# 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

## 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.
References in periodicals archive ?
2010), wood and wood-based materials are not ideally orthortropic materials, so the Young's moduli obtained from the flexural and longitudinal vibration methods often deviate from each other.
Therefore, the Young's moduli corresponding to different depths from the surface can be derived and are shown in Fig.
To construct a suitable model, we proceed heuristically, beginning with the assumption that a separation of variables may be applied to the dependence of elastic moduli on temperature and porosity.
Even if all of the products currently using RSA authentication were upgraded to use 1024-bit moduli, we could still break the code.
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.
LSRs allow more intricate parts, give higher moduli, comparable tensile strength and may have lower density than HCRs.
Kerner studied the gross bulk and shear moduli of a composite containing grains that are assumed not only to be perfectly bonded to a suspending medium or to each other but also to be spherical in shape in the mean (21).
Calculate the freezing moduli of sections that must be fed separately.
Of particular interest are the test methods to determine the in-plane shear moduli of both solid wood and wood-based composites.
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.

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