Proportionality (mathematics) (original) (raw)
في الرياضيات، يقال عن متغيرين اثنين إنهما متناسبين إذا كان تغير أحدهما يؤدي حتما إلى تغير الآخر، و يُحصل على قيم المتغير الثاني بضرب قيم المتغير الأول في عدد معين ثابت ما. هذا العدد الثابت المعين يسمى معامل التناسب.
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| dbo:abstract | في الرياضيات، يقال عن متغيرين اثنين إنهما متناسبين إذا كان تغير أحدهما يؤدي حتما إلى تغير الآخر، و يُحصل على قيم المتغير الثاني بضرب قيم المتغير الأول في عدد معين ثابت ما. هذا العدد الثابت المعين يسمى معامل التناسب. (ar) La proporcionalitat és una relació entre magnituds mesurables. És un dels escassos conceptes matemàtics àmpliament difós en la població. Això es deu al fet que és en bona part intuïtiu i d'ús molt comú. Un factor d'escala és un nombre que balança, o multiplica, alguna quantitat. En l'equació y= Cx, C és el factor d'escala per x. C És també el coeficient de x, i pot ser anomenat la constant de proporcionalitat de y a x. En el camp de mides, el factor d'escala d'un instrument és de vegades referit a la sensibilitat. La proporció de qualsevol de les dues longituds corresponents dins dues figures geomètriques similars és també anomenat un factor d'escala. (ca) Úměrností je v matematice závislost, která zachovává konstantní poměr (přímá úměrnost) nebo součin (nepřímá úměrnost) dvou veličin. V běžném životě i ve fyzikálních zákonech se jedná o nejběžnější funkční závislosti. (cs) Στα μαθηματικά δυο μεγέθη καλούνται ανάλογα όταν οι τιμές τους του ενός είναι πολλαπλάσια των τιμών του άλλου, δηλαδή όταν οι αντίστοιχες τιμές των δύο μεγεθών έχουν σταθερό λόγο. (el) Zwischen zwei veränderlichen Größen besteht Proportionalität, wenn sie immer in demselben Verhältnis zueinander stehen. (de) Matematikan, x eta y bi magnitude proportzionalak direla esaten da, batean izandako aldaketa batek bestean ere aldaketa bat dakarrenean, biderkatzaile baten arabera. Hain zuzen: * x eta y zuzenki proportzionalak direla esaten da, baldin eta y=kx betetzen bada, non k proportzionaltasun-konstantea den; * x eta y alderantziz proportzionalak direla esaten da, baldin eta y=k/x betetzen bada. (eu) La proporcionalidad es una relación o razón constante entre diferentes magnitudes que se vayan a medir. (es) En mathématiques, on dit que deux suites de nombres sont proportionnelles quand, en multipliant (ou en divisant) par une même constante non nulle, les termes de l'une on obtient les termes de l'autre. Le facteur constant entre l'une et l'autre de ces suites est appelé coefficient de proportionnalité. Ces suites de nombres étant par exemple des grandeurs mesurées. Exemple : dans un magasin, le prix des pommes est de 2 euros le kilogramme. Il y a proportionnalité entre la somme S à payer et le poids P de pommes achetées, avec un coefficient de proportionnalité égal à 2. * pour 1 kg, on doit payer 2 euros ; * pour 3 kg, on doit payer 6 euros ; * pour 1,5 kg, on doit payer 3 euros ; * pour 5 kg, on doit payer 10 euros ; * pour 10 kg, on doit payer 20 euros,le quotient est constant et est égal au coefficient de proportionnalité : . Les Anciens comme Euclide auraient écrit que 2 est à 1 comme 6 est à 3 ou comme 3 est à 1,5. La proportionnalité peut être représentée par le symbole ∝, « I ∝ V » signifiant « I est proportionnel à V ». (fr) In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio, which is called the coefficient of proportionality or proportionality constant. Two sequences are inversely proportional if corresponding elements have a constant product, also called the coefficient of proportionality. This definition is commonly extended to related varying quantities, which are often called variables. This meaning of variable is not the common meaning of the term in mathematics (see variable (mathematics)); these two different concepts share the same name for historical reasons. Two functions and are proportional if their ratio is a constant function. If several pairs of variables share the same direct proportionality constant, the equation expressing the equality of these ratios is called a proportion, e.g., a/b = x/y = ⋯ = k (for details see Ratio).Proportionality is closely related to linearity. (en) Dalam matematika, dua variabel dikatakan sebanding atau berada dalam hubungan proporsionalitas/kesebandingan, jika keduanya saling terkait melalui perkalian dengan sebuah konstanta atau tetapan. Misalnya, jika kedua variabel tersebut memiliki rasio yang tetap atau konstan, maka kedua variabel tersebut disebut sebanding atau berbanding lurus. Jika kedua variabel tersebut memiliki hasil kali yang tetap, maka disebut "berbanding terbalik". Nilai dari konstanta (rasio atau hasil kali) tersebut disebut koefisien proporsionalitas atau tetapan proporsionalitas. (in) 비례(比例, proportionality)는 두 양이 서로 일정비율로 증가하거나 감소하는 관계이다. 보통 세 개 이상의 양을 비교하기 위해 비례식을 세울 때에는 비교적 복잡한 계산이 따르므로 수학에서는 일반적으로 비례식을 세울 때에는 두 양의 비로 간단히 표현한다. 비례를 수식으로 설명하면 다음과 같다. 두 변수 x, y에 대해, (a는 실수,상수),(k는 0이아닌 실수,상수)가 있다고 하면에서 x가 (일정한값)으로 정해질때 , 는 항상 (일정한값)×k만큼 변하는 관계를 비례라고 한다. 하나 주의해야 할 것은 비례관계를 비례식 꼴로 나타낼 수 있는 경우와 나타낼 수 없는 경우가 있는데, 비례식으로 나타낼 수 있는 경우는 정비례와 반비례의 경우뿐이다. (ko) In matematica, due variabili e si dicono direttamente proporzionali se esiste una relazione funzionale della forma: caratterizzata da una costante numerica non nulla . (it) 比例（ひれい、英: proportionality）とは、変数を用いて書かれる二つの量に対し一方が他方の定数倍であるような関係のことである。 (ja) Evenredigheid is in de wiskunde het verband tussen twee grootheden waarbij de verhouding of het product constant is en niet nul. In het eerste geval is het verband recht evenredig, in het tweede omgekeerd evenredig. De term evenredig is bedacht door de wetenschapper Simon Stevin. (nl) Пропорциональными называются две взаимно зависимые величины, если отношение их значений остаётся неизменным. Равенство между отношениями двух или нескольких пар чисел или величин в математике называется пропорцией. Для обозначения пропорциональных величин используется символ (Юникод: U+223C ∼ tilde operator) подобно тому как используется знак равенства. Например, означает, что величина постоянна. В англоязычной литературе обычно используется знак (Юникод: U+221D ∝ proportional to): (ru) Proporcjonalność prosta – zależność między dwiema zmiennymi wielkościami x i y, w której iloraz tych wielkości jest stały (y/x = const). Prowadzi to do wzoru gdzie a jest liczbą rzeczywistą różną od 0, pozwalającego wyliczyć jedną z nich w zależności od drugiej. Obie wielkości są wprost proporcjonalne. (pl) A proporcionalidade, para a matemática, a química e a física, é a mais simples e comum relação entre grandezas. A proporcionalidade direta é um conceito matemático amplamente difundido na população leiga pois é bastante útil e de fácil resolução através da "regra de três". Quando existe proporcionalidade direta, a razão (divisão) entre os correspondentes valores das duas grandezas relacionadas é uma constante, e a esta constante dá-se o nome de constante de proporcionalidade. (pt) Inom matematiken är två kvantiteter proportionella om den ena kvantiteten är en konstant multipel av den andra, det vill säga om deras förhållande är konstant. (sv) 在数学上，要定义“比例”，必须先定义“比”。比（ratio）是兩個非零數量 與 之間的比較關係，記為 ，在計算時則常写作： 或 。 比例（proportion）或比例式，是“两个比”相等的式子；表示同类型（相同单位）的“两个比之间”的关系。因此，比值相等的两个比才能组成比例，且比例必须以等式的形式呈现。例如： 或 才能称作比例，而 或 只能称作比。 组成比例的四个数，称为比例的项；等式最两端的两项称为外项，等式中央的两项称为内项。与比不同的是：比由两个数组成；比例由四个数组成。 若两个變量的关系符合：其中一个量等于另一个量乘以一个常数 （， 稱為 比例常数 或 比例係數），或等价地表达为：两變數的比值為一個定值（此定值或商，稱為 比（ratio），但比的定义不限于定值），则称两者是“成比例的”，或称两者“成正比”。 若几对变量共享相同的直接比例常数，则表示这些比值相等的方程称为比例式（proportion）或等比关系。例如：b/a = y/x = ⋯ = k 。比例性（proportionality）则与线性关系（linearity）密切相关。 (zh) Пропорційними називаються дві взаємно залежні величини, якщо відношення їх значень залишається незмінним. Рівність між відношеннями двох чи декількох пар чисел або величин в математиці називається пропорцією. (uk) |
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| rdfs:comment | في الرياضيات، يقال عن متغيرين اثنين إنهما متناسبين إذا كان تغير أحدهما يؤدي حتما إلى تغير الآخر، و يُحصل على قيم المتغير الثاني بضرب قيم المتغير الأول في عدد معين ثابت ما. هذا العدد الثابت المعين يسمى معامل التناسب. (ar) Úměrností je v matematice závislost, která zachovává konstantní poměr (přímá úměrnost) nebo součin (nepřímá úměrnost) dvou veličin. V běžném životě i ve fyzikálních zákonech se jedná o nejběžnější funkční závislosti. (cs) Στα μαθηματικά δυο μεγέθη καλούνται ανάλογα όταν οι τιμές τους του ενός είναι πολλαπλάσια των τιμών του άλλου, δηλαδή όταν οι αντίστοιχες τιμές των δύο μεγεθών έχουν σταθερό λόγο. (el) Zwischen zwei veränderlichen Größen besteht Proportionalität, wenn sie immer in demselben Verhältnis zueinander stehen. (de) Matematikan, x eta y bi magnitude proportzionalak direla esaten da, batean izandako aldaketa batek bestean ere aldaketa bat dakarrenean, biderkatzaile baten arabera. Hain zuzen: * x eta y zuzenki proportzionalak direla esaten da, baldin eta y=kx betetzen bada, non k proportzionaltasun-konstantea den; * x eta y alderantziz proportzionalak direla esaten da, baldin eta y=k/x betetzen bada. (eu) La proporcionalidad es una relación o razón constante entre diferentes magnitudes que se vayan a medir. (es) Dalam matematika, dua variabel dikatakan sebanding atau berada dalam hubungan proporsionalitas/kesebandingan, jika keduanya saling terkait melalui perkalian dengan sebuah konstanta atau tetapan. Misalnya, jika kedua variabel tersebut memiliki rasio yang tetap atau konstan, maka kedua variabel tersebut disebut sebanding atau berbanding lurus. Jika kedua variabel tersebut memiliki hasil kali yang tetap, maka disebut "berbanding terbalik". Nilai dari konstanta (rasio atau hasil kali) tersebut disebut koefisien proporsionalitas atau tetapan proporsionalitas. (in) 비례(比例, proportionality)는 두 양이 서로 일정비율로 증가하거나 감소하는 관계이다. 보통 세 개 이상의 양을 비교하기 위해 비례식을 세울 때에는 비교적 복잡한 계산이 따르므로 수학에서는 일반적으로 비례식을 세울 때에는 두 양의 비로 간단히 표현한다. 비례를 수식으로 설명하면 다음과 같다. 두 변수 x, y에 대해, (a는 실수,상수),(k는 0이아닌 실수,상수)가 있다고 하면에서 x가 (일정한값)으로 정해질때 , 는 항상 (일정한값)×k만큼 변하는 관계를 비례라고 한다. 하나 주의해야 할 것은 비례관계를 비례식 꼴로 나타낼 수 있는 경우와 나타낼 수 없는 경우가 있는데, 비례식으로 나타낼 수 있는 경우는 정비례와 반비례의 경우뿐이다. (ko) In matematica, due variabili e si dicono direttamente proporzionali se esiste una relazione funzionale della forma: caratterizzata da una costante numerica non nulla . (it) 比例（ひれい、英: proportionality）とは、変数を用いて書かれる二つの量に対し一方が他方の定数倍であるような関係のことである。 (ja) Evenredigheid is in de wiskunde het verband tussen twee grootheden waarbij de verhouding of het product constant is en niet nul. In het eerste geval is het verband recht evenredig, in het tweede omgekeerd evenredig. De term evenredig is bedacht door de wetenschapper Simon Stevin. (nl) Пропорциональными называются две взаимно зависимые величины, если отношение их значений остаётся неизменным. Равенство между отношениями двух или нескольких пар чисел или величин в математике называется пропорцией. Для обозначения пропорциональных величин используется символ (Юникод: U+223C ∼ tilde operator) подобно тому как используется знак равенства. Например, означает, что величина постоянна. В англоязычной литературе обычно используется знак (Юникод: U+221D ∝ proportional to): (ru) Proporcjonalność prosta – zależność między dwiema zmiennymi wielkościami x i y, w której iloraz tych wielkości jest stały (y/x = const). Prowadzi to do wzoru gdzie a jest liczbą rzeczywistą różną od 0, pozwalającego wyliczyć jedną z nich w zależności od drugiej. Obie wielkości są wprost proporcjonalne. (pl) A proporcionalidade, para a matemática, a química e a física, é a mais simples e comum relação entre grandezas. A proporcionalidade direta é um conceito matemático amplamente difundido na população leiga pois é bastante útil e de fácil resolução através da "regra de três". Quando existe proporcionalidade direta, a razão (divisão) entre os correspondentes valores das duas grandezas relacionadas é uma constante, e a esta constante dá-se o nome de constante de proporcionalidade. (pt) Inom matematiken är två kvantiteter proportionella om den ena kvantiteten är en konstant multipel av den andra, det vill säga om deras förhållande är konstant. (sv) 在数学上，要定义“比例”，必须先定义“比”。比（ratio）是兩個非零數量 與 之間的比較關係，記為 ，在計算時則常写作： 或 。 比例（proportion）或比例式，是“两个比”相等的式子；表示同类型（相同单位）的“两个比之间”的关系。因此，比值相等的两个比才能组成比例，且比例必须以等式的形式呈现。例如： 或 才能称作比例，而 或 只能称作比。 组成比例的四个数，称为比例的项；等式最两端的两项称为外项，等式中央的两项称为内项。与比不同的是：比由两个数组成；比例由四个数组成。 若两个變量的关系符合：其中一个量等于另一个量乘以一个常数 （， 稱為 比例常数 或 比例係數），或等价地表达为：两變數的比值為一個定值（此定值或商，稱為 比（ratio），但比的定义不限于定值），则称两者是“成比例的”，或称两者“成正比”。 若几对变量共享相同的直接比例常数，则表示这些比值相等的方程称为比例式（proportion）或等比关系。例如：b/a = y/x = ⋯ = k 。比例性（proportionality）则与线性关系（linearity）密切相关。 (zh) Пропорційними називаються дві взаємно залежні величини, якщо відношення їх значень залишається незмінним. Рівність між відношеннями двох чи декількох пар чисел або величин в математиці називається пропорцією. (uk) La proporcionalitat és una relació entre magnituds mesurables. És un dels escassos conceptes matemàtics àmpliament difós en la població. Això es deu al fet que és en bona part intuïtiu i d'ús molt comú. (ca) En mathématiques, on dit que deux suites de nombres sont proportionnelles quand, en multipliant (ou en divisant) par une même constante non nulle, les termes de l'une on obtient les termes de l'autre. Le facteur constant entre l'une et l'autre de ces suites est appelé coefficient de proportionnalité. Ces suites de nombres étant par exemple des grandeurs mesurées. Exemple : dans un magasin, le prix des pommes est de 2 euros le kilogramme. Il y a proportionnalité entre la somme S à payer et le poids P de pommes achetées, avec un coefficient de proportionnalité égal à 2. (fr) In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio, which is called the coefficient of proportionality or proportionality constant. Two sequences are inversely proportional if corresponding elements have a constant product, also called the coefficient of proportionality. Two functions and are proportional if their ratio is a constant function. (en) |
| rdfs:label | تناسب (رياضيات) (ar) التناسبية (ar) Proporcionalitat (ca) Úměrnost (cs) Proportionalität (de) Αναλογία (μαθηματικά) (el) Proporcionalidad (es) Proportzionaltasun (matematika) (eu) Proportionnalité (fr) Kesebandingan (matematika) (in) Proporzionalità (matematica) (it) 比例 (ja) 비례 (ko) Evenredigheid (nl) Proportionality (mathematics) (en) Proporcjonalność prosta (pl) Пропорциональность (ru) Proporcionalidade (pt) Proportionalitet (matematik) (sv) Пропорційність (математика) (uk) 比例 (zh) |
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