Semioval

Semioval is a geometric shape formed by dividing an ellipse with a straight line that passes through the ellipse’s center. The resulting region is one half of the ellipse, and its boundary consists of a straight chord along the dividing line and an elliptic arc connecting the endpoints of that chord. When the cut line aligns with a principal axis, the semioval is often described as horizontal or vertical; for a generic line through the center, the semioval’s orientation is determined by that line.

Area and perimeter: The area of any semioval obtained in this way equals half the area of the entire ellipse, namely πab/2, where a and b are the ellipse’s semi-major and semi-minor axes. The perimeter consists of the straight chord length, which is 2d where d is the distance from the center to the ellipse along the cut, plus the length of the elliptical arc between the intersection points. The arc length depends on the cut angle and ellipse parameters and generally does not have a simple closed form.

Properties: The two halves created by the central cut are congruent and mirror images across the cutting line. The shape is defined by the ellipse and the central chord, making orientation a primary characteristic of the semioval.

Variation and related shapes: The concept generalizes to rotated ellipses; any line through the center yields a semioval with the same area but a different boundary arc. The term is often used informally to describe half-ellipse or elliptical segments bounded by a central chord.

Applications and usage: Semioval forms appear in design, logo geometry, and architectural motifs as simple, rounded half-elliptical shapes. In mathematics, semioval is described as a specific case of an elliptical segment. See also ellipse, oval, semicircle, elliptical segment.