Ellipsein

Ellipsein is a mathematical term that refers to a specific type of conic section. An ellipse is defined as the set of all points in a plane such that the sum of the distances from two fixed points, called foci, is constant. This constant sum is equal to the length of the major axis of the ellipse.

The standard equation for an ellipse centered at the origin is (x^2 / a^2) + (y^2 / b^2) = 1, where 'a' is the semi-major axis and 'b' is the semi-minor axis. If the major axis is horizontal, then a > b. If the major axis is vertical, then b > a. The foci are located along the major axis, at a distance 'c' from the center, where c^2 = a^2 - b^2 (assuming a > b).

Ellipses have numerous applications in various fields. For instance, the orbits of planets around the sun are elliptical, with the sun at one focus. They are also used in the design of optical instruments like reflecting telescopes and in acoustics, where sound emitted from one focus will be reflected to the other focus. The shape of a stretched circle is an ellipse, and it is a fundamental shape in geometry and calculus.