omkredse

Omkredse is the length of the boundary of a two-dimensional figure, or the distance around it. In Danish mathematics, omkreds (singular) or omkredse (plural) is commonly translated as perimeter or circumference. The concept applies to any closed planar shape; for irregular shapes, the exact perimeter is the sum of all boundary segments, while for smooth curves it is the length of the curve.

For a circle with radius r, the perimeter (circumference) is C = 2πr, or equivalently C = πd where d is the diameter. For a regular polygon with n equal sides of length s, C = n·s. In general, if a polygon is formed by vertices (x_i, y_i), the perimeter is the sum of distances between successive vertices.

Practical measurement uses rulers or measuring tapes and standard length units such as millimeters, centimeters, meters. In many applications, especially in education, π is approximated as 3.14 or 22/7.

Relation to area: for circles, area A = πr^2, which grows with the square of the radius, while the perimeter grows linearly with r; for polygons, the area depends on side lengths and angles. Special cases include convex and concave shapes; all closed boundaries have a finite omkreds if the boundary is rectifiable.

See also: perimeter, circumference.