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单词 ellipse
释义

ellipse


el·lipse

E0092900 (ĭ-lĭps′)n.1. A plane curve, especially:a. A conic section whose plane is not parallel to the axis, base, or generatrix of the intersected cone.b. The locus of points for which the sum of the distances from each point to two fixed points is equal.2. Ellipsis.
[French, from Latin ellīpsis, from Greek elleipsis, a falling short, ellipse, from elleipein, to fall short (from the relationship between the line joining the vertices of a conic and the line through the focus and parallel to the directrix of a conic) : en-, in; see en-2 + leipein, to leave; see leikw- in Indo-European roots.]

ellipse

(ɪˈlɪps) n (Mathematics) a closed conic section shaped like a flattened circle and formed by an inclined plane that does not cut the base of the cone. Standard equation x2/a2 + y2/b2 = 1, where 2a and 2b are the lengths of the major and minor axes. Area: πab[C18: back formation from ellipsis]

el•lipse

(ɪˈlɪps)

n. a plane curve such that the sums of the distances of each point in its periphery from two fixed points, the foci, are equal; a conic section formed by the intersection of a right circular cone by a plane that cuts the axis and the surface of the cone. See also diag. at conic section. [1745–55; < French < Latin ellīpsis ellipsis]
ellipse

el·lipse

(ĭ-lĭps′) A closed, symmetric curve shaped like an oval, which can be formed by intersecting a cone with a plane that is not parallel or perpendicular to the cone's base. The sum of the distances of any point on an ellipse from two fixed points (called the foci) remains constant no matter where the point is on the curve.
Thesaurus
Noun1.ellipse - a closed plane curve resulting from the intersection of a circular cone and a plane cutting completely through itellipse - a closed plane curve resulting from the intersection of a circular cone and a plane cutting completely through it; "the sums of the distances from the foci to any point on an ellipse is constant"ovalconic, conic section - (geometry) a curve generated by the intersection of a plane and a circular conecircle - ellipse in which the two axes are of equal length; a plane curve generated by one point moving at a constant distance from a fixed point; "he calculated the circumference of the circle"
Translations
椭圆

ellipse

(iˈlips) noun a geometrical figure that is a regular oval. 橢圓 椭圆elˈliptical adjective 橢圓的 椭圆的

ellipse


ellipse,

closed plane curve consisting of all points for which the sum of the distances between a point on the curve and two fixed points (foci) is the same. It is the conic sectionconic section
or conic
, curve formed by the intersection of a plane and a right circular cone (conical surface). The ordinary conic sections are the circle, the ellipse, the parabola, and the hyperbola.
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 formed by a plane cutting all the elements of the cone in the same nappe. The center of an ellipse is the point halfway between its foci. The major axis is the chord that passes through the foci. The minor axis is the chord that passes through the center perpendicular to the major axis. The latus rectum is the chord through either focus perpendicular to the major axis. The vertices are the two points of intersection of the major axis with the curve. The eccentricity of an ellipse, a ratio of two lengths, is a measure of its flatness; it is the distance from the center to either focus divided by the distance from the center to either vertex. The circlecircle,
closed plane curve consisting of all points at a given distance from some fixed point, called the center. A circle is a conic section cut by a plane perpendicular to the axis of the cone.
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 may be considered an ellipse of eccentricity zero, i.e., one in which the center and the two foci all coincide.

ellipse

A closed curve that is a type of conic section with an eccentricity less than one. The longest line that can be drawn through the center of an ellipse is the major axis whereas the shortest line is the minor axis. The two axes are at right angles. There are two foci, which lie on the major axis and are symmetrically positioned on opposite sides of the center. The sum of the distances from the foci to a point moving round the ellipse is constant and equal to the length of the major axis. An orbiting body moves in an ellipse with the primary at one of the foci. See also Kepler's laws; orbit.

Ellipse

A closed loop obtained by cutting a right circular cone by a plane.

Ellipse

 

the intersection of a plane and one of the nappes of a circular conical surface (Figure 1).

Figure 1

An ellipse may also be defined as the locus of points M in the plane for which the sum of the distances from two fixed points F1 and F2 in the plane is constant; F1 and F2 are known as the foci of the ellipse. If a system of coordinates xOy is chosen as shown in Figure 2, then the equation of the ellipse assumes the form

Here, OF1 = OF2 = c, 2a = F1M + F2M, and Ellipse.

Figure 2

An ellipse is a quadratic curve. It is symmetric with respect to its axes AB and CD, and its center O is its center of symmetry. The line segments AB = 2a and CD = 2b are called the major and minor axes of the ellipse, respectively. The number e = cla < 1 is known as the eccentricity of the ellipse; if a = b, then e = 0 and the ellipse is a circle. The lines whose equations are x = –a/e and x = a/e are called the directrices of the ellipse; the ratio of the distance of a point of the ellipse from the nearest focus and the distance of the point from the nearest directrix is constant and equal to the eccentricity. The points A and B where the ellipse intersects its major axis are called its vertices. (See alsoCONIC SECTION.)

ellipse

[ə′lips] (mathematics) The locus of all points in the plane at which the sum of the distances from a fixed pair of points, the foci, is a given constant.

ellipse

a closed conic section shaped like a flattened circle and formed by an inclined plane that does not cut the base of the cone. Standard equation x2/a2 + y2/b2 = 1, where 2a and 2b are the lengths of the major and minor axes. Area: πab

ellipse


ellipse

(i-lips′) [L. ellipsis, fr Gr. elleipsis, a falling short] In geometry, an oval or egg-shaped figure. In surgery, incisions of such shape are commonly made to remove lesions from the skin. elliptic (-lip′tik), adjectiveelliptical (′ti-kăl) elliptically (′ti-k(ă-)lē)

ellipse


  • noun

Synonyms for ellipse

noun a closed plane curve resulting from the intersection of a circular cone and a plane cutting completely through it

Synonyms

  • oval

Related Words

  • conic
  • conic section
  • circle
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