Racetrackshaped

Racetrack-shaped, often called stadium-shaped, refers to a planar figure formed by two parallel straight sides connected at their ends by semicircles. The shape resembles a running track or stadium, hence the name. It is a simple example of a convex, smooth curve used in geometry and design.

The shape can be described by two parameters: the straight-side length L and the radius R of the end semicircles. The width of the figure is 2R, measured between the two parallel straight sides. When L > 0 and R > 0, the racetrack shape consists of a central rectangle of length L and width 2R with semicircles of radius R attached to its left and right ends.

Formulas for the standard racetrack shape are as follows. The area is A = 2RL + πR^2, equal to the area of the central rectangle plus the areas of the two semicircles. The perimeter is P = 2L + 2πR, consisting of the two straight sides of length L and the curved ends totaling a full circle’s circumference (2πR). Degenerate cases include L = 0, which yields a circle of radius R with area πR^2 and circumference 2πR; and R = 0, which collapses the shape to a line segment of length 2L.

Relation to other shapes: the racetrack shape is distinct from a rounded rectangle, which has quarter-circles at corners rather than end semicircles and does not have parallel straight sides of the same arrangement. Applications include geometric modeling, computer graphics collision shapes, architecture, and the design of running tracks and stadium-inspired logos.