ellipsejä

An ellipse is a closed curve in a plane that is the locus of all points such that the sum of the distances from two fixed points, called foci, is constant. This constant sum is equal to the distance between the two foci multiplied by a factor greater than one. Alternatively, an ellipse can be defined as a conic section formed by the intersection of a cone and a plane that is not parallel to the cone's axis and does not pass through the apex.

The shape of an ellipse is characterized by its semi-major axis and semi-minor axis. The semi-major axis is half the longest diameter of the ellipse, and the semi-minor axis is half the shortest diameter. The distance between the two foci is denoted by 2c, and the sum of the distances from any point on the ellipse to the foci is 2a, where 'a' is the length of the semi-major axis. The relationship between a, the semi-minor axis 'b', and the distance from the center to a focus 'c' is given by the equation a² = b² + c².

An ellipse is symmetrical about both its major and minor axes. When the two foci coincide, the ellipse becomes a circle, which is a special case of an ellipse where the semi-major and semi-minor axes are equal. Ellipses have various applications in fields such as astronomy, where planetary orbits are elliptical, and engineering, in the design of optical systems and gears.