Unruled

Unruled is an adjective used to describe something that is not governed by rules or not marked by lines, depending on context. In stationery and publishing, unruled refers to pages without lines, grids, or margins. Unruled paper is commonly used for drawing, freehand writing, or sketching, and it contrasts with ruled, dotted, or gridded formats.

In geometry, unruled describes a surface that contains no straight line lying entirely on the surface. A ruled surface is one that can be generated by a straight line (a generator) moving along a directing curve; common examples include planes, cones, cylinders, the hyperboloid of one sheet, and the hyperbolic paraboloid. An unruled surface cannot be produced in this way. The sphere and most ellipsoids are standard examples of unruled surfaces. The concept distinguishes developable or line-generated surfaces from those requiring curved generators.

Usage notes: the term is specialized and most often found in mathematics, geometry texts, or technical descriptions. Outside of these contexts, unruled is rarely used in everyday language, where phrases like blank, plain, or non-ruled might be preferred. In literature or catalog entries, the word helps convey precise properties about lines, grids, or governing rules, whether describing physical media or geometric objects.