An ellipse, in mathematics, is a closed curve formed by the intersection of a plane and a cone. More precisely, an ellipse can be defined as a set of points in a plane, wherein the sum of the distances from any point on the curve to two fixed points, called the foci, remains constant.
This geometric figure possesses several fundamental characteristics. First, an ellipse is symmetric with respect to its major axis, which is the longer diameter of the curve. Similarly, the minor axis represents the shorter diameter, perpendicular to the major axis. Moreover, the center of the ellipse, known as the midpoint between its foci, acts as the point of symmetry.
Furthermore, an ellipse can be described by two essential parameters: its semi-major axis and semi-minor axis. The semi-major axis corresponds to half the length of the major axis, while the semi-minor axis corresponds to half the length of the minor axis. These parameters allow the calculation of other properties, such as the eccentricity, which measures how elongated the ellipse is.
Ellipses frequently appear in a variety of fields, including astronomy, physics, and engineering. In astronomy, the paths of planets and comets around the sun are often elliptical. In physics, ellipses play a role in describing the motion of objects under the influence of gravity. In engineering, ellipses are prevalent in optics, antenna design, and mechanics, among other applications. Due to their unique properties and wide range of applications, ellipses are extensively studied in mathematics and utilized within numerous disciplines.
