Vertex coordinate
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Vokabelliste Mathematik English (n) Factorial (number) over (number) ... satisfies equation ... "a bar" ( a ) "a hat" ( â ) "a dot" ( a ) a squared antiderivative a to the power of 2 abscissa absolute (of a number) absolute value add addition adjacent side angle angle bisector approximation arbitrary area as x approaches … asymptote binomial binomial coefficient bounded bracket (round, square, angle, curly) calculate cancel cathetus cathetus (side of a right-angled triangle) chain rule chain rule for integration characteristic point chord chord circle circle circumference clockwise coefficient complement component condition cone cone continuous coordinate system corollary cosine cotangent Deutsch *+(n) Fakultät (= n!) (Zahl) geteilt durch (Zahl) … erfüllt Gleichung … a quer a Dach a Punkt a quadrat Stammfunktion a hoch 2 Abszisse Betrag (einer Zahl) *+Absolutwert addieren Addition *+angrenzende Seite Winkel Winkelhalbierende Näherung beliebig Fläche wenn x gegen … strebt Asymptote Binom *+binomialer Koeffizient beschränkt Klammer ( runde, eckige, Spitz …., geschweifte) *+rechnen, berechnen kürzen one of the two sides of a right-angled triangle that enclose the right angle Kathete Kettenregel *+Kettenregel zur Integration *+charakteristischer Punkt Sehne the section of a straight line crossing a circle which lies inside the circle Kreis the locus of all points of the 2-dim Euclidean space with a fixed distance from a defined other point (the center) also: the curve defined by the equation x2 + y2 = r2 Umfang im Uhrzeigersinn Koeffizient *+Komplement *+Komponente Voraussetzung Kegel a solid obtained by the rotation of an equal-sided triangle around the straight line going through the vertex of the equal sides and the mid-point of the opposite side stetig Koordinatensystem, Achsenkreuz Folgesatz Cosinus Cotangens 1 Vokabelliste Mathematik English counter-clockwise cube cube cuboid cuboid curve curve decimal fraction decimal number decimal number decreasing define definite integral definite integral definition definition range, domain definition set/range degree denominator derivative derivative derive designation determine diameter diameter differentiable direction (of a vector) direction of a vector distance distance divide division divisor domain drawing element ellipse ellipse Deutsch gegen den Uhrzeigersinn Würfel a solid with a surface consisting of six squares Quader a solid with a surface consisting of 6 rectangles Kurve a 1-dimensional structure of maximal generality, e.g. a plain curve: circle e.g. a spatial curve: helix *+Dezimalbruch Dezimalzahl a number, for which fractions are given as a sum of weighted powers of 10-1 fallend definieren bestimmtes Integral bestimmtes Integral Definition Definitionsbereich *+Definitionsmenge/-bereich *+Grad Nenner Ableitung a function derived from a particular other function, indicating how ableiten *+Bezeichnung bestimmen Durchmesser the section of a straight line through the center of a circle differenzierbar Richtung (eines Vektors) Abstand *+Abstand/Entfernung teilen Division Teiler Definitionsbereich Zeichnung *+Element Ellipse a curve which can be given by an equation in two variables: x2 y2 1 a2 b2 equal equal-sided equality equation equilateral even number example exercise expand expand gleich gleichschenklig *+Gleichheit *+Gleichung gleichseitig *+gerade Zahl *+Beispiel *+Übung erweitern to multiply numerator and denominator of a fraction with the same number 2 Vokabelliste Mathematik English expanded fraction exponent exponent exponential function extremum/extrema factor factor/complete the square factorial factorial factorization family of curves f double-prime (f'') finite formula f prime (f') fraction fraction fraction bar function given the functions … graph(curve) graph of a function greater or equal than greater than greatest common devisor greatest common devisor hatch hence homework hyperbola hyperbola Deutsch *+erweiterter Bruch Exponent the number telling the power to which a basis number is raised Exponentialfuktion (ax), E-funktion (ex) *+Extremwert/Extremwerte Faktor *+quadratische Ergänzung Fakultät the product of n numbers *+Faktorisierung Kurvenschar f 2-Strich (2. Ableitung von f) endlich Formel f Strich (1. Ableitung von f) Bruch two integer numbers divided Bruchstrich Funktion Gegeben seien die Funktionen … *+Kurve a curve in the plane, where the coordinates of the points of the curve are given by the domain values and the corresponding function values of the function größer gleich größer größter gemeinsamer Teiler the greatest of the prime factors common for numerator and denominator of a fraction schraffieren folglich, daraus folgt ... *+Hausaufgabe Hyperbel a curve which can be given by an equation in two variables, e.g. x2 y2 : 1 a2 b2 hypotenuse hypotenuse image range, domain of function image set increasing indefinite integral inequality inequation infinite inflection point inflection point insert integer integer integer (number) integral integral Hypotenuse the side of a right-angled triangle that is opposite to the right angle Wertebereich *+Bildmenge steigend unbestimmtes Integral *+Ungleichheit, Ungleichung Ungleichung unendlich Wendepunkt a point of a curve at which the curvature of a curve is changing sign einsetzen *+Ganzzahl the positive and negative natural numbers Ganzzahl Integral a function derived of another function as a limit n of a series of function values and lengths of intervals 3 Vokabelliste Mathematik English integration by parts intersect intersection Intersection set/point Interval Inverse function Inverse number least common denominator least common denominator less or equal than less than let ...be ... limit line segment logarithm logarithm lower sum magnitude (of a vector) magnitude of a vector mapping mapping maximum memorize by rote/learn by heart minimum monotonous (strictly m.) multiple multiplication multiply natural logarithm necessary condition negative integer Newton Quotient norm (of a vector) normal normal vector normal vector number numerator numerator odd number of 1st order opposite side orthogonal orthogonal pair of compasses parabola parallel parallelepiped parallelogram partial fraction decomposition periodical number/function perpendicular perpendicular Deutsch of the argument partielle Integration Sich schneiden Schnittpunkt *+Schnitt-menge/-punkt *+Intervall Umkehrfunktion *+inverse Zahl Hauptnenner the least of the denominators of several fractions kleiner gleich kleiner es sei, gegeben sei Limes (Grenzwert) Strecke Logarithmus the inverse of exponentiation *+Untersumme Betrag (eines Vektors) the distance of two points, one given by the sum of this vector and another vector, and the other one given by the other vector Abbildung a set of equations in two or more variables that define points of an n-dimensional space Maximum *+auswendig lernen *+Minimum monoton (streng m.) Vielfaches Multiplikation multiplizieren natürlicher Logarithmus *+notwendige Bedingung *+negative ganze Zahl Newton Quotient die Norm (eines Vektors) Normale Normalenvektor a vector that is perpendicular to a line or a plane *+Zahl Zähler in a fraction the part above the fraction bar *+ungerade Zahl erster Ordnung *+gegenüberliegende Seite *+orthogonal/senkrecht same meaning as perpendicular *+Zirkel Parabel parallel Parallepiped (Spat) Parallelogram *+Partialbruchzerlegung *+periodische Zahl/Funktion unter rechtem Winkel *+senkrecht 4 Vokabelliste Mathematik English perpendicular (the perpendicular) perpendicular to each other piecewise (e.g. ... continuous) plane plug in point polynomial polynomial position vector positive integer power function product product rule proof proof proper subset property pyramid quadrant quotient quotient rule radian radius range rate of change rational number real number rectangle reduce reduce reduced fraction remainder term resulting vector root root rotation rule ruler scalar scalar product sequence sequence series series set set side of a triangle similarity simplify sine slope slope of a curve solid Deutsch die Normale (Gerade im rechten Winkel zu …) senkrecht zueinander stückweise (z.B. ... stetig) Ebene einsetzen Punkt Polynom a weighted sum of powers of a variable Ortsvektor *+natürliche Zahl *+Potenzfunktion Produkt Produktregel Beweis Beweis *+echte Teilmenge *+Eigenschaft Pyramide (unregelmäßiger Körper über einem Vieleck, typisch Dreieck oder Viereck) Quadrant *+Quotient Quotientenregel *+radian Radius Wertebereich *+Veränderungsrate rationale Zahl reelle Zahl Rechteck kürzen divide numerator and denominator of a fraction by a common primefactor *+gekürzter Bruch *+Restglied resultierender Vektor (die Resultierende) Wurzel the inverse of raising to a power Drehung *+Regel Lineal Skalar Skalarprodukt Folge a set of numbers given by a term of a variable that is given for a range of integers (may be infinite) Reihe the sum of the elements of a sequence Menge a number of objects that satisfy a common definition Seite eines Dreiecks Ähnlichkeit vereinfachen Sinus Steigung *+Steigung einer Kurve Körper 5 Vokabelliste Mathematik English solution solve solve the equation square square root straight line strictly (increasing/decreasing) subset subset substitution subtract subtraction sufficient condition summand table tangent tangent line tangent line tangent plane term tetrahedron theorem theorem thesis triangle triangle trigonometry union unit upper sum vector vector vector product vertex vertex coordinates vertex of a curve vertex of a parabola vertex of a triangle volume volume of revolution we consider we have ... x-axis zero (of a function) Deutsch Lösung bestimmen der Lösungen Lösen Sie die Gleichung Quadrat Quadratwurzel Gerade streng monoton (steigend/fallend) *+Teil-/Untermenge none, some or all of the elements of a set Substitution subtrahieren Subtraktion *+hinreichende Bedingung Summand Tabelle Tangens Tangente a straight line through a point of a curve with a direction such that if the direction would change infinitesimally, another point of the curve would become common with the straight line Tangentialebene Ausdruck, Term Tetraeder, (gleichseitige) Dreieckspyramide Satz A mathematical statement, which can be proven to be true wrt to other statements that already have been proven Behauptung Dreieck a geometric object consisting of three intersecting straight lines *+Trigonometrie *+Vereinigung Einheit *+Obersumme Vektor a mathematical object that specifies a relation of two points in space, where often one of the two is the origin of a coordinate system Vektorprodukt something "not smooth", which may e.g. be the corner of a triangle or a discontinuity in the curvature of a curve Koordinaten des Scheitelpunkts (einer Parabel) Spitze/Knick einer Kurve Scheitel einer Parabel Ecke eines Dreiecks Volumen Rotationsvolumen (eines Rotationskörpers) wir betrachten/untersuchen es gilt x-Achse Nullstelle (einer Funktion) 6
