Construct · 3 fields · 6 citations

Where does rigidity collide?

One name. Different field. Different construct. One map.

● jingle · one word, three constructs Nearest construct by meaningstiffnesscompare the meanings
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Every construct on the map is compared with every other by the meaning of its definitions, and the closest one is surfaced here. The nearest construct to rigidity is stiffness.

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rigidity3 CONSTRUCTSRigidity modulusCOULOMB · SHEAR MODULUSStructural rigidityCAUCHY · NO DEFORMATIONNominal rigidityKEYNES · STICKY WAGES

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1784Rigidity modulus1813Structural rigidity1936Nominal rigidity
2026

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Mechanics and materials

Resistance to shear deformation

In mechanics, rigidity is a body's resistance to deformation, quantified as the modulus of rigidity (the shear modulus): the ratio of a shearing stress to the shearing strain it produces. Coulomb's 1784 Recherches théoriques et expérimentales sur la force de torsion first measured this resistance, showing that the twist of a metal wire is proportional to the applied torque, and the quantity was later formalised within continuum elasticity and systematised in Love's 1927 A treatise on the mathematical theory of elasticity. Here the referent is a measurable material property with units of pressure, and it is unlike the failure of nominal prices to adjust in an economy or the property of a geometric structure that admits no deformation.[1][2]

Unit
The shear modulus, a stress-to-strain ratio, in pascals or gigapascals
Recovery means
Within the elastic range the body returns to its original shape once the load is removed
Measured by
Determined by torsion or shear tests relating applied stress to the resulting strain

Mathematics

the property of a structure that admits no nontrivial deformation, so it is fixed by its defining constraints.

In mathematics, rigidity is the property of a structure that admits no nontrivial deformation: any continuous change that preserves the defining constraints must be trivial, so the structure is fixed by those constraints. Cauchy's 1813 Sur les polygones et les polyèdres proved the first such result, that a convex polyhedron cannot be flexed and is determined by the shape of its faces, and Mostow's 1968 Quasi-conformal mappings in n-space and the rigidity of hyperbolic space forms extended the idea, showing that the geometry of a closed hyperbolic manifold is fixed by its fundamental group. The referent is a yes-or-no structural property established by proof, not a material's measured stiffness or a market's slow price adjustment.[3][4]

Unit
A structure's space of deformations, counted as trivial or nontrivial
Recovery means
Not applicable
Measured by
Established by proof that the space of deformations reduces to the trivial ones

Macroeconomics

Prices or wages fail to adjust

In macroeconomics, nominal rigidity is the failure of nominal prices or wages to adjust quickly to changes in demand or money, so that markets do not clear in the short run. Keynes's 1936 The general theory of employment, interest and money placed the downward rigidity of money wages at the centre of involuntary unemployment, and Calvo's 1983 Staggered prices in a utility-maximizing framework gave the standard modern mechanism, in which only a fraction of firms reset their price in any period. The referent is a friction in how nominal values move over time, gauged by how sluggishly they respond, and it has nothing to do with a material's shear modulus or a geometric structure that cannot be deformed.[5][6]

Unit
The degree to which a nominal price or wage fails to adjust over a period
Recovery means
Nominal values adjust gradually as contracts and prices are reset
Measured by
Estimated from the frequency and size of price or wage changes in micro data

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Nearby collisions

elasticity3 fields · 7 citationsjingle · one word, three sciencesstiffness3 fields · 3 citationsjingle · one word, three constructsplasticity4 fields · 6 citationsjingle · one word, four sciences

References

  1. Coulomb, C. A. (1784). Recherches théoriques et expérimentales sur la force de torsion et sur l'élasticité des fils de métal. Mémoires de l'Académie Royale des Sciences, 229–269.
  2. Love, A. E. H. (1927). A treatise on the mathematical theory of elasticity (4th ed.). Cambridge University Press.
  3. Cauchy, A. L. (1813). Sur les polygones et les polyèdres, second mémoire. Journal de l'École Polytechnique, 9(16), 87–98.
  4. Mostow, G. D. (1968). Quasi-conformal mappings in n-space and the rigidity of hyperbolic space forms. Publications Mathématiques de l'IHÉS, 34, 53–104. https://doi.org/10.1007/BF02684590
  5. Keynes, J. M. (1936). The general theory of employment, interest and money. Macmillan.
  6. Calvo, G. A. (1983). Staggered prices in a utility-maximizing framework. Journal of Monetary Economics, 12(3), 383–398. https://doi.org/10.1016/0304-3932(83)90060-0

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