| Information | |
|---|---|
| has gloss | (noun) a curve or surface whose equation (in Cartesian coordinates) is of the second degree quadric, quadric surface |
| has gloss | eng: In mathematics, a quadric, or quadric surface, is any D-dimensional hypersurface in (D + 1)-dimensional space defined as the locus of zeros of a quadratic polynomial. In coordinates }, the general quadric is defined by the algebraic equation |
| lexicalization | eng: quadric surface |
| lexicalization | eng: Quadrics |
| lexicalization | eng: quadric |
| subclass of | (noun) the trace of a point whose direction of motion changes curve, curved shape |
| has subclass | (noun) a quadric surface generated by rotating a hyperbola around its main axis hyperboloid |
| has instance | e/Hypercone |
| has instance | e/Klein quadric |
| has instance | e/Oblate spheroid |
| has instance | e/Prolate |
| has instance | e/Quadric (projective geometry) |
| has instance | e/pt/Oblato |
| has instance | e/sv/Elliptisk paraboloid |
| has instance | e/vi/Mặt trụ |
| Meaning | |
|---|---|
| Arabic | |
| has gloss | ara: في الهندسة الرياضية، سطح الدرجة الثانية أو السطح الثنائي (Quadric Surface) هو أي سطح فائق في فضاء متعدد الأبعاد تحقق نقاطه أنها جذور كثير حدود من الدرجة الثانية. يمكن القول بأن سطح الدرجة الثانية هو أي سطح يقطعه مستقيم ما في نقطتين أو بمعنى آخر هو السطح الذي يقطعه مستوى ما في قطع مخروطي. |
| lexicalization | ara: سطح ثنائي |
| lexicalization | ara: سطح درجة ثانية |
| Catalan | |
| has gloss | cat: En matemàtiques, una quàdrica o superfície quàdrica és una hipersuperfície definida en un espai vectorial n-dimensional, pels punts que anul·len un polinomi quadràtic. Si les coordenades daquest espai són \left\x_1},x_2},...,x_n}\right\}\,, lequació de qualsevol quàdrica en aquest espai serà \sum_i,j=1}^n}P_i,j}x_i}x_j}+\sum_k=1}^n}Q_k}x_k}+R=0\,, on no tots els valors de P_(i,j)}\, són iguals a 0\,. En general, els coeficients daquesta equació seran valors de qualsevol cos, sobre el que sha definit lespai vectorial. Malgrat això, a partir dara, només considerarem quàdriques sobre el cos \mathbbR}\,. |
| lexicalization | cat: quàdrica |
| lexicalization | cat: Superfícies quàdriques |
| Show unreliable ▼ | |
| lexicalization | cat: quàdric |
| Mandarin Chinese | |
| lexicalization | cmn: èr cì qū mian |
| lexicalization | cmn: 二次曲面 |
| Danish | |
| has gloss | dan: En keglesnitsflade er en algebraisk flade af anden orden i tre variable. Dette begrundes med at fællesmængden mellem en algebraisk flade af anden orden og en plan er et keglesnit. |
| lexicalization | dan: keglesnitsflade |
| German | |
| has gloss | deu: Eine Quadrik oder auch Fläche zweiter Ordnung ist, in Abhängigkeit von der Anzahl der Variablen, eine Kurve, Fläche oder Hyperfläche zweiter Ordnung. Ihre Gleichung entsteht durch Nullsetzen einer quadratischen Funktion. |
| lexicalization | deu: Quadrik |
| Esperanto | |
| has gloss | epo: En matematiko kvadriko, aŭ kvadrika surfaco, estas D-dimensia hipersurfaco difinita kiel situo de nuloj de kvadrata polinomo. En koordinatoj \x_0, x_1, x_2, \ldots, x_D\} en D+1-dimensia spaco, la ĝenerala kvadriko estas difinita per la algebra ekvacio |
| lexicalization | epo: Kvadrikoj |
| lexicalization | epo: kvadriko |
| French | |
| has gloss | fra: En mathématiques, et plus précisément en géométrie euclidienne, une quadrique, ou surface quadratique, est une surface de l'espace euclidien de dimension 3, lieu des points vérifiant une équation cartésienne de degré 2 :Ax^2+By^2+Cz^2+2Dyz+2Exz+2Fxy+Gx+Hy+Iz+J=0 les coefficients A à J étant réels, avec A,B,C,D,E,F non tous nuls. |
| lexicalization | fra: quadrique |
| Italian | |
| has gloss | ita: In matematica e in particolare in geometria una quadrica (o superficie quadrica) è una (iper-)superficie di uno spazio D-dimensionale sui complessi o sui reali rappresentata da unequazione polinomiale del secondo ordine nelle variabili spaziali (coordinate). Se le coordinate spaziali sono \x_1, x_2, ... x_D\}, allora la generale quadrica nello spazio CD (o RD) è definita da unequazione della forma : \sum_i,j=1}^D Q_i,j} x_i x_j + \sum_i=1}^D P_i x_i + R = 0, dove Q è una matrice (non nulla), P un vettore e R una costante. |
| lexicalization | ita: quadrica |
| Japanese | |
| has gloss | jpn: 二次超曲面（にじちょうきょくめん、quadric surface）とは、円錐曲線の概念を一般次元ユークリッド空間 Rn に拡張したものであり、2次多項式の零点集合として表されるような超曲面のことをさす。3次元空間における二次超曲面は二次曲面ともよばれる。 |
| lexicalization | jpn: 二次曲面 |
| Dutch | |
| has gloss | nld: Een kwadratisch oppervlak kan omschreven worden als een D-dimensionaal oppervlak dat door een vergelijking van tweede orde beschreven wordt. |
| lexicalization | nld: Kwadratisch oppervlak |
| Norwegian | |
| has gloss | nor: I matematikk er en andregradsflate (eller -overflate) en D-dimensjonal hyperflate definert som løsningsmengden til et kvadratisk polynom. Med koordinater \x_0, x_1, x_2, \ldots, x_D\} defineres den vanlige andregradsflaten av ligningen : \sum_i,j=0}^D Q_i,j} x_i x_j + \sum_i=0}^D P_i x_i + R = 0 |
| lexicalization | nor: andregradsflate |
| Polish | |
| has gloss | pol: Kwadryka lub powierzchnia drugiego stopnia – w matematyce powierzchnia dana równaniem drugiego stopnia ze względu na współrzędne x,\ y,\ z\;: : a_11}x^2+a_22}y^2+a_33}z^2+2a_12} xy+2a_23} yz+2a_13} zx+2a_14} x+2a_24} y+2a_34} z+a_44}=0,\qquad (1)\; gdzie : a_11},a_22},a_33},a_12},a_23},a_13},a_14},a_24},a_34},a_44}\in \mathbb R, przy czym nie zachodzi : a_11}=a_22}=a_33}=a_12}=a_23}=a_13}=0\; (przynajmniej jeden z powyższych współczynników musi być różny od zera). |
| lexicalization | pol: Kwadryka |
| Portuguese | |
| has gloss | por: Quádrica ou superfície quádrica é, em matemática, o conjunto dos pontos do espaço tridimensional cujas coordenadas formam um polinômio de segundo grau de no máximo três variáveis denominada de equação cartesiana da superfície: |
| lexicalization | por: Quádricas |
| lexicalization | por: quádrica |
| Russian | |
| has gloss | rus: Поверхность второго порядка — геометрическое место точек, декартовы прямоугольные координаты которых удовлетворяют уравнению вида : a_11}x^2 + a_22}y^2+a_33}z^2+2a_12}xy+2a_23}yz+2a_13}xz+2a_14}x+2a_24}y+2a_34}z+a_44}=0 |
| lexicalization | rus: Поверхность второго порядка |
| Slovak | |
| lexicalization | slk: kvadrika |
| Castilian | |
| has gloss | spa: Una cuádrica es una superficie determinada por una ecuación de segundo grado, es decir, de la forma: P(x_1,x_2 ... x_n) = 0 \ |
| lexicalization | spa: Cuadrica |
| lexicalization | spa: cuádrica |
| Swedish | |
| has gloss | swe: I matematik så är en andragradsyta, en D-dimensionell hyperyta definierad som lösningsmängden till ett kvadratiskt polynom. Med koordinater \x_0, x_1, x_2, \ldots, x_D\}, så definieras den allmänna andragradsytan av ekvationen : \sum_i,j=0}^D Q_i,j} x_i x_j + \sum_i=0}^D P_i x_i + R = 0 |
| lexicalization | swe: andragradsyta |
| lexicalization | swe: Andragradsytor |
| Thai | |
| has gloss | tha: ผิวกำลังสอง (quadric surface) หรือ ควอดริก (quadric) ในคณิตศาสตร์ ใช้หมายถึง ผิว (hypersurface) ใน D มิติ ซึ่งกำหนดโดย คำตอบ หรือ ทางเดินรากของสมการพหุนามกำลังสอง (quadratic polynomial) ถ้าเราพิจารณาพิกัด \x_0, x_1, x_2, \ldots, x_D\} ผิวกำลังสองถูกกำหนดด้วยสมการพีชคณิตดังต่อไปนี้ : \sum_i,j=0}^D Q_i,j} x_i x_j + \sum_i=0}^D P_i x_i + R = 0 |
| lexicalization | tha: ผิวกำลังสอง |
| Vietnamese | |
| has gloss | vie: Mặt bậc hai hay mặt cong bậc hai là mặt trong không gian afin ba chiều, quỹ tích những điểm thỏa mãn phương trình bậc hai dạng :a11.x² + a22.y² + a33.z² + a12.xy + a13.xz + a23.yz + a14.x + a24.y + a34.z + a44 = 0 |
| lexicalization | vie: mặt bậc hai |
| Chinese | |
| has gloss | zho: 二次曲面指任何n維的超曲面，其定義為多元二次方程的解的軌跡。 |
| lexicalization | zho: 二次曲面 |
| Links | |
|---|---|
| Show unreliable ▼ | |
| similar | e/Quadric |
| Media | |
|---|---|
| media:img | Cil.png |
| media:img | Con.png |
| media:img | Eccentricity.svg |
| media:img | El Par.png |
| media:img | Gnuplot ellipsoid.svg |
| media:img | Hib com.png |
| media:img | Hib sim.png |
| media:img | Hip Par.png |
| media:img | Hip el.png |
| media:img | Horizonte astronómico.png |
| media:img | Hyperb1N.png |
| media:img | Par.png |
| media:img | Quadratischeform 1.png |
| media:img | Quadratischeform 2.png |
| media:img | Quadric Cone.jpg |
| media:img | Quadric Ellipsoid.jpg |
| media:img | Quadric Elliptic Cylinder.jpg |
| media:img | Quadric Elliptic Paraboloid.jpg |
| media:img | Quadric Hyperbolic Cylinder.jpg |
| media:img | Quadric Hyperbolic Paraboloid.jpg |
| media:img | Quadric Hyperboloid 1.jpg |
| media:img | Quadric Hyperboloid 2.jpg |
| media:img | Quadric Parabolic Cylinder.jpg |
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