Oblongatan

Oblongatan is a term used in geometry to describe a family of elongated, oval-like closed curves. The shape is convex, smooth-bounded, and exhibits bilateral symmetry along its major axis.

Etymology: The name blends oblong with a suffix -atan, intended to denote a canonical rounded-oval form in a systematic way.

Construction: Oblongatans can be generated by offsetting a rectangle of aspect ratio r > 1 by a fixed radius, producing a rounded-rectangle boundary, or by the convex hull of two equal circles arranged along a line with centers separated by a fixed distance.

Properties: The family is parameterized by aspect ratio and rounding radius. For suitable parameters the boundary is C∞ smooth and strictly convex. The curvature is highest near the midpoints of the long edges and lowest near the rounded ends.

Variants: Oblongatan variants can feature different curvature profiles along the boundary; examples are described as “heavy” and “light” oblongatans, denoting relatively more or less pronounced rounding.

Applications: Oblongatans are used in teaching convex geometry as a simple, controllable model. In design, oblongatans serve as ergonomic outlines and in computer graphics as a primitive shape for collision detection and rendering.

History: The term was proposed in the early 2010s by researchers exploring standardized convex shapes; it has since appeared in textbooks and software libraries as an example of rounded-rectangle forms.

See also: Oval, Rectangle with rounded corners, Capsule (stadium), Smooth convex curves.