Soikeita

Soikeita is the plural form of the Finnish word soikea, meaning oval or elliptical. In mathematics, soikeita commonly refers to ellipses, which are closed planar curves determined by a fixed geometric relationship rather than a single size or shape. A central property is that the sum of the distances from any point on an ellipse to two fixed points, called the foci, is constant. This constant equals 2a, where a is the semi-major axis.

In standard position, an ellipse centered at the origin with its major axis along the x-axis is described by the equation x^2/a^2 + y^2/b^2 = 1, with a ≥ b > 0. The distance from the center to each focus is c = sqrt(a^2 − b^2), and the eccentricity e = c/a measures how elongated the ellipse is. The area is πab. There is no simple exact formula for the circumference, though several approximations exist.

Ellipses may also be rotated or translated. A rotated ellipse can be written in a general second-degree form Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0 with B^2 − 4AC < 0, or described in rotated-axes coordinates using a, b and a rotation angle θ. A common parametric form is x = h + a cos t, y = k + b sin t, which traces the ellipse with center (h, k).

Applications and occurrences of soikeita include astronomy, where planetary orbits are approximately elliptical, as well as optics, engineering, architecture, and computer graphics, where ellipses model shapes, trajectories, or focal properties in designs and simulations.