Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 n. Physics A quantity that expresses the degree to which a substance possesses a property, such as elasticity.
 n. Mathematics The absolute value of a complex number.
 n. A number by which two given numbers can be divided and produce the same remainder.
 n. The number by which a logarithm in one system must be multiplied to obtain the corresponding logarithm in another system.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. The base with respect to which a congruence is computed.
 n. The absolute value of a complex number.
 n. A coefficient that expresses how much of a certain property is possessed by a certain substance.
 n. An operator placed between two numbers, to get the remainder of the division of those numbers.
from the GNU version of the Collaborative International Dictionary of English
 n. A quantity or coefficient, or constant, which expresses the measure of some specified force, property, or quality, as of elasticity, strength, efficiency, etc.; a parameter.
from The Century Dictionary and Cyclopedia
 n. In mathematics, a real positive number that serves as measure or parameter of a function or effect. Represented by M. or
μ .  n. In physics, the measure of an effect under conditions whose measure is unity. Thus, a physical modulus is not a number, but a physical quantity.
 n. [capitalized] In conchology, a genus of gastropods, referred to the Littorinidæ or periwinkles, or made type of the family Modulidæ. The shell is depressed and trochiform, with a deeply cut columellar tooth and manywhorled operculum.
 n. then the modulus of transformation is
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 n. the absolute value of a complex number
 n. (physics) a coefficient that expresses how much of a specified property is possessed by a specified substance
 n. an integer that can be divided without remainder into the difference between two other integers
Etymologies
Examples

For example, the semantic constraint of the function "modulus" is an integer.

In the lower part, the Young’s modulus is half that of the upper part.

The transverse strength is also called modulus of rupture.

However, by conducting AFM nanoindentation experiments, the researchers found that the mummified skin had a slightly higher Young's modulus, meaning that it was slightly less elastic and stiffer than recent skin.

Stevens proposed that subjects could quantitatively estimate the magnitude of a physical stimulus Stevens 'magnitude estimation procedure: Provide "modulus" (baseline) stimulus (e.g., loud tone, electric shock) and call it 100 Have subject estimate intensity of subsequent stimuli on scale 0 ... 100 e.g. if tone sounds half as loud rate it 50 More ef ﬁ cient than Weber's procedure!

* On the integers more generally, [[modular arithmetic]] operates on the equivalence classes defined by remainder on division my a fixed '' modulus '' '' M ''.

Cars are complex objects that represent the outcomes of literally millions of discrete compromises governing everything from, say, the elastic modulus of an engine mount to the degree of sassiness in the rake of a windshield.

Goldlevel Orca frames with highmodulus (HM) carbon fabric retail for $3500, while Silverlevel Orcas, containing a mix of HM and midmodulus fibers run $2500.

Starting with their impact resistant, ultrastrong BallisTec carbon fiber, Cannondale strategically added more brittle but stiffer highmodulus carbon to improve rigidity.
Eurobike 2010 tech gallery – Getting fired up for cyclocross

A mixture of highmodulus (HM) and high resistance (HR) fibers is employed, and Look president Thierry Fournier cautions people from drawing conclusions based on thinking that HM fibers are “better” than lessstiff HR fibers.
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