# Modulus

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Related to Modulus: elastic modulus

## 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 ?
Where: Ea is the modulus of elasticity in Pa, f is the concentrated load at mid span in N, lis the effective length in mm, D is the deformation in mm and d is the diameter of the stalk in mm.
surr] are the corresponding average shear modulus in the tumor and surrounding tissue, respectively.
As the increases in amplitude were minor, so were the modulus increases, with the results remaining very similar to the reference modulus [77, 80].
Here, another simple method using Equation 5 is proposed using the Young's modulus value obtained from the longitudinal vibration test.
The general rule followed in testing the algorithm is that the length of the modulus is less than or equal to half the product length in bits.
I agree with Mr Hough's comment that the material modulus is not a measure of lens stiffness.
The Young's modulus can be measured by several experimental techniques including the tensile test, (8) the bending test, (9-14) and nanoindentation.
the Young's modulus and modulus of rupture) of coconut logs directly by full scale testing.

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