裏，雙曲坐標系（英語：Hyperbolic coordinates）是一種二維坐標系統。它可以用來表達一個點在二維平面的第一象限的位置。從雙曲坐標變換到直角坐標：、。有時候，參數稱為雙曲角，稱為幾何平均。反映射為、。這是一個連續函數，但不是一個解析函數。 (zh) Гиперболическая система координат в математике — система координат, позволяющая задать положение точек в первом квадранте Q декартовой плоскости. . Значения гиперболических координат принадлежат гиперболической плоскости, которая определяется так: . Данная система удобна для сравнения прямых пропорций из Q в логарифмической шкале и оценки отклонений от прямой пропорции. Для в примем и . Параметр u представляет собой к (x, y), в то время как v — среднее геометрическое x и y. Обратное отображение: . Функция непрерывна, но не является аналитической (ru)
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dcterms:subject	Hyperbolic geometry Coordinate systems
Wikipage page ID	1264398 (xsd:integer)
Wikipage revision ID	1121789649 (xsd:integer)
Link from a Wikipage to another Wikipage	Cartesian plane Proper time Algebraic function Hyperbolic angle Petal Rindler coordinates Curve Duopoly Electrical power Continuous mapping Analytic function Mathematics Measure (mathematics) Geometric mean Ohm's law Origin (mathematics) Frequency Geodesic Geometric series Leonhard Euler Line (mathematics) Logarithmic scale Horocycle Stock split Open problem E (mathematical constant) Economics Hyperbolic geometry Oxford University Press Isobaric process Legislator Urban density Thermodynamics Quadrature (mathematics) Representative democracy Theory of relativity Hermann Minkowski Isothermal process Hyperbola Hyperbolic geometry Hyperbolic motion Hyperbolic sector Hypersurface Archimedes Area Coordinate systems Work (thermodynamics) Poincaré half-plane model Population density Special relativity Squeeze mapping Gregoire de Saint-Vincent Ideal gas law Metric space Natural logarithm Open set Rectangle Wolfgang Rindler Unit square Wavelength Euclidean topology Direct proportion Exchange rate Transcendental function Introduction to the Analysis of the Infinite Basket of consumer goods Arithmetic series Hyperbolic plane Quadrature of the parabola A. A. de Sarasa
Link from a Wikipage to an external page	http://www.univ-nancy2.fr/DepPhilo/walter/papers/nes.pdf
sameAs	Hyperbolic coordinates Hyperbolic coordinates

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