rigidities

Rigidity refers to the extent to which a system resists deformation or change of state. In physics and engineering, it describes stiffness—the resistance of a body to elastic deformation under load—quantified by elastic moduli such as Young's modulus and the shear modulus. In mathematics, rigidity is the property that a shape or structure cannot be moved or deformed without altering some measured quantity, such as edge lengths or angles. In social sciences, rigidity denotes slow or reluctant adjustment of prices, wages, or institutions.

In mechanics, a perfectly rigid body is an idealization that maintains its shape under force; real materials display finite rigidity. Materials with high stiffness resist bending and stretching (steel, ceramics), while those with low stiffness deform easily (rubber, polymers). The overall rigidity of a structure depends on material properties, geometry, joints, and constraints, and is analyzed with models that predict deformation under service loads.

In geometry and graph theory, a framework made of rigid bars and joints is rigid if its overall shape cannot be altered without changing bar lengths. A triangle is rigid in the plane, whereas a simple quadrilateral can flex unless reinforced by a diagonal or additional bars. Rigidity theory studies conditions for local or global rigidity and has applications in architectural design, robotics, and the study of molecules.

In economics, price and wage rigidity refer to sluggish adjustments to shocks, often due to menu costs, contracts, or expectations. Such rigidity can lead to short-run disequilibria, persistent unemployment, or delayed responses to policy changes, and is a central consideration in macroeconomic models.