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An ellipse (red) obtained as the intersection of a cone with an inclined plane. Ellipse: notations Ellipses: examples with increasing eccentricity. 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.
Use an ellipsis (plural ellipses) if material is omitted in the course of a quotation, unless square brackets are used to gloss the quotation (see § Brackets and parentheses, and the points below). Wikipedia's style for an ellipsis is three unspaced dots (...); do not use the precomposed ellipsis character (…
If an ellipsis ends the sentence, then there are three dots, each separated by a space, followed by the final punctuation (e.g. Hah . . . ?). In some legal writing, an ellipsis is written as three asterisks, *** or * * *, to make it obvious that text has been omitted or to signal that the omitted text extends beyond the end of the paragraph.
Ellipsis is the narrative device of omitting a portion of the sequence of events, allowing the reader to fill in the narrative gaps. Aside from its literary use, the ellipsis has a counterpart in film production. It is there to suggest an action by simply showing what happens before and after what is observed.
An example of a generalized coordinate would be to describe the position of a pendulum using the angle of the pendulum relative to vertical, rather than by the x and y position of the pendulum. Although there may be many possible choices for generalized coordinates for a physical system, they are generally selected to simplify calculations ...
An ellipse has two axes and two foci. Unlike most other elementary shapes, such as the circle and square, there is no algebraic equation to determine the perimeter of an ellipse. Throughout history, a large number of equations for approximations and estimates have been made for the perimeter of an ellipse.
The semi-minor axis of an ellipse runs from the center of the ellipse (a point halfway between and on the line running between the foci) to the edge of the ellipse. The semi-minor axis is half of the minor axis. The minor axis is the longest line segment perpendicular to the major axis that connects two points on the ellipse's edge.
For example, on a triaxial ellipsoid, the meridional eccentricity is that of the ellipse formed by a section containing both the longest and the shortest axes (one of which will be the polar axis), and the equatorial eccentricity is the eccentricity of the ellipse formed by a section through the centre, perpendicular to the polar axis (i.e. in ...