fixedsides

Fixedsides is a term used in geometry and related fields to describe a set of shapes or configurations in which the lengths of some or all sides are specified and held constant. The emphasis is on side constraints rather than on angle or area constraints, and the term is often used descriptively in teaching, problem statements, or discussions of rigidity and flexibility.

In planar geometry, fixing all side lengths can lead to different degrees of freedom depending on the number of sides. A triangle with its three sides fixed has a unique shape up to congruence (by the SSS criterion). By contrast, a quadrilateral with fixed side lengths can typically assume a family of shapes with varying angles and diagonals, illustrating the difference between rigidity and flexibility in polygons. The concept helps distinguish problems where side lengths alone determine the configuration from those where additional constraints are required.

In mechanical design and robotics, fixed-length links in a jointed mechanism form a fixed-sides system where the configuration space is determined by the angles that satisfy the fixed-length constraints. This viewpoint underpins knuckle and linkage analyses, as well as certain puzzle designs and architectural considerations.

Examples commonly discussed under fixedsides include a triangle with specified side lengths and a flexible quadrilateral with the same side lengths but variable angles. The term is not a standard mathematical designation but a convenient label for discussions of side-length constraints and their geometric implications.

See also: rigidity, triangle inequality, polygon, linkages, congruence.