ellipse


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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
References in periodicals archive ?
The design isn't the only modern element at Ellipse. The building is wired with free Wi-Fi and outfitted with a third-floor business center that includes a glass-enclosed meeting room for the work-from-home crowd.
2 (hemisphere: left versus right hemisphere) x 4 (lobe: frontal, parietal, temporal, and occipital) x 4 (type: ellipse, triangle, smiling face, and angry face) within-group repeated-measures ANOVAs were done separately for the six early ERP components (N1, P1, N2, P2, N3, and P3).
This US FDA approval of MR-conditional labeling for the Ellipse ICD with the Tendril MRI pacing lead and Durata and Optisure high voltage leads adds another patient-centric benefit to the device and will help further improve access for patients suffering from abnormally fast heart rhythms who need an ICD and who may need an MRI scan in the future.
13, we set the parameters in each experiment as followed: the hard circle model with l = 0.3m, same as Antoine's [4] velocity model; the hard ellipse model with 2a = 0.3m, 2b = 0.2m and the dynamic ellipse model with 2a' = 2 x ([a'.sub.min] + [[tau].sub.a]v) , [a'.sub.min] = 0.18m , 2b' = 0.2m
The conclusion of this parametric study is that the most favourable super-elliptic profile for the theoretical model of rectangular block is a simple ellipse (super-ellipse of 2nd order) with a depth of 12 [micro]m.
The back side one-third area was occupied by bone and muscles; therefore, this area was subtracted from the area of the peritoneal cavity ellipse. Then, the area of the intestinal tract (10 [cm.sup.2]) was subtracted, to finally calculate the VFA.
is the probability impedance ellipse and an approximation of [[OMEGA].sub.Z].
Since the authors' previous temperature estimation model was one-dimensional (calculated only the maximum temperature rise when the heat source passes in the rolling direction of the contact), there were some areas in which the temperature was not accurately expressed compared to actual temperature distribution inside the contact ellipse. Therefore, the objective of this study was to clearly define the physical characteristics of the accuracy-lowering factors, in addition to improving these factors and the method of calculating estimated temperature.
Where we would consider the circle as a special case of the ellipse, Galileo would not but feel that the ellipse is a distorted circle: a form which was, so to speak, unworthy of celestial bodies ...
Since ACL is attached to the bone three-dimensionally, the aim of this study is to show that tibial tunnel aperture area surface calculated by means of the 3D bone surface model differs from common computations which present tibial tunnel aperture area as an ellipse.
Ellipse's magnetic growing rod technology is currently being adopted in the pediatric deformity and orthopedic markets, providing for new growth opportunities beyond NuVasive's current portfolio of solutions that address adult degenerative and deformity spinal conditions.
Wuensch might want to consider a second career as a clairvoyant; less than a week into the new year, NuVasive granted her prophesy, purchasing skeletal specialist Ellipse Technologies Inc.