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Statements

Subject Item: dbr:Calculus
dbo:wikiPageWikiLink: dbr:Curve

Subject Item: dbr:Carl_Friedrich_Gauss
dbo:wikiPageWikiLink: dbr:Curve

Subject Item: dbr:Cartesian_coordinate_system
dbo:wikiPageWikiLink: dbr:Curve

Subject Item: dbr:Cassini_oval
gold:hypernym: dbr:Curve

Subject Item: dbr:Pseudo-Euclidean_space
dbo:wikiPageWikiLink: dbr:Curve

Subject Item: dbr:Pursuit_curve
dbo:wikiPageWikiLink: dbr:Curve

Subject Item: dbr:Quadratic_function
dbo:wikiPageWikiLink: dbr:Curve

Subject Item: dbr:Quaternions_and_spatial_rotation
dbo:wikiPageWikiLink: dbr:Curve

Subject Item: dbr:Scale_invariance
dbo:wikiPageWikiLink: dbr:Curve

Subject Item: dbr:Science_of_Logic
dbo:wikiPageWikiLink: dbr:Curve

Subject Item: dbr:Elements_of_art
dbo:wikiPageWikiLink: dbr:Curve

Subject Item: dbr:Envelope_(waves)
gold:hypernym: dbr:Curve

Subject Item: dbr:List_of_curves
dbo:wikiPageWikiLink: dbr:Curve

Subject Item: dbr:List_of_curves_topics
dbo:wikiPageWikiLink: dbr:Curve

Subject Item: dbr:List_of_differential_geometry_topics
dbo:wikiPageWikiLink: dbr:Curve

Subject Item: dbr:Menger_sponge
dbo:wikiPageWikiLink: dbr:Curve
gold:hypernym: dbr:Curve

Subject Item: dbr:Meniscus
gold:hypernym: dbr:Curve

Subject Item: dbr:Motive_(algebraic_geometry)
dbo:wikiPageWikiLink: dbr:Curve

Subject Item: dbr:Lüroth_quartic
gold:hypernym: dbr:Curve

Subject Item: dbr:Method_of_normals
dbo:wikiPageWikiLink: dbr:Curve

Subject Item: dbr:Meusnier's_theorem
dbo:wikiPageWikiLink: dbr:Curve

Subject Item: dbr:Montgomery_curve
dbo:wikiPageWikiLink: dbr:Curve

Subject Item: dbr:Moore_curve
gold:hypernym: dbr:Curve

Subject Item: dbr:Mordell_curve
gold:hypernym: dbr:Curve

Subject Item: dbr:Troposkein
gold:hypernym: dbr:Curve

Subject Item: dbr:Path_integrals_in_polymer_science
dbo:wikiPageWikiLink: dbr:Curve

Subject Item: dbr:Prime_geodesic
dbo:wikiPageWikiLink: dbr:Curve
gold:hypernym: dbr:Curve

Subject Item: dbr:Time_series
dbo:wikiPageWikiLink: dbr:Curve

Subject Item: dbr:Prime_manifold
dbo:wikiPageWikiLink: dbr:Curve

Subject Item: dbr:Topological_curve
dbo:wikiPageWikiLink: dbr:Curve
dbo:wikiPageRedirects: dbr:Curve

Subject Item: dbr:Benoît_Paul_Émile_Clapeyron
dbo:wikiPageWikiLink: dbr:Curve

Subject Item: dbr:Book_embedding
dbo:wikiPageWikiLink: dbr:Curve

Subject Item: dbr:Alfvén's_theorem
dbo:wikiPageWikiLink: dbr:Curve

Subject Item: dbr:Algebraic_manifold
dbo:wikiPageWikiLink: dbr:Curve

Subject Item: dbr:Anosov_diffeomorphism
dbo:wikiPageWikiLink: dbr:Curve

Subject Item: dbr:Antarctic_Convergence
gold:hypernym: dbr:Curve

Subject Item: dbr:Arc_length
rdfs:seeAlso: dbr:Curve
dbo:wikiPageWikiLink: dbr:Curve

Subject Item: dbr:Areal_velocity
dbo:wikiPageWikiLink: dbr:Curve

Subject Item: dbr:History_of_bras
dbo:wikiPageWikiLink: dbr:Curve

Subject Item: dbr:History_of_the_function_concept
dbo:wikiPageWikiLink: dbr:Curve

Subject Item: dbr:Homotopy_groups_of_spheres
dbo:wikiPageWikiLink: dbr:Curve

Subject Item: dbr:Horseshoe_Curve_(Pennsylvania)
gold:hypernym: dbr:Curve

Subject Item: dbr:Hyperbolic_spiral
gold:hypernym: dbr:Curve

Subject Item: dbr:Jordan_curve_theorem
dbo:wikiPageWikiLink: dbr:Curve

Subject Item: dbr:Biarc
dbo:wikiPageWikiLink: dbr:Curve

Subject Item: dbr:List_of_Dutch_discoveries
dbo:wikiPageWikiLink: dbr:Curve

Subject Item: dbr:Resultant
dbo:wikiPageWikiLink: dbr:Curve

Subject Item: dbr:Curve
rdf:type: dbo:Band owl:Thing
rdfs:label: 曲线 Kurva Corba Καμπύλη Kromme Courbe Curve منحنى 曲線 Крива Kurva Linio (geometrio) Křivka 곡선 Kurve (Mathematik) Curva Cuar Krzywa Curva Кривая Kurba (matematika) Curva (matematica)
rdfs:comment: En kurva är ett begrepp inom geometri och matematisk analys. En kurva är en kontinuerlig avbildning från ett intervall I av de reella talen till ett topologiskt rum. Kurvan sägs vara sluten om och , det vill säga formad så, att om man åker längs kurvan återkommer man dit man startade. Om kurvan dessutom är injektiv på intervallet sägs den vara enkel. Det innebär att den inte skär sig själv. In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight. Intuitively, a curve may be thought of as the trace left by a moving point. This is the definition that appeared more than 2000 years ago in Euclid's Elements: "The [curved] line is […] the first species of quantity, which has only one dimension, namely length, without any width nor depth, and is nothing else than the flow or run of the point which […] will leave from its imaginary moving some vestige in length, exempt of any width." Dalam matematika, kurva (juga disebut garis lengkung dalam teks yang lebih tua) adalah objek yang mirip dengan garis yang tidak harus lurus. Secara intuitif, kurva dapat dianggap sebagai jejak yang ditinggalkan oleh titik bergerak. Ini adalah definisi yang muncul, lebih dari 2000 tahun yang lalu dalam buku : "Garis [melengkung] adalah [...] spesies kuantitas pertama, yang hanya memiliki satu dimensi, yaitu panjang, tanpa lebar atau kedalaman apa pun, dan tidak lain adalah aliran atau jalur dari titik yang [...] akan tinggalkan dari imajinernya, memindahkan beberapa sisa di panjang, dikecualikan dari lebar apa pun." 数学における曲線（きょくせん、英: curve, curved line）は、一般にまっすぐとは限らない幾何学的対象としての「線」を言う。つまり、曲線とは曲率が零とは限らないという意味での直線の一般化である。数学の様々な分野において、その研究領域に応じたそれぞれやや異なる意味で「曲線」の語が用いられる（から、精確な意味は文脈に即して捉えるべきである）が、それらの意味の多くは以下に挙げる定義の特別な実例になっているはずである。すなわち、曲線とは局所的に直線と同相であるような位相空間を言う。それは日常語で言えば、曲線は点の集合であって、それらの点が十分近くであれば直線のように見えるが、変形があってもよいというような意味である。数学の各分野で扱われる。最初に触れる曲線の簡単な例というのはほとんどの場合「平面曲線」（例えば平らな紙の上に描いた曲がった線）であろうが、螺旋のように三次元的なものもある。幾何学的な必要性や、例えば古典力学からの要請で任意次元の空間に埋め込まれた曲線の概念も必要とされる。一般相対論において世界線とは時空内の曲線である。注一般用語として、「曲線」が（成長曲線やフィリップス曲線の例に見るように）函数のグラフ、あるいはより多様なの意味で用いられることがあるが、本項で言う意味とは（近い関連はあるにせよ）異なるものと理解すべきである。 I réimse na matamaitice, líne is ea cuar nach bhfuil díreach (nó líne ar aon déanamh le stua ciorcail). In matematica, una curva è un oggetto unidimensionale e continuo, come ad esempio la circonferenza e la retta. Una curva può giacere su un piano, nello spazio euclideo, o in uno spazio topologico più generale. Una curva può essere pensata intuitivamente come la traiettoria descritta da un oggetto puntiforme che si muove con continuità in qualche spazio. Per definire la curva si fa ricorso alle nozioni di funzione continua e funzione differenziabile. Krzywa – uogólnienie linii prostej. Mimo intuicyjnej prostoty, pojęcie krzywej okazało się bardzo trudne do ścisłego zdefiniowania. Poprawna definicja powinna obejmować „dowolną linię” (w szczególności na płaszczyźnie lub przestrzeni trójwymiarowej), w tym także linię prostą, która mogłaby się rozgałęziać i przerywać. Křivka je v matematice geometrický jednorozměrný objekt, případně zobrazení z přímky do nějakého prostoru (tzv. parametrizovaná křivka). Jednoduché příklady křivek jsou přímka nebo kružnice. Matematiko > Geometrio > Linio Linio aŭ kurbo estas matematika termino, unu el fundamentaj terminoj de matematikaj fakoj kiel geometrio, diferenciala geometrio, topologio. La termino estas uzata en ĉiutaga lingvo. Linio (de lat. Linea - lina fadeno) estas unu el unuarangaj nocioj en geometrio. Difini ĝin estas nefacile kaj diversaj branĉoj de matematiko traktas ĝin malsame. En mathématiques, plus précisément en géométrie, une courbe, ou ligne courbe, est un objet du plan ou de l'espace usuel, similaire à une droite mais non nécessairement linéaire. Par exemple, les cercles, les droites, les segments et les lignes polygonales sont des courbes. La notion générale de courbe se décline en plusieurs objets mathématiques ayant des définitions assez proches : arcs paramétrés, lignes de niveau, sous-variétés de dimension 1. Schématiquement, ces différents modes d'introduction donnent des éclairages complémentaires sur la notion générale de courbe : Крива́я или ли́ния — геометрическое понятие, определяемое в разных разделах математики различно. في الرياضيات، المنحنى هو كائن رياضي يتألف من مجموعة من النقاط حيث تظهر النقاط المتجاورة كخط متشوه. ويكون الخط المستقيم حالة خاصة من المنحني، حيث أن نصف قطر الانحناء يصل إلى اللانهاية.ويمكن أن تكون المنحنيات ثنائية الأبعاد (المنحنيات في المستوي) أو ثلاثية الأبعاد (المنحنيات في الفراغ الإقليدي). من أبسط الأمثلة على المنحنيات الدائرة. Een kromme of curve (Latijn: curvus, gebogen, gekromd) is een in het algemeen niet-rechte lijn, met echter een rechte als bijzonder geval. Een kromme in twee dimensies is een vlakke kromme, een kromme in drie dimensies is een ruimtekromme. Afhankelijk van de context worden in de wiskunde specifiekere definities gebruikt. Een voorbeeld van een kromme is de grafiek van een continue functie. Corba és un terme abstracte que s'usa per descriure el camí d'un punt mogut contínuament. Tal camí és sovint generat per una equació. Exemples senzills són les circumferències, les el·lipses, els polígons, les paràboles, les corbes tècniques, les hipèrboles, les espirals i les rectes. In der Mathematik ist eine Kurve (von lateinisch curvus „gebogen, gekrümmt“) ein eindimensionales Objekt. Im Gegensatz etwa zu einer Geraden muss eine Kurve grundsätzlich keinen geraden, sondern kann vielmehr jeden beliebigen Verlauf annehmen. Je nach Teilgebiet der Mathematik gibt es unterschiedliche Präzisierungen dieser Beschreibung. Ως Καμπύλη γραμμή στη γεωμετρία χαρακτηρίζεται οποιαδήποτε γραμμή της οποίας κανένα τμήμα της δεν είναι ευθύγραμμο. Επίσης ορίζεται και ως γραμμή που μεταβάλλει κατεύθυνση χωρίς να σχηματίζει καμία γωνία. * Κάθε επιμέρους τμήμα μιας καμπύλης λέγεται καμπύλο τμήμα ή τόξο της καμπύλης. * Μια καμπύλη γραμμή λέγεται κλειστή όταν τα άκρα της συμπίπτουν. Το αντίθετο λέγεται ανοικτή. 수학에서 곡선(曲線)은 연속적인 점들의 집합으로, 어떤 공간 안에 존재하는 1차원적인 도형을 의미한다. 수학적인 의미에서 직선이나 선분은 곡선에 포함되며, 원이나 포물선 등도 곡선의 예이다. 曲（qū）线（curve，curved line）是平滑弯曲的线段或线条，也指动点运动方向连续变化的轨迹。 Em matemática, uma curva ou linha curva é, em termos gerais, um objeto semelhante a uma linha reta, mas que não é obrigatoriamente retilíneo. Tecnicamente, uma curva é o lugar geométrico ou trajetória seguida por um ponto que se move de acordo com uma ou mais leis especificadas, neste caso, as leis comporão uma condição necessária e suficiente para a existência do objeto definido. Frequentemente há maior interesse nas curvas em um espaço euclidiano de duas dimensões (curvas planas) ou três dimensões (curvas espaciais). Крива́ — лінія в евклідовому просторі або в многовиді. Рівняння кривої можна задавати в параметричній формі: де — координати точок кривої в деякій системі координат, заданій в евклідовому просторі або многовиді, а — скалярний параметр (його можна фізично уявляти моментом часу t=time, а саму криву як траєкторію руху точки) Розглянемо рівняння кривої в Декартовій системі координат -вимірного евклідового простору. Введемо позначення радіус-вектора точки кривої: Matematikan, kurba dimentsio bateko lerro jarraitua da, norabidea pixkanaka aldatzen duena. Kurba itxien adibideak elipsea eta zirkunferentzia dira. Parabola, hiperbola eta katenaria kurba irekiak dira. Zuzena erradio infinitu duen kurba da. En matemática (inicialmente estudiado en geometría elemental y, de forma más rigurosa, en geometría diferencial), la curva (o línea curva) es una línea continua de una dimensión, que varía de dirección paulatinamente. Ejemplos sencillos de curvas cerradas simples son la elipse o la circunferencia o el óvalo, el cicloide; ejemplos de , la parábola, la hipérbola y la catenaria y una infinidad de curvas estudiadas en la geometría analítica plana. La recta asume el caso límite de una circunferencia de radio de curvatura infinito y de curvatura 0; además, una recta es la de un intervalo abierto. Todas las curvas tienen dimensión topológica igual a 1. La noción curva, conjuntamente con la de superficie, es uno de los objetos primordiales de la geometría diferencial, ciertamente con profusa apl
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dcterms:subject: dbc:Curves dbc:Topology dbc:Metric_geometry dbc:General_topology
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dbp:author: A.S. Parkhomenko B.I. Golubov
dbp:date: May 2019
dbp:id: r/r080130 l/l059020
dbp:reason: This contradicts the definition given in Differential geometry of curves
dbp:title: Line Rectifiable curve
dbo:abstract: In matematica, una curva è un oggetto unidimensionale e continuo, come ad esempio la circonferenza e la retta. Una curva può giacere su un piano, nello spazio euclideo, o in uno spazio topologico più generale. Una curva può essere pensata intuitivamente come la traiettoria descritta da un oggetto puntiforme che si muove con continuità in qualche spazio. Per definire la curva si fa ricorso alle nozioni di funzione continua e funzione differenziabile. 数学における曲線（きょくせん、英: curve, curved line）は、一般にまっすぐとは限らない幾何学的対象としての「線」を言う。つまり、曲線とは曲率が零とは限らないという意味での直線の一般化である。数学の様々な分野において、その研究領域に応じたそれぞれやや異なる意味で「曲線」の語が用いられる（から、精確な意味は文脈に即して捉えるべきである）が、それらの意味の多くは以下に挙げる定義の特別な実例になっているはずである。すなわち、曲線とは局所的に直線と同相であるような位相空間を言う。それは日常語で言えば、曲線は点の集合であって、それらの点が十分近くであれば直線のように見えるが、変形があってもよいというような意味である。数学の各分野で扱われる。最初に触れる曲線の簡単な例というのはほとんどの場合「平面曲線」（例えば平らな紙の上に描いた曲がった線）であろうが、螺旋のように三次元的なものもある。幾何学的な必要性や、例えば古典力学からの要請で任意次元の空間に埋め込まれた曲線の概念も必要とされる。一般相対論において世界線とは時空内の曲線である。注一般用語として、「曲線」が（成長曲線やフィリップス曲線の例に見るように）函数のグラフ、あるいはより多様なの意味で用いられることがあるが、本項で言う意味とは（近い関連はあるにせよ）異なるものと理解すべきである。 수학에서 곡선(曲線)은 연속적인 점들의 집합으로, 어떤 공간 안에 존재하는 1차원적인 도형을 의미한다. 수학적인 의미에서 직선이나 선분은 곡선에 포함되며, 원이나 포물선 등도 곡선의 예이다. In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight. Intuitively, a curve may be thought of as the trace left by a moving point. This is the definition that appeared more than 2000 years ago in Euclid's Elements: "The [curved] line is […] the first species of quantity, which has only one dimension, namely length, without any width nor depth, and is nothing else than the flow or run of the point which […] will leave from its imaginary moving some vestige in length, exempt of any width." This definition of a curve has been formalized in modern mathematics as: A curve is the image of an interval to a topological space by a continuous function. In some contexts, the function that defines the curve is called a parametrization, and the curve is a parametric curve. In this article, these curves are sometimes called topological curves to distinguish them from more constrained curves such as differentiable curves. This definition encompasses most curves that are studied in mathematics; notable exceptions are level curves (which are unions of curves and isolated points), and algebraic curves (see below). Level curves and algebraic curves are sometimes called implicit curves, since they are generally defined by implicit equations. Nevertheless, the class of topological curves is very broad, and contains some curves that do not look as one may expect for a curve, or even cannot be drawn. This is the case of space-filling curves and fractal curves. For ensuring more regularity, the function that defines a curve is often supposed to be differentiable, and the curve is then said to be a differentiable curve. A plane algebraic curve is the zero set of a polynomial in two indeterminates. More generally, an algebraic curve is the zero set of a finite set of polynomials, which satisfies the further condition of being an algebraic variety of dimension one. If the coefficients of the polynomials belong to a field k, the curve is said to be defined over k. In the common case of a real algebraic curve, where k is the field of real numbers, an algebraic curve is a finite union of topological curves. When complex zeros are considered, one has a complex algebraic curve, which, from the topological point of view, is not a curve, but a surface, and is often called a Riemann surface. Although not being curves in the common sense, algebraic curves defined over other fields have been widely studied. In particular, algebraic curves over a finite field are widely used in modern cryptography. Matematikan, kurba dimentsio bateko lerro jarraitua da, norabidea pixkanaka aldatzen duena. Kurba itxien adibideak elipsea eta zirkunferentzia dira. Parabola, hiperbola eta katenaria kurba irekiak dira. Zuzena erradio infinitu duen kurba da. في الرياضيات، المنحنى هو كائن رياضي يتألف من مجموعة من النقاط حيث تظهر النقاط المتجاورة كخط متشوه. ويكون الخط المستقيم حالة خاصة من المنحني، حيث أن نصف قطر الانحناء يصل إلى اللانهاية.ويمكن أن تكون المنحنيات ثنائية الأبعاد (المنحنيات في المستوي) أو ثلاثية الأبعاد (المنحنيات في الفراغ الإقليدي). من أبسط الأمثلة على المنحنيات الدائرة. 曲（qū）线（curve，curved line）是平滑弯曲的线段或线条，也指动点运动方向连续变化的轨迹。 Corba és un terme abstracte que s'usa per descriure el camí d'un punt mogut contínuament. Tal camí és sovint generat per una equació. Exemples senzills són les circumferències, les el·lipses, els polígons, les paràboles, les corbes tècniques, les hipèrboles, les espirals i les rectes. En mathématiques, plus précisément en géométrie, une courbe, ou ligne courbe, est un objet du plan ou de l'espace usuel, similaire à une droite mais non nécessairement linéaire. Par exemple, les cercles, les droites, les segments et les lignes polygonales sont des courbes. La notion générale de courbe se décline en plusieurs objets mathématiques ayant des définitions assez proches : arcs paramétrés, lignes de niveau, sous-variétés de dimension 1. Schématiquement, ces différents modes d'introduction donnent des éclairages complémentaires sur la notion générale de courbe : * une courbe peut être décrite par un point qui se meut suivant une loi déterminée. La donnée d'une valeur du paramètre temps permet alors de repérer un point sur la courbe. Intuitivement, cela signifie que les courbes sont des objets de dimension 1 ; * une courbe peut être vue comme un domaine du plan ou de l'espace qui vérifie un nombre suffisant de conditions, lui conférant encore un caractère unidimensionnel. Ainsi, une courbe plane peut être représentée dans un repère cartésien par la donnée de lois décrivant abscisse et ordonnée en fonction du paramètre (équation paramétrique) : ; dans le cas d'une courbe régulière, on peut déterminer alors un paramétrage adapté (pour lequel le vecteur vitesse est unitaire), l’abscisse curviligne, qui permet également de définir la longueur ; la courbe peut aussi être représentée par la donnée d'une équation cartésienne, ou implicite : . I réimse na matamaitice, líne is ea cuar nach bhfuil díreach (nó líne ar aon déanamh le stua ciorcail). Een kromme of curve (Latijn: curvus, gebogen, gekromd) is een in het algemeen niet-rechte lijn, met echter een rechte als bijzonder geval. Een kromme in twee dimensies is een vlakke kromme, een kromme in drie dimensies is een ruimtekromme. Afhankelijk van de context worden in de wiskunde specifiekere definities gebruikt. Een voorbeeld van een kromme is de grafiek van een continue functie. Em matemática, uma curva ou linha curva é, em termos gerais, um objeto semelhante a uma linha reta, mas que não é obrigatoriamente retilíneo. Tecnicamente, uma curva é o lugar geométrico ou trajetória seguida por um ponto que se move de acordo com uma ou mais leis especificadas, neste caso, as leis comporão uma condição necessária e suficiente para a existência do objeto definido. Frequentemente há maior interesse nas curvas em um espaço euclidiano de duas dimensões (curvas planas) ou três dimensões (curvas espaciais). Em tópicos diferentes dentro da matemática o termo possui significados distintos dependendo da área de estudo, então o sentido exato depende do contexto. Um exemplo simples de uma curva é a espiral, mostrada a direita. Um grande número de outras curvas já foi bem estudado em diversos campos da matemática. O termo curva também tem vários significados na linguagem não matemática. Por exemplo, ele pode ser quase um sinônimo de função matemática (como em curva de aprendizado), ou gráfico de uma função (como em curva de Phillips) Se o intervalo for fechado e as imagens dos pontos inicial e final coincidirem a curva diz-se fechada.Se a função for injectiva (exceptuando a possibilidade de a curva ser fechada), a curva diz-se simples.A curva pode ainda ser adjectivada com as propriedades adicionais que tenha a função. Por exemplo, se a função for diferenciável, a curva diz-se diferenciável, etc. Křivka je v matematice geometrický jednorozměrný objekt, případně zobrazení z přímky do nějakého prostoru (tzv. parametrizovaná křivka). Jednoduché příklady křivek jsou přímka nebo kružnice. Ως Καμπύλη γραμμή στη γεωμετρία χαρακτηρίζεται οποιαδήποτε γραμμή της οποίας κανένα τμήμα της δεν είναι ευθύγραμμο. Επίσης ορίζεται και ως γραμμή που μεταβάλλει κατεύθυνση χωρίς να σχηματίζει καμία γωνία. * Κάθε επιμέρους τμήμα μιας καμπύλης λέγεται καμπύλο τμήμα ή τόξο της καμπύλης. * Μια καμπύλη γραμμή λέγεται κλειστή όταν τα άκρα της συμπίπτουν. Το αντίθετο λέγεται ανοικτή. Επίσης τόσο στη γεωμετρία όσο και στη φυσική ως καμπύλη ορίζεται η γραμμή που παριστά τις διαδοχικές θέσεις ενός σημείου που κινείται, όχι ευθύγραμμα, σύμφωνα με κάποιο καθορισμένο νόμο. Έτσι η περιφέρεια κύκλου είναι κλειστή καμπύλη της οποίας όλα τα σημεία απέχουν ίση απόσταση από κάποιο άλλο εκτός σημείο (κέντρο).Στις γραφικές παραστάσεις η καμπύλη παριστά μεταβολές κατάστασης ή εκφράζει νόμους ενός φαινομένου (συντεταγμένες), π.χ. βαρομετρική καμπύλη, μεταβολής θερμοκρασίας κ.λπ). Στην αρχαία ελληνική υπονοώντας τη λέξη ως "καμπύλες" χαρακτηρίζονταν οι ράβδοι που κρατούσαν οι χωρικοί, οι ζητιάνοι, οι ταξιδιώτες, οι παιδαγωγοί κ.λπ σε αντίθεση με τους πλούσιους που κρατούσαν τις "ορθές" (βακτηρίες). Крива́я или ли́ния — геометрическое понятие, определяемое в разных разделах математики различно. In der Mathematik ist eine Kurve (von lateinisch curvus „gebogen, gekrümmt“) ein eindimensionales Objekt. Im Gegensatz etwa zu einer Geraden muss eine Kurve grundsätzlich keinen geraden, sondern kann vielmehr jeden beliebigen Verlauf annehmen. Eindimensional bedeutet dabei informell, dass man sich auf der Kurve nur in eine Richtung (bzw. in die Gegenrichtung) bewegen kann. Ob die Kurve in der zweidimensionalen Ebene liegt („ebene Kurve“), in einem höherdimensionalen Raum (siehe Raumkurve), oder gar in einer Mannigfaltigkeit (beispielsweise in einer Lorentzschen Mannigfaltigkeit) ist in diesem begrifflichen Zusammenhang unerheblich. Je nach Teilgebiet der Mathematik gibt es unterschiedliche Präzisierungen dieser Beschreibung. Dalam matematika, kurva (juga disebut garis lengkung dalam teks yang lebih tua) adalah objek yang mirip dengan garis yang tidak harus lurus. Secara intuitif, kurva dapat dianggap sebagai jejak yang ditinggalkan oleh titik bergerak. Ini adalah definisi yang muncul, lebih dari 2000 tahun yang lalu dalam buku : "Garis [melengkung] adalah [...] spesies kuantitas pertama, yang hanya memiliki satu dimensi, yaitu panjang, tanpa lebar atau kedalaman apa pun, dan tidak lain adalah aliran atau jalur dari titik yang [...] akan tinggalkan dari imajinernya, memindahkan beberapa sisa di panjang, dikecualikan dari lebar apa pun." Definisi kurva ini telah diformalkan dalam matematika modern sebagai: Sebuah Kurva adalah gambar fungsi kontinu dari suatu interval ke ruang topologi. Dalam beberapa konteks, fungsi yang mendefinisikan kurva disebut parametrization, dan kurva adalah . Dalam artikel ini, kurva ini kadang-kadang disebut kurva topologi untuk membedakannya dari kurva yang lebih terbatas seperti kurva yang dapat dibedakan. Definisi ini mencakup sebagian besar kurva yang dipelajari dalam matematika; pengecualian yang menonjol adalah (yang merupakan gabungan dari kurva dan titik yang terisolasi), dan (lihat di bawah). Kurva level dan kurva aljabar kadang-kadang disebut , karena mereka umumnya didefinisikan oleh . Namun demikian, kelas kurva topologi sangat luas, dan mengandung beberapa kurva yang tidak terlihat seperti yang diharapkan seseorang untuk kurva, atau bahkan tidak dapat ditarik. Ini adalah kasus kurva mengisi ruang dan . Untuk mengasuransikan lebih banyak keteraturan, fungsi yang mendefinisikan suatu kurva sering kali dianggap dapat dibedakan, dan kurva tersebut kemudian dikatakan . Krzywa – uogólnienie linii prostej. Mimo intuicyjnej prostoty, pojęcie krzywej okazało się bardzo trudne do ścisłego zdefiniowania. Poprawna definicja powinna obejmować „dowolną linię” (w szczególności na płaszczyźnie lub przestrzeni trójwymiarowej), w tym także linię prostą, która mogłaby się rozgałęziać i przerywać. En matemática (inicialmente estudiado en geometría elemental y, de forma más rigurosa, en geometría diferencial), la curva (o línea curva) es una línea continua de una dimensión, que varía de dirección paulatinamente. Ejemplos sencillos de curvas cerradas simples son la elipse o la circunferencia o el óvalo, el cicloide; ejemplos de , la parábola, la hipérbola y la catenaria y una infinidad de curvas estudiadas en la geometría analítica plana. La recta asume el caso límite de una circunferencia de radio de curvatura infinito y de curvatura 0; además, una recta es la de un intervalo abierto. Todas las curvas tienen dimensión topológica igual a 1. La noción curva, conjuntamente con la de superficie, es uno de los objetos primordiales de la geometría diferencial, ciertamente con profusa aplicación de las herramientas del cálculo diferencial. Matematiko > Geometrio > Linio Linio aŭ kurbo estas matematika termino, unu el fundamentaj terminoj de matematikaj fakoj kiel geometrio, diferenciala geometrio, topologio. La termino estas uzata en ĉiutaga lingvo. Linio (de lat. Linea - lina fadeno) estas unu el unuarangaj nocioj en geometrio. Difini ĝin estas nefacile kaj diversaj branĉoj de matematiko traktas ĝin malsame. En kurva är ett begrepp inom geometri och matematisk analys. En kurva är en kontinuerlig avbildning från ett intervall I av de reella talen till ett topologiskt rum. Kurvan sägs vara sluten om och , det vill säga formad så, att om man åker längs kurvan återkommer man dit man startade. Om kurvan dessutom är injektiv på intervallet sägs den vara enkel. Det innebär att den inte skär sig själv. Exempel på slutna kurvor är cirklar och ellipser. En kurva som är både sluten och enkel säges helt enkelt vara en enkel sluten kurva, eller en Jordankurva. Enligt Jordans kurvsats delar en sådan kurva in ett plan i två delar; en inre och en yttre del. I exempelvis komplex analys talar man om positiva respektive negativa leder runt enkla slutna kurvor. Genom avbildningen definieras en riktning på kurvan. Riktningen sägs vara i positiv led om den går ett varv moturs runt varje punkt som kurvan omsluter. Ett exempel på en kurva som går i positivt led är då går från 0 till . Kurvintegraler över en enkel sluten kurva i det komplexa planet byter tecken om man byter riktning. Крива́ — лінія в евклідовому просторі або в многовиді. Рівняння кривої можна задавати в параметричній формі: де — координати точок кривої в деякій системі координат, заданій в евклідовому просторі або многовиді, а — скалярний параметр (його можна фізично уявляти моментом часу t=time, а саму криву як траєкторію руху точки) Розглянемо рівняння кривої в Декартовій системі координат -вимірного евклідового простору. Введемо позначення радіус-вектора точки кривої:
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