Ligesidede

Ligesidede is a geometric term used in some Nordic-language contexts to describe polygons whose sides all have the same length. In English, such polygons are typically called equilateral polygons; the term ligesidede is most often found in Danish- and Norwegian-language textbooks and historical treatises. The concept is foundational in elementary geometry, appearing before the refinement to regular polygons.

The etymology combines lig(e) meaning "equal" and side, forming a compound that explicitly expresses equal side length. In practice, ligesidede describes any polygon with n sides in which every edge has length s. For a triangle this yields the equilateral triangle, for quadrilaterals it yields rhombuses, and for higher polygons it guarantees equal edges without guaranteeing equal angles. Therefore, a ligesidede polygon is not necessarily regular.

Key properties include that all such polygons have the same perimeter formula P = n·s, but their areas vary with the interior angles and the polygon's overall shape. Among quadrilaterals, a square is the unique case that is both ligesidede and equiangular; a rhombus is ligesidede but not square unless it is a square.

Applications appear mainly in geometry education and tiling discussions, where distinguishing equilateral from regular shapes helps students understand symmetry and space-filling patterns. The term is less common in modern English-language texts but remains present in some Nordic curricula and translations of classical geometry works.

See also: Equilateral polygon; Regular polygon; Rhombus; Equiangular.

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