linjeform

Linjeform is a term used primarily in Danish-language discussions of art, design, and geometry to describe forms defined by lines. In visual arts and graphic design, linjeform refers to the way a composition uses lines as its main building blocks. The character of the lines—direction, curvature, thickness, spacing—creates contour, rhythm, and emphasis, often with a minimal or abstract aesthetic. Linjeform can be used to convey movement, structure, and clarity, and it frequently appears in line drawings, ink illustrations, and architectural sketches. In architecture and product design, a linjeform approach emphasizes the removal of extraneous surfaces, focusing on the silhouette and the interplay of line and negative space.

In mathematics, the term linjeform also appears as a translation of linear form, describing a linear functional: a map from a vector space to its underlying field that preserves addition and scalar multiplication. A typical expression is f(v) = a1 v1 + a2 v2 + ..., which can be represented as a dot product with a fixed vector. Linear forms are foundational in areas such as geometry, optimization, and calculus, and they contrast with nonlinear forms that involve higher-degree terms or nonlinear operations.

Historically, linjeform has been discussed in Danish-language curricula and criticism as part of broader explorations of form, contour, and line quality. The term may be encountered in art theory, design theory, and mathematical texts, sometimes with variations in translation to related terms such as lineær form in Danish.