diam

Diam, short for diameter, is a measure of width that represents the greatest distance between two points in a given set, or, for circles and spheres, the distance across the shape through its center. In geometry, the diameter of a circle or sphere is commonly denoted by d.

In a circle, the diameter is a line segment with endpoints on the circumference and passing through the center. It is the circle’s longest chord and equals twice the radius: d = 2r. This leads to standard formulas: the circumference is C = πd and the area is A = πr^2 = (π/4)d^2. For a sphere, the diameter is similarly the distance between two opposite points on the surface and equals 2r.

In broader use, the diameter of a set S in a metric space is defined as diam(S) = sup{ ||x − y|| : x, y ∈ S }. If S is finite, this becomes the maximum distance between two points in S. The diameter is invariant under isometries and reflects the object’s overall size in that space. For an ellipse with semi-major axis a and semi-minor axis b, the diameter along the major axis is 2a; the maximum distance between two points on the ellipse occurs at the endpoints of the major axis.

In practical applications, diam is used in engineering drawings and manufacturing specifications to denote the width of circular features such as holes and rods. It is often written as diam or abbreviated with the diameter symbol Ø, such as Ø10 mm. The term radius is related but distinct: the radius is half the diameter and defines the distance from the center to the boundary.