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rigid

 
Dictionary: rig·id   (rĭj'ĭd) pronunciation
adj.
  1. Not flexible or pliant; stiff.
  2. Not moving; fixed.
  3. Marked by a lack of flexibility; rigorous and exacting: "We have watered down a rigid training . . . until we now have an educational diet in many of our public high schools that nourishes neither the classes nor the masses" (Agnes Meyer).
  4. Scrupulously maintained or performed: rigid discipline. See synonyms at stiff.

[Middle English rigide, from Latin rigidus, from rigēre, to be stiff.]

rigidly rig'id·ly adv.
rigidness rig'id·ness n.

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Thesaurus: rigid
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adjective

  1. Not changing shape or bending: inelastic, inflexible, stiff, unbending, unyielding. See flexible/rigid.
  2. Incapable of changing or being modified: immutable, inalterable, inflexible, invariable, ironclad, unalterable, unchangeable. See flexible/rigid.
  3. Firmly, often unreasonably immovable in purpose or will: adamant, adamantine, brassbound, die-hard, grim, implacable, incompliant, inexorable, inflexible, intransigent, iron, obdurate, relentless, remorseless, stubborn, unbendable, unbending, uncompliant, uncompromising, unrelenting, unyielding. Idioms: stubborn as amuleox. See resist/yield.
  4. Rigorous and unsparing in treating others: demanding, exacting, hard, harsh, severe, stern, strict, tough, unyielding. See easy/hard.

Antonyms: rigid
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adj

Definition: stiff, strict, severe
Antonyms: bending, flexible, lenient, limber, pliable, pliant, soft, yielding


Word Tutor: rigid
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pronunciation

IN BRIEF: Stiff and firm; held firmly. Also: Strict; not changing.

pronunciation The rigid wooden beams supported the roof of the house.

Wikipedia: Rigidity (mathematics)
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In mathematics, a rigid collection C of mathematical objects (for instance sets or functions) is one in which every c  C is uniquely determined by less information about c than one would expect.

It should be emphasized that the above statement does not define a mathematical property. Instead, it describes in what sense the adjective rigid is typically used in mathematics, by mathematicians.

Some examples include:

  1. Harmonic functions on the unit disk are rigid in the sense that they are uniquely determined by their boundary values.
  2. Holomorphic functions are determined by the set of all derivatives at a single point. A smooth function from the real line to the complex plane is not, in general, determined by all its derivatives at a single point, but it is if we require additionally that it be possible to extend the function to one on a neighbourhood of the real line in the complex plane. The Schwarz lemma is an example of such a rigidity theorem.
  3. By the fundamental theorem of algebra, polynomials in C are rigid in the sense that any polynomial is completely determined by its values on any infinite set, say N, or the unit disk. Note that by the previous example, a polynomial is also determined within the set of holomorphic functions by the finite set of its non-zero derivatives at any single point.
  4. Linear maps L(XY) between vector spaces XY are rigid in the sense that any LL(XY) is completely determined by its values on any set of basis vectors of X.
  5. Mostow's rigidity theorem, which states that negatively curved manifolds are isomorphic if some rather weak conditions on them hold.
  6. A well-ordered set is rigid in the sense that the only (order-preserving) automorphism on it is the identity function. Consequently, an isomorphism between two given well-ordered sets will be unique.

This article incorporates material from rigid on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.


Translations: Rigid
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Dansk (Danish)
adj. - stiv, uelastisk, ufleksibel, ubøjelig, streng
n. - (ngt. der er stift osv.)

Nederlands (Dutch)
stijf, star

Français (French)
adj. - rigide, strict, raide
n. - rigidité

Deutsch (German)
adj. - steif, hart, starr
n. - Steifheit

Ελληνική (Greek)
adj. - άκαμπτος, αλύγιστος, δύσκαμπτος, ακίνητος (κν. κοκαλωμένος), αυστηρός, άτεγκτος

Italiano (Italian)
rigido

Português (Portuguese)
adj. - rígido, inflexível, rigoroso

Русский (Russian)
жесткий, негнущийся, негибкий

Español (Spanish)
adj. - rígido, tieso, inflexible, severo, riguroso
n. - persona severa o inflexible

Svenska (Swedish)
adj. - rigid, fast, sträng

中文(简体)(Chinese (Simplified))
坚硬的, 不易弯曲的, 坚固的, 严格的, 硬式飞艇

中文(繁體)(Chinese (Traditional))
adj. - 堅硬的, 不易彎曲的, 堅固的, 嚴格的
n. - 硬式飛艇

한국어 (Korean)
adj. - 단단한, 엄격한, 딱딱한
n. - 단단함, 엄격함

日本語 (Japanese)
adj. - 硬い, 堅い, 硬直した, 頑固な, 厳しい, 厳格な, 固定した, 厳正な

العربيه (Arabic)
‏(صفه) جامد, صلب, قاس,‏

עברית (Hebrew)
adj. - ‮קשוח, קשה, מאובן, קפדן‬
n. - ‮קשוח, קשה, מאובן, קפדן‬


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Dictionary. The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2007, 2000 by Houghton Mifflin Company. Updated in 2009. Published by Houghton Mifflin Company. All rights reserved.  Read more
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