ellipseɪˈlɪps
ellipse (n)
- plural
- ellipses
English Definitions:
ellipse, oval (noun)
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"
ellipse (Noun)
A closed curve, the locus of a point such that the sum of the distances from that point to two other fixed points (called the foci of the ellipse) is constant; equivalently, the conic section that is the intersection of a cone with a plane that does not intersect the base of the cone.
ellipse (Verb)
To remove from a phrase a word which is grammatically needed, but which is clearly understood without having to be stated.
Ellipse
In mathematics, an ellipse is a plane curve that results from the intersection of a cone by a plane in a way that produces a closed curve. Circles are special cases of ellipses, obtained when the cutting plane is orthogonal to the cone's axis. Analytically, an ellipse is defined as the set of points such that the distance of each point from a given point bears a constant ratio of less than 1 to its distance from a given straight line. An ellipse is also the locus of all points in the plane whose distances to two fixed points add to the same constant. The name ἔλλειψις was given by Apollonius of Perga in his Conics, emphasizing the connection of the curve with "application of areas". Ellipses are closed curves and are the bounded case of the conic sections, the curves that result from the intersection of a circular cone and a plane that does not pass through its apex; the other two cases are parabolas and hyperbolas. Ellipses arise from the intersection of a right circular cylinder with a plane that is not parallel to the cylinder's main axis of symmetry. Ellipses also arise as images of a circle under parallel projection and the bounded cases of perspective projection, which are simply intersections of the projective cone with the plane of projection. It is also the simplest Lissajous figure, formed when the horizontal and vertical motions are sinusoids with the same frequency.
Ellipse
In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special type of ellipse in which the two focal points are the same. The elongation of an ellipse is measured by its eccentricity e {\displaystyle e} , a number ranging from e = 0 {\displaystyle e=0} (the limiting case of a circle) to e = 1 {\displaystyle e=1} (the limiting case of infinite elongation, no longer an ellipse but a parabola). An ellipse has a simple algebraic solution for its area, but only approximations for its perimeter (also known as circumference), for which integration is required to obtain an exact solution. Analytically, the equation of a standard ellipse centered at the origin with width 2 a {\displaystyle 2a} and height 2 b {\displaystyle 2b} is:
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"ellipse." Kamus.net. STANDS4 LLC, 2024. Web. 29 Mar. 2024. <https://www.kamus.net/english/ellipse>.
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