# Modulus

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Related to moduli: Elastic moduli

## modulus

1. Physics a coefficient expressing a specified property of a specified substance
2. Maths another name for the absolute value (sense 2) of a complex number
3. Maths the number by which a logarithm to one base is multiplied to give the corresponding logarithm to another base
4. Maths an integer that can be divided exactly into the difference between two other integers
Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Modulus

a geometric parameter of gears. For cylindrical spur gears the modulus m is equal to the ratio of the diameter dp of the pitch circle to the number of teeth z or the ratio of the pitch t along the pitch circle to the number π: m = dp/z = t/π. For cylindrical helical gears a distinction is made among the transverse modulus ms = dp/z = ts/∊ the normal modulus ms = tn/∊ and the axial modulus ma= /ta/∊, where ts, tn, and ta are, respectively, the transverse, normal, and axial pitches along the pitch cylinder. The values of gear moduli are standardized, which is the basis for standardization of the other gear parameters (the geometric dimensions of gears are made proportional to the modulus) and gear-cutting tools.

## Modulus

(mathematics). (1) The modulus (or absolute value) of a complex number z = x + iy is the number r = (the root is taken with the plus sign). If a complex number z is represented in trigonometric form, z = r(cos ϕ + i sin ϕ), then the modulus is the real number r. The modulus may be geometrically interpreted in the following way. A complex number z = x + iy can be represented by a vector issuing from the origin of a rectangular coordinate system and ending at the point with coordinates (x, y). The length of this vector is the modulus of the complex number z.

(2) The modulus for converting from a logarithm system with base a to a logarithm system with base b is the number M = 1/logab. To obtain the logarithms of the numbers x to the base b, if the logarithms of these numbers are known to the base a, it is necessary to multiply the latter by the modulus: logb = M logax.

## modulus

[′mäj·ə·ləs]
(mathematics)
The modulus of a logarithm with a given base is the factor by which a logarithm with a second base must be multiplied to give the first logarithm.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

## modulo

A mathematical operation (modulus arithmetic) in which the result is the remainder of a division. Also known as the "remainder operator," it is used to solve a variety of problems. For example, the following code in the C language determines if a number is odd or even. The number in AMOUNT is divided by 2, and the result is the remainder. If RESULT is zero, the number is even. The % symbol is the modulo, or "modulus" operator.

```      result = amount % 2;
if (result == 0)
EVEN=YES;
else
EVEN=NO;
```
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References in periodicals archive ?
The elastic moduli of the compacted layers were determined under PFWD (TML model from Japan) varying test parameters.
Obtained P-waves and S-waves velocity data were used for calculating the dynamic elastic moduli. Due to used sampling time the first breaks for P-wave were read with accuracy of 0.5 ms whereas the accuracy of S-wave breaks was about 1ms.
4) The richer the mix; the higher the moduli of elasticity and deformability of laterized concrete.
In the present work, we report the construction of analytical representations of the elastic moduli data using a single model in which the effects of porosity ([phi]) and temperature (T) are treated simultaneously.
The compressive moduli of HMAC-16 were 2300~2900 MPa, 1600~2000 MPa, and 490~560 MPa at the temperature of 15, 20, and 60[degrees]C, and those of HMAC-20 were 2600~3300 MPa, 1700~2300 MPa, and 520~610 MPa and those for HMAC-25 were 2200~2900 MPa, 1500-2000 MPa, and 490~590 MPa, respectively.
The results from this study indicated that the shear storage moduli of all the wood samples decreased steadily with increasing temperature and there was a low temperature transition around -50[degrees]C.
Their topics include moduli spaces of twisted sheaves on a projective variety, integral Hodge classes on uni-ruled or Calabi-Yau threefolds, birational geometry of symplectic resolutions of nilpotent orbits, moduli stacks of second-rank Giesker bundles with a fixed determinate on a nodal curve, vector bundles on curves and theta functions, Abelian varieties with bounded modular height, the moduli of regular holonomic Dx-modules with natural parabolic stability, cohomology groups of stable quasi-Abelian degenerations, semi-stable extensions on arithmetic surfaces, cusp form motives, polarized K3 surfaces, rigid geometry and applications, and moduli of stable parabolic conventions with Riemann-Hilbert correspondence and other features.
LSRs allow more intricate parts, give higher moduli, comparable tensile strength and may have lower density than HCRs.
The foam is a viscous matrix in the third stage as indicated by the storage and elastic moduli, which are equal in this region.
However, differences among shear moduli test methods used by various researchers have produced different shear modulus values.
Zariski builds on the foundation set by Riemann in the famous count of the 3g-3 parameters needed to determine a curve of genus g by studying the moduli space of curves of the same equisingularity in class.
The dynamic storage and loss moduli are merely the Fourier sine and cosine transforms of the stress relaxation modulus, which when plotted as a function of time, provide information concerning the viscoelastic behavior and molecular motions of the system.

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