different between knack vs smoothness

English

Etymology

Use as "special skill" from 1580. Possibly from 14th century Middle English krak (“a sharp blow”), knakke, knakken, from Middle Low German, by onomatopoeia. Latter cognate to German knacken (“to crack”). See also crack.

Pronunciation

• IPA^(key): /næk/
• Audio (UK)

• Rhymes: -æk

Noun

knack (plural knacks)

1. A readiness in performance; aptness at doing something. [from 1580]

   Synonyms: skill, facility, dexterity

   • 2005, Plato, Sophist. Translation by Lesley Brown. 254a.

     The sophist runs for cover to the darkness of what is not and attaches himself to it by some knack of his;
2. A petty contrivance; a toy.

   Synonyms: plaything, knickknack, toy

3. Something performed, or to be done, requiring aptness and dexterity. [from mid 14th c.]

   Synonyms: trick, device

Derived terms

• knackless

Translations

Verb

knack (third-person singular simple present knacks, present participle knacking, simple past and past participle knacked)

1. (obsolete, Britain, dialect) To crack; to make a sharp, abrupt noise; to chink.
2. To speak affectedly.

   (Can we find and add a quotation of Halliwell to this entry?)

Translations

References

English

Etymology

From Middle English smethnes, *smothnes, from Old English sm?þnes, *sm?þnes (“smoothness, a smooth place, a level surface”), equivalent to smooth +? -ness.

Noun

smoothness (countable and uncountable, plural smoothnesses)

1. The condition of being smooth; the degree or measure of said condition.
   • 1998, Vladimir V. Senatov, Normal Approximation: New Results, Methods and Problems, Walter de Gruyter (VSP), page 32,

     The ‘smoothness’ of distributions can be understood in various senses, this is why we used quotation marks before; further we will drop them. The smoothness can be understood as the differentiability of the distribution function, boundedness of some of its derivatives, the existence of the absolutely continuous component, the decrease of the characteristic function with a certain rate, the validity of the Cramér condition, the condition ${\displaystyle \sigma (\Phi )\rightarrow 0}$ as ${\displaystyle n\rightarrow \infty }$, etc.

   • 2013, Robert Otto Rasmussen, et al., Real-time Smoothness Measurements on Portland Cement Concrete Pavements During Construction, Transportation Research Board, page 3,

     With it,^{[a pavement profile]} paving operations can be adjusted "on the fly" to maintain or improve smoothness.

2. (mathematical analysis, of a function) The highest order of derivative (the differentiability class) over a given domain.

3. (approximation theory, numerical analysis, of a function) The quantity measured by the modulus of smoothness.
   • 2013, Feng Dai, Yuan Xu, Approximation Theory and Harmonic Analysis on Spheres and Balls, Springer, page 79,

     A central problem in approximation theory is to characterize the best approximation of a function by polynomials, or other classes of simple functions, in terms of the smoothness of the function. In this chapter, we study the characterization of the best approximation by polynomials on the sphere. In the classical setting of one variable, the smoothness of a function on ${\displaystyle \mathbb {S} ^{1}}$ is described by the modulus of smoothness, defined by the forward difference.

Antonyms

• (condition of being smooth): jerkiness, roughness

Derived terms

• modulus of smoothness

Translations

See also

• differentiability class
• modulus of continuity
• modulus of smoothness
• uniform continuity

Further reading

• Modulus of smoothness on Wikipedia.Wikipedia
• Modulus of continuity on Wikipedia.Wikipedia